Package 'dataSDA'

Description

Interval-valued dataset of 24 units from the UCI Abalone dataset, aggregated by sex and age group. iGAP format (comma-separated interval strings). See abalone.int for the Min-Max column format.

Usage

data(abalone.iGAP)

Format

A data frame with 24 observations (e.g., F-10-12, M-4-6) and 7 character columns in iGAP format (comma-separated "min, max" strings):

• Length: Shell length range.

• Diameter: Shell diameter range.

• Height: Shell height range.

• Whole: Whole weight range.

• Shucked: Shucked weight range.

• Viscera: Viscera weight range.

• Shell: Shell weight range.

Row names encode Sex-AgeGroup (e.g., F-10-12 = Female age 10–12).

Metadata

Source

UCI Machine Learning Repository.

References

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(abalone.iGAP)

Description

Interval-valued dataset of 24 units from the UCI Abalone dataset, aggregated by sex and age group. Min-Max column format (two columns per variable). See abalone.iGAP for the iGAP format version.

Usage

data(abalone.int)

Format

A data frame with 24 observations and 14 columns (7 interval variables in _min/_max pairs):

• Length_min, Length_max: Shell length range.

• Diameter_min, Diameter_max: Shell diameter range.

• Height_min, Height_max: Shell height range.

• Whole_min, Whole_max: Whole weight range.

• Shucked_min, Shucked_max: Shucked weight range.

• Viscera_min, Viscera_max: Viscera weight range.

• Shell_min, Shell_max: Shell weight range.

Row names encode Sex-AgeGroup (e.g., F-10-12 = Female age 10–12).

Metadata

Source

UCI Machine Learning Repository.

References

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(abalone.int)

Description

Interval-valued acid rain pollution indices for sulphates and nitrates (kg/hectares) for 2 US states (Massachusetts and New York).

Usage

data(acid_rain.int)

Format

A data frame with 2 observations and 5 variables in Min-Max format:

• state: State name (character).

• sulphate_l, sulphate_u: Sulphate pollution index range (kg/hectares).

• nitrate_l, nitrate_u: Nitrate pollution index range (kg/hectares).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.21.

Examples

data(acid_rain.int)

Description

Interval-valued dataset of 7 age-group observations with cholesterol and weight measurements. Each observation aggregates individuals in a 10-year age band with interval ranges for cholesterol and weight.

Usage

data(age_cholesterol_weight.int)

Format

A symbolic data frame (symbolic_tbl) with 7 observations and 4 variables:

• Age: Age range (years, interval).

• Cholesterol: Cholesterol level range (mg/dL, interval).

• Weight: Weight range (pounds, interval).

• n: Number of individuals in the age group (numeric).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(age_cholesterol_weight.int)

Description

Histogram-valued dataset of 229 countries with 3 population age pyramid histograms (both sexes, male, female). Each histogram has 21 age bins representing the distribution of the population across age groups.

Usage

data(age_pyramids.hist)

Format

A data frame with 229 observations (countries) and 3 histogram-valued variables:

• Both.Sexes.Population: Histogram of total population by age group.

• Male.Population: Histogram of male population by age group.

• Female.Population: Histogram of female population by age group.

Row names are country names (e.g., WORLD, Afghanistan, Albania).

Metadata

Source

HistDAWass R package (Age_Pyramids_2014 dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: A new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (Age_Pyramids_2014).

Examples

data(age_pyramids.hist)

Description

Aggregate tabular numerical data (n by p) into interval-valued or histogram-valued symbolic data (K by p) based on a grouping mechanism.

Usage

aggregate_to_symbolic(x, type = "int", group_by = "kmeans",
  stratify_var = NULL, K = 5, interval = "range",
  quantile_probs = c(0.05, 0.95), bins = 10, nK = NULL)

Arguments

Details

The function aggregates classical tabular data into symbolic data by:

1. Partitioning observations into groups via group_by (clustering, resampling, or a categorical variable).

2. Within each group, summarizing each numeric variable as an interval (min/max or quantiles) or a histogram.

When stratify_var is provided, grouping and aggregation are performed within each level of the stratification variable. Label values are prefixed by the stratum name (e.g., "setosa.cluster_1").

For type = "hist", bin boundaries are computed from the global data range to ensure comparability across groups.

Non-numeric columns (other than those used for grouping or stratification) are silently excluded from aggregation.

Value

• For type = "int": a symbolic_tbl (RSDA format) with a label column followed by symbolic_interval columns for each numeric variable (K rows, 1 + p columns).

• For type = "hist": a MatH object (K rows by p columns of histogram-valued data).

Examples

# Group by a categorical variable -> interval data
res1 <- aggregate_to_symbolic(iris, type = "int", group_by = "Species")
res1

# K-means clustering -> interval data
res2 <- aggregate_to_symbolic(iris[, 1:4], type = "int",
                               group_by = "kmeans", K = 3)

# Quantile-based intervals
res3 <- aggregate_to_symbolic(iris[, 1:4], type = "int",
                               group_by = "kmeans", K = 3,
                               interval = "quantile",
                               quantile_probs = c(0.1, 0.9))

# Resampling -> interval data
set.seed(42)
res4 <- aggregate_to_symbolic(iris[, 1:4], type = "int",
                               group_by = "resampling", K = 5, nK = 30)

# Histogram aggregation
res5 <- aggregate_to_symbolic(iris, type = "hist",
                               group_by = "Species", bins = 5)

# Hierarchical clustering -> interval data
res6 <- aggregate_to_symbolic(iris[, 1:4], type = "int",
                               group_by = "hclust", K = 3)

# Stratified aggregation
res7 <- aggregate_to_symbolic(iris, type = "int",
                               group_by = "kmeans", K = 2,
                               stratify_var = "Species")

Description

Histogram-valued dataset of 16 airlines flying into JFK Airport. Six variables (Flight Time, Taxi In, Arrival Delay, Taxi Out, Departure Delay, Weather Delay) recorded as frequency distributions. This is the wide (flat table) format; see airline_flights2.modal for the modal-valued version.

Usage

data(airline_flights.hist)

Format

A data frame with 16 observations (Airline1–Airline16) and 17 numeric columns representing 6 histogram variables in wide format:

• Flight Time(<120), Flight Time([120, 220]), Flight Time(>220): Flight time distribution (3 bins).

• Taxi In(<4), Taxi In([4, 10]), Taxi In(>10): Taxi-in time distribution (3 bins).

• Arrival Delay(<0), Arrival Delay([0, 60]), Arrival Delay(>60): Arrival delay distribution (3 bins).

• Taxi Out(<16), Taxi Out([16, 30]), Taxi Out(>30): Taxi-out time distribution (3 bins).

• Departure Delay(<0), Departure Delay([0, 60]), Departure Delay(>60): Departure delay distribution (3 bins).

• Weather Delay(No), Weather Delay(Yes): Weather delay distribution (2 bins).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.7.

Examples

data(airline_flights.hist)

Description

Modal-valued version of the airline flights dataset. See airline_flights.hist for the wide-format version.

Usage

data(airline_flights2.modal)

Format

A symbolic data frame (symbolic_tbl) with 16 observations and 6 modal-valued variables:

• FlightTime: Modal distribution over flight time bins.

• TaxiIn: Modal distribution over taxi-in time bins.

• ArrivalDelay: Modal distribution over arrival delay bins.

• TaxiOut: Modal distribution over taxi-out time bins.

• DepartureDelay: Modal distribution over departure delay bins.

• WeatherDelay: Modal distribution over weather delay bins.

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.7.

Examples

data(airline_flights2.modal)

Description

Convert a 3-dimensional array [n, p, 2] to iGAP format (data.frame with comma-separated interval values).

Usage

ARRAY_to_iGAP(data)

Arguments

Value

A data.frame in iGAP format with comma-separated "min,max" values.

Examples

x <- array(NA, dim = c(4, 3, 2))
x[,,1] <- matrix(c(1,2,3,4, 5,6,7,8, 9,10,11,12), nrow = 4)
x[,,2] <- matrix(c(3,5,6,7, 8,9,10,12, 13,15,16,18), nrow = 4)
dimnames(x) <- list(paste0("obs_", 1:4), c("V1","V2","V3"), c("min","max"))
igap <- ARRAY_to_iGAP(x)
igap

Description

Convert a 3-dimensional array [n, p, 2] to MM format (data.frame with paired _min/_max columns).

Usage

ARRAY_to_MM(data)

Arguments

Value

A data.frame with 2p columns (paired _min/_max).

Examples

x <- array(NA, dim = c(4, 3, 2))
x[,,1] <- matrix(c(1,2,3,4, 5,6,7,8, 9,10,11,12), nrow = 4)
x[,,2] <- matrix(c(3,5,6,7, 8,9,10,12, 13,15,16,18), nrow = 4)
dimnames(x) <- list(paste0("obs_", 1:4), c("V1","V2","V3"), c("min","max"))
mm <- ARRAY_to_MM(x)
mm

Description

Convert a 3-dimensional array [n, p, 2] to RSDA format (symbolic_tbl with symbolic_interval columns).

Usage

ARRAY_to_RSDA(data)

Arguments

Value

A symbolic_tbl with p symbolic_interval columns.

Examples

x <- array(NA, dim = c(4, 3, 2))
x[,,1] <- matrix(c(1,2,3,4, 5,6,7,8, 9,10,11,12), nrow = 4)
x[,,2] <- matrix(c(3,5,6,7, 8,9,10,12, 13,15,16,18), nrow = 4)
dimnames(x) <- list(paste0("obs_", 1:4), c("V1","V2","V3"), c("min","max"))
rsda <- ARRAY_to_RSDA(x)
rsda

Description

Symbolic dataset of autoregressive time series models for 4 banks. Each bank is described by AR model order, parameters, and whether parameters are known.

Usage

data(bank_rates)

Format

A data frame with 4 observations (Bank1–Bank4) and 6 variables:

• bank: Bank identifier (character).

• order: AR model order (numeric).

• phi1: First AR parameter (numeric; NA if unknown).

• phi2: Second AR parameter (numeric; NA if order < 2 or unknown).

• phi1_known: Whether phi1 is known (logical).

• phi2_known: Whether phi2 is known (logical; NA if order < 2).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.9.

Examples

data(bank_rates)

Description

Interval-valued data for 19 baseball teams with aggregated player batting statistics and a pattern variable classifying team performance.

Usage

data(baseball.int)

Format

A symbolic data frame (symbolic_tbl) with 19 observations and 3 variables:

• At_Bats: Range of at-bats across players (interval).

• Hits: Range of hits across players (interval).

• Pattern: Team performance pattern code (character).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(baseball.int)

Description

Interval-valued data for 21 bat species described by 4 morphological measurements. Benchmark dataset for matrix visualization.

Usage

data(bats.int)

Format

A data frame with 21 observations and 9 columns (4 interval variables in _l/_u Min-Max pairs, plus a label):

• species: Bat species name (character).

• head_l, head_u: Head length range (mm).

• tail_l, tail_u: Tail length range (mm).

• height_l, height_u: Ear height range (cm).

• forearm_l, forearm_u: Forearm length range (mm).

Details

Used to demonstrate color coding schemes, the HCT-R2E seriation algorithm, and distance measure comparisons (Gowda-Diday, Hausdorff, City-Block, L1, L2, etc.) for interval data.

Metadata

References

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(bats.int)

Description

Mixed symbolic dataset of 20 bird observations with histogram-valued feather density and body size, categorical tone, and distribution-valued shade (fuzzy taxonomy). From Tables 6.9 and 6.14 of Billard and Diday (2007).

Usage

data(bird_color_taxonomy.hist)

Format

A data frame with 20 observations and 4 variables:

• density: Histogram-valued feather density (up to 4 bins).

• size: Histogram-valued body size (2-bin).

• tone: Categorical tone (dark/light).

• shade: Distribution-valued shade (purple/red/white/yellow with fuzzy weights).

Metadata

Source

Billard, L. and Diday, E. (2007), Tables 6.9/6.14.

References

Billard, L. and Diday, E. (2007). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Tables 6.9 and 6.14.

Examples

data(bird_color_taxonomy.hist)

Description

Three bird species (Geese, Ostrich, Penguin) with interval-valued height, distribution-valued color, and categorical flying/migratory variables.

Usage

data(bird_species_extended.mix)

Format

A data frame with 3 observations and 6 variables:

• species: Species name (character).

• flying: Flying ability (Yes/No, character).

• height_l: Height lower bound (cm, numeric).

• height_u: Height upper bound (cm, numeric).

• color: Color distribution as weighted set string (e.g., "{white, 0.3; black, 0.7}").

• migratory: Migratory behavior (Yes/No, character).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.19.

Examples

data(bird_species_extended.mix)

Description

Symbolic data for 3 bird species (Swallow, Ostrich, Penguin) with interval-valued size, categorical flying, and categorical migration. Foundational SDA example from 600 individual bird observations.

Usage

data(bird_species.mix)

Format

A data frame with 3 observations (Swallow, Ostrich, Penguin) and 5 variables:

• species: Species name (character).

• flying: Flying ability (Yes/No, character).

• size_l, size_u: Size range (cm, Min-Max pair).

• migration: Migratory behavior (TRUE/FALSE, logical).

Metadata

References

Diday, E. and Noirhomme-Fraiture, M. (Eds.) (2008). Symbolic Data Analysis and the SODAS Software. Wiley. Table 1.2, p.6.

Examples

data(bird_species.mix)

Description

Interval-valued morphological measurements for 20 bird specimens. Despite the .mix suffix, this dataset contains only interval-valued variables (density and size).

Usage

data(bird.mix)

Format

A symbolic data frame (symbolic_tbl) with 20 observations and 2 variables:

• Density: Feather density range (interval).

• Size: Body size range (cm, interval).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.5.

Examples

data(bird.mix)

Description

Interval-valued blood pressure and pulse rate measurements for 15 patient groups.

Usage

data(blood_pressure.int)

Format

A symbolic data frame (symbolic_tbl) with 15 observations and 3 interval-valued variables:

• Pulse_Rate: Pulse rate range (beats per minute, interval).

• Systolic_Pressure: Systolic blood pressure range (mmHg, interval).

• Diastolic_Pressure: Diastolic blood pressure range (mmHg, interval).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(blood_pressure.int)

Description

Histogram-valued blood test results for 14 gender-age groups (e.g., Female-20, Male-50). Each observation contains histograms for cholesterol, hemoglobin, and hematocrit, represented as multi-bin distributions.

Usage

data(blood.hist)

Format

A data frame with 14 observations and 3 histogram-valued variables:

• Cholesterol: Histogram of cholesterol levels (mg/dL).

• Hemoglobin: Histogram of hemoglobin levels (g/dL).

• Hematocrit: Histogram of hematocrit levels (%).

Metadata

Source

HistDAWass R package (BLOOD dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (BLOOD dataset).

Examples

data(blood.hist)

Description

Interval-valued specifications for 33 Italian car models, classified into 4 categories (Utilitaria, Berlina, Ammiraglia, Sportiva). An extended version of the classic cars interval dataset with 8 interval-valued variables including dimensions.

Usage

data(car_models.int)

Format

A data frame with 33 observations and 9 variables:

• price: Price range (currency units).

• engine_cc: Engine displacement range (cc).

• top_speed: Top speed range (km/h).

• acceleration: Acceleration range (seconds 0-100 km/h).

• wheelbase: Wheelbase range (cm).

• length: Length range (cm).

• width: Width range (cm).

• height: Height range (cm).

• class: Car category (Utilitaria, Berlina, Ammiraglia, Sportiva).

Metadata

Source

https://github.com/Natandradesa/Kernel-Clustering-for-Interval-Data

References

Andrade, N. A., de Carvalho, F. A. T. and Pimentel, B. A. (2025). Kernel clustering with automatic variable weighting for interval data. Neurocomputing, 617, 128954.

Examples

data(car_models.int)

Description

Interval-valued data for 8 car brands with price and performance specifications. Each brand aggregates multiple models into interval ranges.

Usage

data(car.int)

Format

A symbolic data frame (symbolic_tbl) with 8 observations and 5 variables:

• Car: Car brand name (character).

• Price: Price range (thousands of currency units, interval).

• Max_Velocity: Maximum velocity range (km/h, interval).

• Accn_Time: Acceleration time range (seconds 0–100 km/h, interval).

• Cylinder_Capacity: Engine cylinder capacity range (cc, interval).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(car.int)

Description

Interval-valued data from cardiological examinations of 44 patients. Each patient is described by 5 interval-valued physiological measurements.

Usage

data(cardiological.int)

Format

A data frame with 44 observations and 5 interval-valued variables:

• pulse: Pulse rate range (beats per minute).

• systolic: Systolic blood pressure range (mmHg).

• diastolic: Diastolic blood pressure range (mmHg).

• arterial1: First arterial measurement range.

• arterial2: Second arterial measurement range.

Metadata

Source

Extracted from RSDA package (cardiologicalv2).

References

Rodriguez, O. (2000). Classification et modeles lineaires en analyse des donnees symboliques. Doctoral Thesis, Universite Paris IX-Dauphine.

Examples

data(cardiological.int)

Description

Interval-valued data for 27 car models classified into four classes (Utilitarian, Berlina, Sportive, Luxury), described by Price, EngineCapacity, TopSpeed and Acceleration intervals.

Usage

data(cars.int)

Format

A symbolic data frame (symbolic_tbl) with 27 observations and 5 variables:

• Price: Price range (interval).

• EngCap: Engine capacity range (cc, interval).

• TopSpeed: Top speed range (km/h, interval).

• Acceleration: Acceleration range (seconds 0–100 km/h, interval).

• class: Car class (Utilitarian, Berlina, Sportive, Luxury; set-valued).

Metadata

Source

https://CRAN.R-project.org/package=MAINT.Data

References

Duarte Silva, A.P., Brito, P., Filzmoser, P. and Dias, J.G. (2021). MAINT.Data: Modelling and Analysing Interval Data in R. R Journal, 13(2).

Examples

data(cars.int)

Description

Mixed symbolic dataset of 10 census regions combining 6 different symbolic variable types: histograms (age, home value), distributions (gender, tenure), a multi-valued set (fuel), and an interval (income).

Usage

data(census.mix)

Format

A symbolic data frame (symbolic_tbl) with 10 observations (regions) and 6 variables:

• age: Histogram-valued age distribution (12 age bins).

• home_value: Histogram-valued home value distribution (7 value bins, in $1000s).

• gender: Distribution over gender (male, female).

• fuel: Multi-valued set of fuel types used.

• tenure: Distribution over housing tenure (owner, renter, vacant).

• income: Interval-valued household income range ($1000s).

Row names are Region_1 through Region_10.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 7-23.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 7-23.

Examples

data(census.mix)

Description

Histogram-valued monthly climate data for 60 Chinese weather stations. Each station has 14 climate variables measured across 12 months (168 histogram columns total). Histograms are reduced to 10 decile bins from the original HistDAWass distributions.

Usage

data(china_climate_month.hist)

Format

A data frame with 60 observations (stations) and 168 histogram-valued variables. Variables follow the pattern variable_Month (e.g., mean.temp_Jan). The 14 climate variables are: mean pressure, mean temperature, mean max/min temperature, total precipitation, sunshine duration, mean cloud amount, mean relative humidity, snow days, dominant wind direction, mean wind speed, dominant wind frequency, extreme max/min temperature.

Metadata

Source

HistDAWass R package (China_Month dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (China_Month dataset).

Examples

data(china_climate_month.hist)

Description

Histogram-valued seasonal climate data for 60 Chinese weather stations. Each station has 14 climate variables measured across 4 seasons (56 histogram columns total). Histograms are reduced to 10 decile bins from the original HistDAWass distributions.

Usage

data(china_climate_season.hist)

Format

A data frame with 60 observations (stations) and 56 histogram-valued variables. Variables follow the pattern variable_Season (e.g., mean.temp_Spring). The 14 climate variables are: mean pressure, mean temperature, mean max/min temperature, total precipitation, sunshine duration, mean cloud amount, mean relative humidity, snow days, dominant wind direction, mean wind speed, dominant wind frequency, extreme max/min temperature.

Metadata

Source

HistDAWass R package (China_Seas dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (China_Seas dataset).

Examples

data(china_climate_season.hist)

Description

Interval-valued dataset of monthly temperature ranges for 15 weather stations in China. Each station has 12 monthly temperature intervals (minimum and maximum observed temperatures in degrees Celsius) and an elevation value in meters.

Usage

data(china_temp_monthly.int)

Format

A symbolic data frame (symbolic_tbl) with 15 observations (weather stations) and 13 variables:

• January, February, March, April, May, June, July, August, September, October, November, December: Interval-valued monthly temperature ranges (degrees Celsius).

• Elevation: Station elevation above sea level (numeric, meters).

Row names are station names (e.g., BoKeTu, Hailaer, LaSa).

Metadata

Source

Billard, L. and Diday, E. (2020), Table 7-9.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 7-9.

Examples

data(china_temp_monthly.int)

Description

Interval-valued temperature data (Celsius) for 60 Chinese meteorological stations observed over the four quarters of years 1974 to 1988. One outlier observation (YinChuan_1982) has been discarded.

Usage

data(china_temp.int)

Format

A symbolic data frame (symbolic_tbl) with 899 observations and 5 variables:

• Q1: Quarter 1 (Jan–Mar) temperature range (tenths of degrees Celsius, interval).

• Q2: Quarter 2 (Apr–Jun) temperature range (interval).

• Q3: Quarter 3 (Jul–Sep) temperature range (interval).

• Q4: Quarter 4 (Oct–Dec) temperature range (interval).

• GeoReg: Geographic region classification (factor).

Details

Originates from the Long-Term Instrumental Climatic Database of the People's Republic of China. Widely used in the SDA literature for demonstrating standardization, clustering, self-organizing maps, MLE and MANOVA.

Metadata

Source

https://CRAN.R-project.org/package=MAINT.Data

References

Brito, P. and Duarte Silva, A.P. (2012). Modelling interval data with Normal and Skew-Normal distributions. J. Appl. Stat., 39(1), 3-20.

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(china_temp.int)

Description

Histogram-valued cholesterol distributions for 14 gender-age groups (7 female + 7 male age groups from 20s to 80+). Each observation has a 10-bin histogram of cholesterol levels.

Usage

data(cholesterol.hist)

Format

A data frame with 14 observations and 3 variables:

• gender: Gender (Female or Male).

• age: Age group (20s, 30s, 40s, 50s, 60s, 70s, 80+).

• cholesterol: Histogram-valued cholesterol distribution.

Metadata

Source

Billard, L. and Diday, E. (2006), Table 4.5.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 4.5.

Examples

data(cholesterol.hist)

Description

This function is used to clean up variable names to conform to the RSDA format.

Usage

clean_colnames(data)

Arguments

Value

Data after cleaning variable names.

Examples

data(mushroom.int.mm)
mushroom.clean <- clean_colnames(data = mushroom.int.mm)

Description

Histogram-valued dataset of 12 counties with gender-stratified income histograms and sample sizes. Each county has a male income histogram, a female income histogram, and the number of respondents in each group.

Usage

data(county_income_gender.hist)

Format

A data frame with 12 observations (counties) and 4 variables:

• male_income: Histogram of male household income (4 bins from $0 to $100k).

• female_income: Histogram of female household income (4 bins from $0 to $100k).

• n_males: Number of male respondents (numeric).

• n_females: Number of female respondents (numeric).

Row names are County_1 through County_12.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 6-16.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 6-16.

Examples

data(county_income_gender.hist)

Description

Histogram-valued dataset of 7 forest cover types with 4 topographic histogram variables. Each histogram describes the distribution of a terrain feature across locations classified as that cover type.

Usage

data(cover_types.hist)

Format

A data frame with 7 observations (cover types) and 4 histogram-valued variables:

• elevation: Histogram of elevation values (meters).

• distance_to_water: Histogram of horizontal distance to nearest water source (meters).

• hillshade: Histogram of hillshade index values.

• slope: Histogram of slope values (degrees).

Row names are CoverType_1 through CoverType_7.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 7-21.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 7-21.

Examples

data(cover_types.hist)

Description

Interval-valued credit card spending aggregated by person-month. Three individuals' (Jon, Tom, Leigh) monthly expenditures across five categories.

Usage

data(credit_card.int)

Format

A data frame with 6 observations and 11 columns (5 interval variables in _l/_u Min-Max pairs, plus a label):

• person_month: Person-month identifier (e.g., "Jon - January"; character).

• food_l, food_u: Food expenditure range (USD).

• social_l, social_u: Social expenditure range (USD).

• travel_l, travel_u: Travel expenditure range (USD).

• gas_l, gas_u: Gas expenditure range (USD).

• clothes_l, clothes_u: Clothes expenditure range (USD).

Details

The original classical dataset (Table 2.3) records individual transactions. The symbolic version (Table 2.4) aggregates into interval-valued observations for each person-month combination.

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Tables 2.3-2.4.

Examples

data(credit_card.int)

Description

Modal-valued dataset of 15 gangs described by probability distributions over crime type, gender, and age group. This is the wide (flat table) format; see crime2.modal for the modal-valued version.

Usage

data(crime.modal)

Format

A data frame with 15 observations (gang1–gang15) and 7 numeric columns representing 3 modal variables in wide format:

• Crime(violent), Crime(non-violent), Crime(none): Distribution over crime types (3 bins).

• Gender(male), Gender(female): Distribution over gender (2 bins).

• Age(<20), Age(>=20): Distribution over age groups (2 bins).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(crime.modal)

Description

Modal-valued version of the crime demographics dataset. See crime.modal for the wide-format version.

Usage

data(crime2.modal)

Format

A symbolic data frame (symbolic_tbl) with 15 observations and 3 modal-valued variables:

• Crime: Modal distribution over crime types (violent, non-violent, none).

• Gender: Modal distribution over gender (male, female).

• Age: Modal distribution over age groups (<20, >=20).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley.

Examples

data(crime2.modal)

Description

Daily high and low prices of WTI (West Texas Intermediate) crude oil futures from January 2, 2003 to December 30, 2011 (2261 trading days). This dataset matches the period used by Yang, Han, Hong and Wang (2016) for analyzing crisis impacts on crude oil prices using interval time series modelling.

Usage

data(crude_oil_wti.its)

Format

A data frame with 2261 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low price (USD per barrel).

• high: Daily high price (USD per barrel).

Details

WTI crude oil is a benchmark for oil prices in the Americas. This dataset covers a period that includes the 2003 Iraq War, the 2007–2008 oil price spike (reaching nearly USD 150/barrel), the 2008 global financial crisis, and the subsequent recovery. The wide variation in price levels and volatility regimes makes this dataset ideal for evaluating interval time series models under structural breaks.

Metadata

Source

Yahoo Finance, ticker CL=F. Downloaded via the quantmod package.

References

Yang, W., Han, A., Hong, Y. and Wang, S. (2016). Analysis of crisis impact on crude oil prices: A new approach with interval time series modelling. Quantitative Finance, 16(12), 1917–1928.

Examples

data(crude_oil_wti.its)
head(crude_oil_wti.its)
plot(crude_oil_wti.its$date, crude_oil_wti.its$high, type = "l",
     col = "red", ylab = "Price (USD/barrel)", xlab = "Date",
     main = "WTI Crude Oil Daily High/Low (2003-2011)")
lines(crude_oil_wti.its$date, crude_oil_wti.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Description

Daily high and low prices of the Dow Jones Industrial Average (DJIA) from January 2, 2004 to December 30, 2005 (504 trading days). This dataset matches the period used in the foundational interval time series work by Arroyo, Gonzalez-Rivera and Mate (2011).

Usage

data(djia.its)

Format

A data frame with 504 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low price of the DJIA.

• high: Daily high price of the DJIA.

Details

The DJIA is a price-weighted index of 30 prominent companies listed on stock exchanges in the United States. Each observation represents a trading day with the daily low and high prices forming an interval. This dataset has been used alongside the S&P 500 to compare interval forecasting methods.

Metadata

Source

Yahoo Finance, ticker ^DJI. Downloaded via the quantmod package.

References

Arroyo, J., Gonzalez-Rivera, G. and Mate, C. (2011). Forecasting with interval and histogram data: Some financial applications. In Handbook of Empirical Economics and Finance, pp. 247–280. Chapman and Hall/CRC.

Examples

data(djia.its)
head(djia.its)
plot(djia.its$date, djia.its$high, type = "l", col = "red",
     ylab = "Price", xlab = "Date", main = "DJIA Daily High/Low")
lines(djia.its$date, djia.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Description

Interval-valued dataset of 9 E. coli transport routes with 5 interval variables representing biochemical pathway measurements.

Usage

data(ecoli_routes.int)

Format

A symbolic data frame (symbolic_tbl) with 9 observations (transport routes) and 5 interval-valued variables:

• Y1 through Y5: Interval-valued biochemical pathway measurements.

Row names are Route_1 through Route_9.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 8-10.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 8-10.

Examples

data(ecoli_routes.int)

Description

Interval-valued proportions for 12 sex-age population groups across employment variables (employment type, education, industry sector, occupation, marital status). Used for factorial discriminant analysis.

Usage

data(employment.int)

Format

A data frame with 12 observations and 20 columns (9 interval variables in _l/_u Min-Max pairs, plus a group label and class):

• group: Sex-age group identifier (character).

• full_time_l, full_time_u: Full-time employment proportion range.

• part_time_l, part_time_u: Part-time employment proportion range.

• primary_studies_l, primary_studies_u: Primary studies proportion range.

• secondary_studies_l, secondary_studies_u: Secondary studies proportion range.

• uni_studies_l, uni_studies_u: University studies proportion range.

• employee_l, employee_u: Employee proportion range.

• manufacturing_l, manufacturing_u: Manufacturing sector proportion range.

• construction_l, construction_u: Construction sector proportion range.

• wholesale_retail_l, wholesale_retail_u: Wholesale/retail proportion range.

• class: Group classification (numeric).

Metadata

References

Diday, E. and Noirhomme-Fraiture, M. (Eds.) (2008). Symbolic Data Analysis and the SODAS Software. Wiley. Table 18.1.

Examples

data(employment.int)

Description

Distribution-valued dataset of energy consumption across US states. Each energy type described by Normal distribution parameters (mean, SD).

Usage

data(energy_consumption.distr)

Format

A data frame with 5 observations and 3 variables:

• type: Energy type.

• mean: Mean consumption across 50 states.

• sd: Standard deviation.

Details

Five types: Petroleum, Natural Gas, Coal, Hydroelectric, Nuclear Power. Values are rescaled consumption from the US Census Bureau (2004).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.8.

Examples

data(energy_consumption.distr)

Description

Distribution-valued dataset for 10 towns (geographic areas) with categorical probability distributions for fuel type and central heating. Each observation has two distribution-valued variables.

Usage

data(energy_usage.distr)

Format

A data frame with 10 observations and 2 distribution-valued variables:

• fuel_type: Distribution over fuel types (None, Gas, Oil, Electricity, Coal).

• central_heating: Distribution over central heating (No, Yes).

Row names are Town_1 through Town_10.

Metadata

Source

Billard, L. and Diday, E. (2006), Table 3.7.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 3.7.

Examples

data(energy_usage.distr)

Description

Mixed symbolic dataset from the US EPA with 14 state-group observations and 17 variables of mixed types: interval-valued environmental measurements and modal-valued (distributional) categorical variables.

Usage

data(environment.mix)

Format

A symbolic data frame (symbolic_tbl) with 14 observations and 17 variables:

• URBANICITY: Modal-valued urbanicity distribution (character).

• INCOMELEVEL: Modal-valued income level distribution (character).

• EDUCATION: Modal-valued education distribution (character).

• REGIONDEVELOPME: Modal-valued regional development distribution (character).

• CONTROL: Environmental control index range (interval).

• SATISFY: Satisfaction index range (interval).

• INDIVIDUAL: Individual concern index range (interval).

• WELFARE: Welfare index range (interval).

• HUMAN: Human impact index range (interval).

• POLITICS: Political concern index range (interval).

• BURDEN: Burden index range (interval).

• NOISE: Noise pollution index range (interval).

• NATURE: Nature preservation index range (interval).

• SEASETC: Seas/coastal index range (interval).

• MULTI: Multi-indicator range (interval).

• WATERWASTE: Water/waste index range (interval).

• VEHICLE: Vehicle emissions index range (interval).

Metadata

Source

Extracted from ggESDA package (Environment).

References

Sun, Y. and Billard, L. (2020). Symbolic data analysis with the ggESDA package. Journal of Statistical Software.

Examples

data(environment.mix)

Description

Daily high and low values of the EUR/USD exchange rate from January 1, 2004 to December 30, 2005 (520 trading days). Inspired by the dataset used by Arroyo, Espinola and Mate (2011) for exponential smoothing methods for interval time series.

Usage

data(euro_usd.its)

Format

A data frame with 520 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low EUR/USD exchange rate.

• high: Daily high EUR/USD exchange rate.

Details

The EUR/USD exchange rate is the most traded currency pair in the world foreign exchange market. Each observation represents a trading day with the daily low and high exchange rates (USD per EUR) forming an interval. Note: the original study by Arroyo et al. (2011) used the period 2002–2003 (519 trading days); this dataset covers 2004–2005 because Yahoo Finance historical data for this ticker is only available from late 2003 onward.

Metadata

Source

Yahoo Finance, ticker EURUSD=X. Downloaded via the quantmod package.

References

Arroyo, J., Espinola, R. and Mate, C. (2011). Different approaches to forecast interval time series: A comparison in finance. Computational Economics, 37(2), 169–191.

Examples

data(euro_usd.its)
head(euro_usd.its)
plot(euro_usd.its$date, euro_usd.its$high, type = "l", col = "red",
     ylab = "EUR/USD", xlab = "Date",
     main = "EUR/USD Daily High/Low (2004-2005)")
lines(euro_usd.its$date, euro_usd.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Description

Histogram-valued time series of 108 monthly observations of daily exchange rate returns. Each observation is a histogram distribution of intra-month daily returns.

Usage

data(exchange_rate_returns.hist)

Format

A data frame with 108 observations and 1 histogram-valued variable:

• returns: Histogram of daily exchange rate returns within each month.

Metadata

Source

HistDAWass R package (RetHTS dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (RetHTS dataset).

Examples

data(exchange_rate_returns.hist)

Description

Interval-valued facial measurement data for 27 face images (9 individuals x 3 replications) in iGAP format (comma-separated interval strings). Contains 6 distance measurements between facial landmarks.

Usage

data(face.iGAP)

Format

A data frame with 27 observations and 6 character columns in iGAP format (comma-separated "min,max" strings):

• AD: Distance AD (facial landmark pair).

• BC: Distance BC (facial landmark pair).

• AH: Distance AH (facial landmark pair).

• DH: Distance DH (facial landmark pair).

• EH: Distance EH (facial landmark pair).

• GH: Distance GH (facial landmark pair).

Row names encode individual and replication (e.g., FRA1, FRA2, FRA3).

Metadata

References

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

Examples

data(face.iGAP)

Description

Interval-valued data for 14 business sectors described by job-related financial variables (job cost codes, activity codes, budgets). Used for PCA demonstrations.

Usage

data(finance.int)

Format

A symbolic data frame (symbolic_tbl) with 14 observations and 7 variables:

• Sector: Business sector name (character).

• Job_Cost: Job cost range (currency units, interval).

• Job_Code: Job code range (interval).

• Activity_Code: Activity code range (interval).

• Monthly_Cost: Monthly cost range (currency units, interval).

• Annual_Budget: Annual budget range (currency units, interval).

• n: Number of entities in the sector (numeric).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 5.2.

Examples

data(finance.int)

Description

Histogram-valued dataset of 16 airlines with 5 flight performance histograms. Each histogram has 12 bins describing the distribution of a performance metric across flights for that airline.

Usage

data(flights_detail.hist)

Format

A data frame with 16 observations (airlines) and 5 histogram-valued variables:

• airtime: Histogram of air time (minutes).

• taxi_in: Histogram of taxi-in time (minutes).

• arrival_delay: Histogram of arrival delay (minutes).

• taxi_out: Histogram of taxi-out time (minutes).

• departure_delay: Histogram of departure delay (minutes).

Row names are Airline_1 through Airline_16.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 5-1.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 5-1.

Examples

data(flights_detail.hist)

Description

Histogram-valued dataset of 22 French regions with 4 economic histogram variables related to agricultural production. Each histogram describes the distribution of farm-level values within a region.

Usage

data(french_agriculture.hist)

Format

A data frame with 22 observations (French regions) and 4 histogram-valued variables:

• Y_TSC: Histogram of total standard coefficient.

• X_Wheat: Histogram of wheat production.

• X_Pig: Histogram of pig production.

• X_Cmilk: Histogram of cow milk production.

Row names are French region names (e.g., Ile-de-France, Picardie).

Metadata

Source

HistDAWass R package (Agronomique dataset).

References

Irpino, A. and Verde, R. (2015). Basic statistics for distributional symbolic variables: A new metric-based approach. Advances in Data Analysis and Classification, 9(2), 143–175.

Original data from the HistDAWass R package (Agronomique dataset).

Examples

data(french_agriculture.hist)

Description

Interval-valued dataset of heavy metal concentrations in organs and tissues of 12 freshwater fish species, grouped into 4 feeding categories (Carnivores, Omnivores, Detritivores, Herbivores). Contains 13 interval-valued variables measuring metal concentrations in organs and organ-to-muscle ratios.

Usage

data(freshwater_fish.int)

Format

A data frame with 12 observations and 14 variables:

• body_length: Body length (cm).

• body_weight: Body weight (g).

• muscle: Metal concentration in muscle tissue.

• intestine: Metal concentration in intestine.

• stomach: Metal concentration in stomach.

• gills: Metal concentration in gills.

• liver: Metal concentration in liver.

• kidney: Metal concentration in kidney.

• liver_muscle_ratio: Liver-to-muscle concentration ratio.

• kidney_muscle_ratio: Kidney-to-muscle concentration ratio.

• gills_muscle_ratio: Gills-to-muscle concentration ratio.

• intestine_muscle_ratio: Intestine-to-muscle concentration ratio.

• stomach_muscle_ratio: Stomach-to-muscle concentration ratio.

• class: Feeding category (Carnivores, Omnivores, Detritivores, Herbivores).

Metadata

Source

https://github.com/Natandradesa/Kernel-Clustering-for-Interval-Data

References

Andrade, N. A., de Carvalho, F. A. T. and Pimentel, B. A. (2025). Kernel clustering with automatic variable weighting for interval data. Neurocomputing, 617, 128954.

Examples

data(freshwater_fish.int)

Description

Modal-valued dataset describing fuel consumption patterns across 10 regions by proportions of heating fuel types (gas, oil, electricity, other) and per-capita expenditure.

Usage

data(fuel_consumption.modal)

Format

A symbolic data frame (symbolic_tbl) with 10 observations and 3 variables:

• Region: Region identifier (character).

• Expenditure: Per-capita fuel expenditure (numeric).

• Fuel_Type: Modal distribution over fuel types (gas, oil, electric, other).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 3.7.

Examples

data(fuel_consumption.modal)

Description

Interval-valued morphological measurements for 55 fungi specimens from 3 genera (Amanita, Agaricus, Boletus). Contains 5 interval-valued variables describing pileus and stipe dimensions and spore characteristics.

Usage

data(fungi.int)

Format

A data frame with 55 observations and 6 variables:

• pileus_width: Width of the pileus (cap).

• stipe_width: Width of the stipe (stem).

• stipe_thickness: Thickness of the stipe.

• spore_height: Height of the spores.

• spore_width: Width of the spores.

• class: Fungus genus (Amanita, Agaricus, Boletus).

Metadata

Source

https://github.com/Natandradesa/Kernel-Clustering-for-Interval-Data

References

Andrade, N. A., de Carvalho, F. A. T. and Pimentel, B. A. (2025). Kernel clustering with automatic variable weighting for interval data. Neurocomputing, 617, 128954.

Examples

data(fungi.int)

Description

Interval-valued dataset of dinucleotide relative abundances for 14 genome classes. Each class aggregates multiple genomes; the intervals represent the range of observed abundance values within each class for 10 dinucleotide pairs, plus a count variable.

Usage

data(genome_abundances.int)

Format

A symbolic data frame (symbolic_tbl) with 14 observations (genome classes) and 11 variables:

• CG: Interval-valued CG dinucleotide relative abundance.

• GC: Interval-valued GC dinucleotide relative abundance.

• TA: Interval-valued TA dinucleotide relative abundance.

• AT: Interval-valued AT dinucleotide relative abundance.

• CC: Interval-valued CC dinucleotide relative abundance.

• AA: Interval-valued AA dinucleotide relative abundance.

• AC: Interval-valued AC dinucleotide relative abundance.

• AG: Interval-valued AG dinucleotide relative abundance.

• CA: Interval-valued CA dinucleotide relative abundance.

• GA: Interval-valued GA dinucleotide relative abundance.

• n: Number of genomes in the class (integer).

Row names are Class_1 through Class_14.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 3-16.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 3-16.

Examples

data(genome_abundances.int)

Description

Histogram-valued dataset of 4 regions with a single histogram-valued variable describing the distribution of blood glucose measurements.

Usage

data(glucose.hist)

Format

A data frame with 4 observations (regions) and 1 histogram-valued variable:

• glucose: Histogram of blood glucose levels.

Row names are Region_1 through Region_4.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 4-14.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 4-14.

Examples

data(glucose.hist)

Description

Histogram-valued climate data for 5 hardwood tree species in the southeastern United States. Each observation represents a species with 4 histogram-valued climate variables.

Usage

data(hardwood.hist)

Format

A data frame with 5 observations and 4 histogram-valued variables:

• ANNT: Annual temperature histogram (degrees C).

• JULT: July temperature histogram (degrees C).

• ANNP: Annual precipitation histogram (mm).

• MITM: Moisture index histogram.

Metadata

Source

Extracted from RSDA package (hardwoodBrito).

References

Brito, P. (2007). Modelling and Analysing Interval Data. In V. Esposito Vinzi et al. (Eds.), New Developments in Classification and Data Analysis, pp. 197-208. Springer.

Examples

data(hardwood.hist)

Description

Interval-valued World Bank gender indicators for 183 countries, with ordinal HDI classification. Contains interval ranges for Women, Business and the Law Index Score and proportion of seats held by women in national parliaments.

Usage

data(hdi_gender.int)

Format

A data frame with 183 observations and 6 variables:

• code: ISO 3166-1 alpha-3 country code.

• country: Country name.

• hdi: Human Development Index value (UNDP).

• women_law_index: Women, Business and the Law Index Score range.

• women_parliament: Proportion of seats held by women in national parliaments range (%).

• hdi_category: Ordered factor with HDI classification (Low < Medium < High < Very High).

Metadata

Source

https://github.com/aleixalcacer/OCFIVD

References

Alcacer, A., Barrel, A., Groenen, P. J. F. and Grana, M. (2023). Ordinal classification for interval-valued data and ordinal data. Expert Systems with Applications, 238, 121825.

Examples

data(hdi_gender.int)

Description

Classical (microdata) health insurance dataset of 51 individual patient records with 30 variables including demographics, clinical measurements, and diagnostic indicators. This is the raw data underlying the symbolic health_insurance2.modal dataset.

Usage

data(health_insurance.mix)

Format

A data frame with 51 observations and 30 variables (Y1–Y30):

• Y1: City (character).

• Y2: Gender (M/F, character).

• Y3: Age (integer).

• Y4: Sex (M/D, character).

• Y5: Marital status (S/M, character).

• Y6: Number of dependents (integer).

• Y7: Parents alive indicator (integer).

• Y8: Number of children (integer).

• Y9: Height (cm, integer).

• Y10: Weight (pounds, integer).

• Y11: Systolic blood pressure (mmHg, integer).

• Y12: Diastolic blood pressure (mmHg, integer).

• Y13: Cholesterol (mg/dL, integer).

• Y14: Cholesterol measure 2 (integer).

• Y15: Additional lab measurement (integer).

• Y16: Ratio measurement (numeric).

• Y17: Lab value (integer).

• Y18: Lab value (integer).

• Y19: Lab value (integer).

• Y20: Lab ratio (numeric).

• Y21: Additional lab value (integer).

• Y22: Additional lab value (integer).

• Y23: Blood chemistry value (numeric).

• Y24: Blood chemistry value (numeric).

• Y25: Blood chemistry value (numeric).

• Y26: Blood chemistry value (numeric).

• Y27: Blood chemistry value (numeric).

• Y28: Diagnostic indicator (Y/N, character).

• Y29: Diagnostic indicator (Y/N, character).

• Y30: Count variable (integer).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Tables 2.1-2.2.

Examples

data(health_insurance.mix)

Description

Modal-valued symbolic version of the health insurance dataset, aggregated into 6 disease-type-by-gender groups. See health_insurance.mix for the underlying microdata.

Usage

data(health_insurance2.modal)

Format

A symbolic data frame (symbolic_tbl) with 6 observations and 6 variables:

• Type Gender: Disease type and gender label (character).

• Age: Modal distribution over age bins.

• Marital Status: Modal distribution over marital status (M, S).

• Parents Alive: Modal distribution over number of parents alive (0, 1, 2).

• Weight: Modal distribution over weight bins (pounds).

• Cholesterol: Modal distribution over cholesterol bins (mg/dL).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.2b.

Examples

data(health_insurance2.modal)

Description

Bivariate histogram-valued dataset with 10 observations, each described by a 2-bin hematocrit histogram and a 2-bin hemoglobin histogram. Used for bivariate symbolic regression demonstrations.

Usage

data(hematocrit_hemoglobin.hist)

Format

A data frame with 10 observations and 2 histogram-valued variables:

• hematocrit: Histogram-valued hematocrit distribution (%).

• hemoglobin: Histogram-valued hemoglobin distribution (g/dL).

Metadata

Source

Billard, L. and Diday, E. (2006), Table 6.8.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 6.8.

Examples

data(hematocrit_hemoglobin.hist)

Description

Histogram-valued hematocrit distributions for 14 gender-age groups (7 female + 7 male age groups from 20s to 80+). Each observation has a 10-bin histogram of hematocrit percentages.

Usage

data(hematocrit.hist)

Format

A data frame with 14 observations and 3 variables:

• gender: Gender (Female or Male).

• age: Age group (20s, 30s, 40s, 50s, 60s, 70s, 80+).

• hematocrit: Histogram-valued hematocrit distribution (%).

Metadata

Source

Billard, L. and Diday, E. (2006), Table 4.14.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 4.14.

Examples

data(hematocrit.hist)

Description

Histogram-valued hemoglobin distributions for 14 gender-age groups (7 female + 7 male age groups from 20s to 80+). Each observation has a 10-bin histogram of hemoglobin levels (g/dL).

Usage

data(hemoglobin.hist)

Format

A data frame with 14 observations and 3 variables:

• gender: Gender (Female or Male).

• age: Age group (20s, 30s, 40s, 50s, 60s, 70s, 80+).

• hemoglobin: Histogram-valued hemoglobin distribution (g/dL).

Metadata

Source

Billard, L. and Diday, E. (2006), Table 4.6.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 4.6.

Examples

data(hemoglobin.hist)

Description

Classical (microdata) dataset of 20 observations illustrating hierarchical categorical structures with a response variable Y and hierarchical predictors X1–X5. See hierarchy.int for the interval-valued version.

Usage

data(hierarchy)

Format

A data frame with 20 observations and 6 variables:

• Y: Response variable (numeric).

• X1: Hierarchy level 1 category (a/b/c, character).

• X2: Hierarchy level 2 category (a1/a2, character; NA for non-a).

• X3: Hierarchy level 3 category (a11/a12, character; NA for non-a1).

• X4: Numeric predictor for group b (numeric; NA for non-b).

• X5: Numeric predictor for group c (numeric; NA for non-c).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.15.

Examples

data(hierarchy)

Description

Mixed symbolic dataset of 10 observations with hierarchical categorical variables, conditional histogram variables, and an interval-valued variable. From Table 6.20 of Billard and Diday (2007).

Usage

data(hierarchy.hist)

Format

A symbolic data frame (symbolic_tbl) with 10 observations and 7 variables:

• duration_time: Histogram-valued duration (2-bin).

• hierarchy_1: Categorical hierarchy level 1 (a/b/c).

• hierarchy_2: Categorical hierarchy level 2 (a1/a2), conditional on hierarchy_1 = a.

• hierarchy_3: Categorical hierarchy level 3 (a11/a12), conditional on hierarchy_2 = a1.

• glucose: Histogram-valued glucose (2-bin), conditional.

• pulse_rate: Histogram-valued pulse rate (2-bin), conditional.

• cholesterol: Interval-valued cholesterol level.

Metadata

Source

Billard, L. and Diday, E. (2007), Table 6.20.

References

Billard, L. and Diday, E. (2007). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 6.20.

Examples

data(hierarchy.hist)

Description

Interval-valued version of the hierarchy dataset. See hierarchy for the classical version.

Usage

data(hierarchy.int)

Format

A symbolic data frame (symbolic_tbl) with 20 observations and 6 variables:

• Y: Response variable range (interval).

• X1: Hierarchy level 1 category (a/b/c, character).

• X2: Hierarchy level 2 category (a1/a2, character; NA for non-a).

• X3: Hierarchy level 3 category (a11/a12, character; NA for non-a1).

• X4: Predictor range for group b (interval; NA for non-b).

• X5: Predictor range for group c (interval; NA for non-c).

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 2.15.

Examples

data(hierarchy.int)

Description

Functions to compute the mean, variance, covariance, and correlation of histogram-valued data.

Usage

hist_mean(x, var_name, method = "BG", ...)

hist_var(x, var_name, method = "BG", ...)

hist_cov(x, var_name1, var_name2, method = "BG", ...)

hist_cor(x, var_name1, var_name2, method = "BG", ...)

Arguments

Details

Four functions are provided:

• hist_mean: Compute the mean of histogram-valued data.

• hist_var: Compute the variance of histogram-valued data.

• hist_cov: Compute the covariance between two histogram-valued variables.

• hist_cor: Compute the correlation between two histogram-valued variables.

Four methods are supported for all functions:

BG

Bertrand and Goupil (2000) method. Uses histogram bin boundaries and probabilities to compute first and second moments.

BD

Billard and Diday (2006) method. A signed decomposition using the sign of each bin's midpoint deviation from the overall mean and a quadratic form on the bin boundaries.

B

Billard (2008) method. Uses cross-products of deviations of the bin boundaries from the overall mean.

L2W

L2 Wasserstein method. Uses optimal-transport (Wasserstein) distances between the quantile functions of the histogram distributions.

For the mean, BG, BD, and B return the same value because they share the same first-order moment definition; only L2W uses a different (quantile-based) mean. For variance, covariance, and correlation, all four methods generally produce different results.

For hist_cor, the BG, BD, and B correlations all use the Bertrand-Goupil standard deviation $S(Y)$ in the denominator, following Irpino and Verde (2015, Eqs. 30–32). Only the L2W method uses its own Wasserstein-based standard deviation in the denominator.

Value

A numeric value or vector for hist_mean and hist_var; a single numeric value for hist_cov and hist_cor.

Author(s)

Po-Wei Chen, Han-Ming Wu

See Also

int_mean int_var int_cov int_cor

Examples

library(HistDAWass)
x <- HistDAWass::BLOOD
hist_mean(x, var_name = "Cholesterol", method = "BG")
hist_mean(x, var_name = "Cholesterol", method = "BD")
hist_var(x, var_name = "Cholesterol", method = "BG")
hist_var(x, var_name = "Cholesterol", method = "BD")
hist_cov(x, var_name1 = "Cholesterol", var_name2 = "Hemoglobin", method = "BG")
hist_cor(x, var_name1 = "Cholesterol", var_name2 = "Hemoglobin", method = "BG")

Description

Interval-valued data for 8 horse breeds (CES, CMA, PEN, TES, CEN, LES, PES, PAM) described by 6 variables: minimum/maximum weight, minimum/maximum height, cost of mares, cost of fillies.

Usage

data(horses.int)

Format

A symbolic data frame (symbolic_tbl) with 8 observations and 7 variables:

• Breed: Horse breed code (CES, CMA, PEN, TES, CEN, LES, PES, PAM; character).

• Minimum_Weight: Minimum weight range (kg, interval).

• Maximum_Weight: Maximum weight range (kg, interval).

• Minimum_Height: Minimum height range (cm, interval).

• Maximum_Height: Maximum height range (cm, interval).

• Mares_Cost: Cost of mares range (currency units, interval).

• Fillies_Cost: Cost of fillies range (currency units, interval).

Details

Extensively used in SDA for demonstrating divisive clustering, distance computation, hierarchy/pyramid construction, and complete objects.

Metadata

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis. Wiley. Table 7.14.

Examples

data(horses.int)

Description

Histogram-valued cost distributions for 15 hospitals. Each observation is a hospital with a 10-bin histogram of patient costs.

Usage

data(hospital.hist)

Format

A data frame with 15 observations and 1 histogram-valued variable:

• cost: Histogram-valued cost distribution (currency units).

Row names are H1 through H15.

Metadata

Source

Billard, L. and Diday, E. (2006), Table 3.12.

References

Billard, L. and Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining. Wiley, Chichester. Table 3.12.

Examples

data(hospital.hist)

Description

Distribution-valued dataset of 12 counties with 3 categorical probability distribution variables describing household fuel type, number of rooms, and household income brackets.

Usage

data(household_characteristics.distr)

Format

A data frame with 12 observations (counties) and 3 distribution-valued variables:

• fuel_type: Distribution over fuel types (gas, electric, oil, wood, none).

• rooms: Distribution over room counts ({1,2}, {3,4,5}, {>=6}).

• household_income: Distribution over income brackets (<10, [10,25), [25,50), [50,75), [75,100), [100,150), [150,200), >=200).

Row names are County_1 through County_12.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 6-1.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 6-1.

Examples

data(household_characteristics.distr)

Description

Daily high and low values of the Brazilian IBOVESPA stock market index from January 3, 2000 to December 28, 2012 (3216 trading days). This dataset matches the period used by Maciel, Ballini and Gomide (2016) for evolving granular analytics for interval time series forecasting.

Usage

data(ibovespa.its)

Format

A data frame with 3216 observations and 3 variables:

• date: Trading date (Date class).

• low: Daily low value of the IBOVESPA index.

• high: Daily high value of the IBOVESPA index.

Details

The IBOVESPA (Indice Bovespa) is the benchmark index of the Brazilian stock exchange (B3, formerly BM&FBOVESPA). It tracks the performance of the most actively traded stocks on the Sao Paulo stock exchange. The 13-year span of this dataset covers multiple market regimes including the 2008 global financial crisis, making it suitable for evaluating forecasting models under diverse conditions.

Metadata

Source

Yahoo Finance, ticker ^BVSP. Downloaded via the quantmod package.

References

Maciel, L., Ballini, R. and Gomide, F. (2016). Evolving granular analytics for interval time series forecasting. Granular Computing, 1(4), 213–224.

Examples

data(ibovespa.its)
head(ibovespa.its)
plot(ibovespa.its$date, ibovespa.its$high, type = "l", col = "red",
     ylab = "Index Value", xlab = "Date",
     main = "IBOVESPA Daily High/Low (2000-2012)")
lines(ibovespa.its$date, ibovespa.its$low, col = "blue")
legend("topleft", c("High", "Low"), col = c("red", "blue"), lty = 1)

Description

Convert iGAP format to a 3-dimensional array [n, p, 2].

Usage

iGAP_to_ARRAY(data, location = NULL)

Arguments

Value

A numeric array of dimension [n, p, 2] with dimnames.

Examples

data(abalone.iGAP)
arr <- iGAP_to_ARRAY(abalone.iGAP, 1:7)
dim(arr)

Description

To convert iGAP format to MM format.

Usage

iGAP_to_MM(data, location = NULL)

Arguments

Value

Return a dataframe with the MM format.

Examples

data(abalone.iGAP)
abalone <- iGAP_to_MM(abalone.iGAP, 1:7)

Description

To convert iGAP format interval dataframe to RSDA format (symbolic_tbl).

Usage

iGAP_to_RSDA(data, location = NULL)

Arguments

Value

Return a symbolic_tbl dataframe with complex-encoded interval columns.

Examples

data(abalone.iGAP)
rsda <- iGAP_to_RSDA(abalone.iGAP, 1:7)

Description

Automatically detect the format of interval data and convert it to the target format.

Usage

int_convert_format(x, to = "MM", from = NULL, ...)

Arguments

Details

This function provides a unified interface for all interval format conversions. It automatically detects the source format (unless specified) and applies the appropriate conversion function.

Supported conversions:

• RSDA ??? MM, iGAP, ARRAY

• MM ??? iGAP, RSDA, ARRAY

• iGAP ??? MM, RSDA, ARRAY

• ARRAY ??? RSDA, MM, iGAP

• SODAS ??? MM, iGAP, ARRAY

Value

Interval data in the target format

Author(s)

Han-Ming Wu

See Also

int_detect_format int_list_conversions RSDA_to_MM RSDA_to_ARRAY MM_to_RSDA MM_to_ARRAY ARRAY_to_RSDA ARRAY_to_MM ARRAY_to_iGAP iGAP_to_MM iGAP_to_RSDA iGAP_to_ARRAY MM_to_iGAP

Examples

# Auto-detect and convert to MM
data(mushroom.int)
data_mm <- int_convert_format(mushroom.int, to = "MM")

# Explicitly specify source format
data(abalone.iGAP)
data_mm <- int_convert_format(abalone.iGAP, from = "iGAP", to = "MM")

# Convert MM to iGAP
data_igap <- int_convert_format(data_mm, to = "iGAP")

 # Convert multiple datasets to MM
datasets <- list(mushroom.int, abalone.int, car.int)
mm_datasets <- lapply(datasets, int_convert_format, to = "MM")

# Check what conversions are available
int_list_conversions()

Description

Automatically detect the format of interval data.

Usage

int_detect_format(x)

Arguments

Details

Detection rules:

• RSDA: has class "symbolic_tbl" and contains complex columns

• MM: data.frame with paired "_min" and "_max" columns

• iGAP: data.frame with columns containing comma-separated values (e.g., "1.2,3.4")

• ARRAY: a 3-dimensional array with dim[3] = 2 (min/max slices)

• SODAS: character string ending with ".xml" (file path)

• SDS: alias for SODAS

Value

A character string indicating the detected format: "RSDA", "MM", "iGAP", "ARRAY", "SODAS", or "unknown"

Examples

data(mushroom.int)
int_detect_format(mushroom.int)  # Should return "RSDA"

data(abalone.iGAP)
int_detect_format(abalone.iGAP)  # Should return "iGAP"

# ARRAY format
x <- array(1:24, dim = c(4, 3, 2))
int_detect_format(x)  # Should return "ARRAY"

Description

List all available format conversion functions.

Usage

int_list_conversions(from = NULL, to = NULL)

Arguments

Value

A data.frame showing available conversions

Examples

# List all conversions
int_list_conversions()

# List conversions from RSDA
int_list_conversions(from = "RSDA")

# List conversions to MM
int_list_conversions(to = "MM")

Description

Functions to compute various distance measures between interval-valued observations.

int_dist_all computes all available distance measures at once.

Usage

int_dist(x, method = "euclidean", gamma = 0.5, q = 1, p = 2, ...)

int_dist_matrix(x, method = "euclidean", gamma = 0.5, q = 1, p = 2, ...)

int_pairwise_dist(x, var_name1, var_name2, method = "euclidean", ...)

int_dist_all(x, gamma = 0.5, q = 1)

Arguments

Details

Available distance methods:

• GD: Gowda-Diday distance (Gowda & Diday, 1991)

• IY: Ichino-Yaguchi distance (Ichino, 1988)

• L1: L1 (midpoint Manhattan) distance

• L2: L2 (Euclidean midpoint) distance

• CB: City-Block distance (Souza & de Carvalho, 2004)

• HD: Hausdorff distance (Chavent & Lechevallier, 2002)

• EHD: Euclidean Hausdorff distance

• nEHD: Normalized Euclidean Hausdorff distance

• snEHD: Span Normalized Euclidean Hausdorff distance

• TD: Tran-Duckstein distance (Tran & Duckstein, 2002)

• WD: L2-Wasserstein distance (Verde & Irpino, 2008)

• euclidean: Euclidean distance on interval centers (same as L2)

• hausdorff: Hausdorff distance (same as HD)

• manhattan: Manhattan distance (same as L1)

• city_block: City-block distance (same as CB)

• minkowski: Minkowski distance with parameter p

• wasserstein: Wasserstein distance (same as WD)

• ichino: Ichino-Yaguchi distance (simplified version)

• de_carvalho: De Carvalho distance

Value

A distance matrix (class 'dist') or numeric vector

Author(s)

Han-Ming Wu

References

Gowda, K. C., & Diday, E. (1991). Symbolic clustering using a new dissimilarity measure. Pattern Recognition, 24(6), 567-578.

Ichino, M. (1988). General metrics for mixed features. Systems and Computers in Japan, 19(2), 37-50.

Chavent, M., & Lechevallier, Y. (2002). Dynamical clustering of interval data. In Classification, Clustering and Data Analysis (pp. 53-60). Springer.

Tran, L., & Duckstein, L. (2002). Comparison of fuzzy numbers using a fuzzy distance measure. Fuzzy Sets and Systems, 130, 331-341.

Verde, R., & Irpino, A. (2008). A new interval data distance based on the Wasserstein metric.

Kao, C.-H. et al. (2014). Exploratory data analysis of interval-valued symbolic data with matrix visualization. CSDA, 79, 14-29.

See Also

int_dist_matrix int_dist_all int_pairwise_dist

Examples

# Using symbolic_tbl format
data(mushroom.int)
d1 <- int_dist(mushroom.int[, 3:4], method = "euclidean")
d2 <- int_dist(mushroom.int[, 3:4], method = "hausdorff")
d3 <- int_dist(mushroom.int[, 3:4], method = "GD")

# Using array format: 4 concepts, 3 variables
x <- array(NA, dim = c(4, 3, 2))
x[,,1] <- matrix(c(1,2,3,4, 5,6,7,8, 9,10,11,12), nrow=4)
x[,,2] <- matrix(c(3,5,6,7, 8,9,10,12, 13,15,16,18), nrow=4)
d4 <- int_dist(x, method = "snEHD")
d5 <- int_dist(x, method = "IY", gamma = 0.3)

Description

Functions to compute geometric characteristics of interval-valued data.

Usage

int_width(x, var_name, ...)

int_radius(x, var_name, ...)

int_center(x, var_name, ...)

int_overlap(x, var_name1, var_name2, ...)

int_containment(x, var_name1, var_name2, ...)

int_midrange(x, var_name, ...)

Arguments

Details

These functions compute basic geometric properties:

• int_width: Width of each interval (upper - lower)

• int_radius: Radius of each interval (width / 2)

• int_center: Center point of each interval ((lower + upper) / 2)

• int_overlap: Overlap measure between two interval variables

• int_containment: Check if one interval contains another

• int_midrange: Half-range of each interval ((upper - lower) / 2)

Value

A numeric matrix or value

Author(s)

Han-Ming Wu

See Also

int_width int_radius int_center int_overlap

Examples

data(mushroom.int)

# Calculate interval widths
int_width(mushroom.int, var_name = "Pileus.Cap.Width")
int_width(mushroom.int, var_name = 2:3)

# Calculate interval radius
int_radius(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"))

# Get interval centers
int_center(mushroom.int, var_name = 2:4)

# Measure overlap between two variables
int_overlap(mushroom.int, "Pileus.Cap.Width", "Stipe.Length")

# Check containment
int_containment(mushroom.int, "Pileus.Cap.Width", "Stipe.Length")

# Calculate midrange
int_midrange(mushroom.int, var_name = 2:3)

Description

Functions to compute position and scale statistics for interval-valued data.

Usage

int_median(x, var_name, method = "CM", ...)

int_quantile(x, var_name, probs = c(0.25, 0.5, 0.75), method = "CM", ...)

int_range(x, var_name, method = "CM", ...)

int_iqr(x, var_name, method = "CM", ...)

int_mad(x, var_name, method = "CM", ...)

int_mode(x, var_name, method = "CM", breaks = 30, ...)

Arguments

Details

These functions provide position and scale measures:

• int_median: Median of interval data

• int_quantile: Quantiles of interval data

• int_range: Range (max - min) of interval data

• int_iqr: Interquartile range (Q3 - Q1)

• int_mad: Median absolute deviation

• int_mode: Mode of interval data (estimated via histogram)

Value

A numeric matrix or value

Author(s)

Han-Ming Wu

See Also

int_mean int_var int_median int_quantile

Examples

data(mushroom.int)

# Calculate median
int_median(mushroom.int, var_name = "Pileus.Cap.Width")
int_median(mushroom.int, var_name = 2:3, method = c("CM", "EJD"))

# Calculate quantiles
int_quantile(mushroom.int, var_name = 2, probs = c(0.25, 0.5, 0.75))

# Calculate interquartile range
int_iqr(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"))

# Calculate range
int_range(mushroom.int, var_name = "Pileus.Cap.Width")

# Calculate MAD
int_mad(mushroom.int, var_name = 2:3, method = "CM")

# Estimate mode
int_mode(mushroom.int, var_name = "Stipe.Length", method = "CM")

Description

Functions to compute robust statistics for interval-valued data.

Usage

int_trimmed_mean(x, var_name, trim = 0.1, method = "CM", ...)

int_winsorized_mean(x, var_name, trim = 0.1, method = "CM", ...)

int_trimmed_var(x, var_name, trim = 0.1, method = "CM", ...)

int_winsorized_var(x, var_name, trim = 0.1, method = "CM", ...)

Arguments

Details

These functions provide robust alternatives to standard statistics:

• int_trimmed_mean: Mean after trimming extreme values

• int_winsorized_mean: Mean after winsorizing extreme values

• int_trimmed_var: Variance after trimming extreme values

• int_winsorized_var: Variance after winsorizing extreme values

Trimming vs Winsorizing:

• Trimming: Remove extreme values

• Winsorizing: Replace extreme values with less extreme values

Value

A numeric matrix

Author(s)

Han-Ming Wu

See Also

int_mean int_var int_trimmed_mean

Examples

data(mushroom.int)

# Trimmed mean (10% from each end)
int_trimmed_mean(mushroom.int, var_name = "Pileus.Cap.Width", trim = 0.1)

# Winsorized mean
int_winsorized_mean(mushroom.int, var_name = 2:3, trim = 0.05, method = "CM")

# Trimmed variance
int_trimmed_var(mushroom.int, var_name = c("Stipe.Length"), trim = 0.1)

Description

Functions to compute shape statistics (skewness, kurtosis) for interval-valued data.

Usage

int_skewness(x, var_name, method = "CM", ...)

int_kurtosis(x, var_name, method = "CM", ...)

int_symmetry(x, var_name, method = "CM", ...)

int_tailedness(x, var_name, method = "CM", ...)

Arguments

Details

These functions measure distribution shape:

• int_skewness: Measure of asymmetry (skewness)

• int_kurtosis: Measure of tail heaviness (kurtosis)

• int_symmetry: Symmetry coefficient

• int_tailedness: Tailedness measure (alias for excess kurtosis)

Skewness interpretation:

• = 0: Symmetric distribution

• > 0: Right-skewed (positive skew)

• < 0: Left-skewed (negative skew)

Kurtosis interpretation (excess kurtosis):

• = 0: Normal distribution (mesokurtic)

• > 0: Heavy tails (leptokurtic)

• < 0: Light tails (platykurtic)

Value

A numeric matrix

Author(s)

Han-Ming Wu

See Also

int_mean int_var int_skewness int_kurtosis

Examples

data(mushroom.int)

# Calculate skewness
int_skewness(mushroom.int, var_name = "Pileus.Cap.Width")
int_skewness(mushroom.int, var_name = 2:3, method = c("CM", "EJD"))

# Calculate kurtosis
int_kurtosis(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"))

# Check symmetry
int_symmetry(mushroom.int, var_name = 2:4, method = "CM")

# Check tailedness
int_tailedness(mushroom.int, var_name = "Pileus.Cap.Width", method = "CM")

Description

Functions to compute similarity measures between interval-valued observations.

Usage

int_jaccard(x, var_name1, var_name2, ...)

int_dice(x, var_name1, var_name2, ...)

int_cosine(x, var_name1, var_name2, ...)

int_overlap_coefficient(x, var_name1, var_name2, ...)

int_tanimoto(x, var_name1, var_name2, ...)

int_similarity_matrix(x, method = "jaccard", ...)

Arguments

Details

These functions compute various similarity measures:

• int_jaccard: Jaccard similarity coefficient

• int_dice: Dice similarity coefficient

• int_cosine: Cosine similarity

• int_overlap_coefficient: Overlap coefficient

• int_tanimoto: Tanimoto coefficient (generalized Jaccard)

• int_similarity_matrix: Pairwise similarity matrix across all observations

All similarity measures range from 0 (no similarity) to 1 (perfect similarity).

Value

A numeric matrix or value

Author(s)

Han-Ming Wu

See Also

int_dist int_cor int_jaccard

Examples

data(mushroom.int)

# Jaccard similarity
int_jaccard(mushroom.int, "Pileus.Cap.Width", "Stipe.Length")

# Dice coefficient
int_dice(mushroom.int, 2, 3)

# Cosine similarity
int_cosine(mushroom.int, 
           var_name1 = c("Pileus.Cap.Width"), 
           var_name2 = c("Stipe.Length", "Stipe.Thickness"))

# Overlap coefficient
int_overlap_coefficient(mushroom.int, 2, 3:4)

# Tanimoto coefficient
int_tanimoto(mushroom.int, "Pileus.Cap.Width", "Stipe.Length")

# Similarity matrix across all observations
int_similarity_matrix(mushroom.int, method = "jaccard")

Description

Functions to compute the mean, variance, covariance, and correlation of interval-valued data.

Usage

int_mean(x, var_name, method = "CM", ...)

int_var(x, var_name, method = "CM", ...)

int_cov(x, var_name1, var_name2, method = "CM", ...)

int_cor(x, var_name1, var_name2, method = "CM", ...)

Arguments

Details

Available methods (applicable to all four functions):

• CM: Center Method — uses midpoints (a + b) / 2

• VM: Vertices Method — uses all 2^p vertex combinations

• QM: Quantiles Method — uses equally spaced quantile points

• SE: Set Expansion — uses endpoints only (quantiles with m = 1)

• FV: Fitted Values — uses linear regression fitted values

• EJD: Empirical Joint Distribution

• GQ: Symbolic Covariance method (Billard and Diday, 2006)

• SPT: Total Sum of Products (Billard, 2008)

Value

A numeric matrix for int_mean and int_var (methods x variables); a named list of covariance/correlation matrices for int_cov and int_cor (one matrix per method).

Author(s)

Han-Ming Wu

See Also

int_mean int_var int_cov int_cor

Examples

data(mushroom.int)
int_mean(mushroom.int, var_name = "Pileus.Cap.Width")
int_mean(mushroom.int, var_name = 2:3)

var_name <- c("Stipe.Length", "Stipe.Thickness")
method <- c("CM", "FV", "EJD")
int_mean(mushroom.int, var_name, method)
int_var(mushroom.int, var_name, method)

var_name1 <- "Pileus.Cap.Width"
var_name2 <- c("Stipe.Length", "Stipe.Thickness")
method <- c("CM", "VM", "EJD", "GQ", "SPT")
int_cov(mushroom.int, var_name1, var_name2, method)
int_cor(mushroom.int, var_name1, var_name2, method)

Description

Functions to compute uncertainty and variability measures for interval-valued data.

Usage

int_entropy(x, var_name, method = "CM", base = 2, ...)

int_cv(x, var_name, method = "CM", ...)

int_dispersion(x, var_name, method = "CM", ...)

int_imprecision(x, var_name, ...)

int_granularity(x, var_name, ...)

int_uniformity(x, var_name, ...)

int_information_content(x, var_name, method = "CM", ...)

Arguments

Details

These functions measure uncertainty and variability:

• int_entropy: Shannon entropy (information content)

• int_cv: Coefficient of variation (CV = SD / Mean)

• int_dispersion: General dispersion index

• int_imprecision: Imprecision based on interval width

• int_granularity: Variability in interval sizes

• int_uniformity: Uniformity of interval widths (inverse of granularity)

• int_information_content: Normalized entropy (entropy / log2(n))

Value

A numeric matrix or value

Author(s)

Han-Ming Wu

See Also

int_var int_entropy int_cv

Examples

data(mushroom.int)

# Calculate entropy
int_entropy(mushroom.int, var_name = "Pileus.Cap.Width")

# Coefficient of variation
int_cv(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"), method = c("CM", "EJD"))

# Measure imprecision
int_imprecision(mushroom.int, var_name = c("Stipe.Length", "Stipe.Thickness"))

# Dispersion index
int_dispersion(mushroom.int, var_name = "Pileus.Cap.Width", method = "CM")

# Check data granularity
int_granularity(mushroom.int, var_name = 2:4)

# Check uniformity
int_uniformity(mushroom.int, var_name = 2:3)

# Information content
int_information_content(mushroom.int, var_name = "Stipe.Length", method = "CM")

Description

Histogram-valued dataset of 3 iris species (Versicolor, Virginica, Setosa) with 4 histogram-valued morphological variables and a species label. Each histogram describes the distribution of measurements within a species.

Usage

data(iris_species.hist)

Format

A data frame with 3 observations and 5 variables:

• species: Species name (factor: Versicolor, Virginica, Setosa).

• sepal_width: Histogram-valued sepal width distribution.

• sepal_length: Histogram-valued sepal length distribution.

• petal_width: Histogram-valued petal width distribution.

• petal_length: Histogram-valued petal length distribution.

Row names are species names.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 4-10.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 4-10.

Examples

data(iris_species.hist)

Description

Interval-valued version of the classic iris dataset, aggregated from Fisher's iris data into 30 interval observations across 3 species (Setosa, Versicolor, Virginica). Each observation represents a group of flowers with ranges for sepal and petal measurements.

Usage

data(iris.int)

Format

A data frame with 30 observations and 5 variables:

• sepal_length: Sepal length range (cm).

• sepal_width: Sepal width range (cm).

• petal_length: Petal length range (cm).

• petal_width: Petal width range (cm).

• class: Species (Setosa, Versicolor, Virginica).

Metadata

Source

https://github.com/Natandradesa/Kernel-Clustering-for-Interval-Data

References

Andrade, N. A., de Carvalho, F. A. T. and Pimentel, B. A. (2025). Kernel clustering with automatic variable weighting for interval data. Neurocomputing, 617, 128954.

Examples

data(iris.int)

Description

Monthly interval-valued wind speed data at 5 meteorological stations in Ireland from January 1961 to December 1978 (216 months). For each month and station, the interval is defined as [minimum daily average wind speed, maximum daily average wind speed] across all days in that month.

Usage

data(irish_wind.its)

Format

A data frame with 216 observations and 11 columns (5 interval variables in _l/_u Min-Max pairs, plus a date):

• date: First day of the month (Date class).

• BIR_l, BIR_u: Monthly [min, max] daily wind speed at Birr (knots).

• DUB_l, DUB_u: Monthly [min, max] daily wind speed at Dublin Airport (knots).

• KIL_l, KIL_u: Monthly [min, max] daily wind speed at Kilkenny (knots).

• SHA_l, SHA_u: Monthly [min, max] daily wind speed at Shannon Airport (knots).

• VAL_l, VAL_u: Monthly [min, max] daily wind speed at Valentia Observatory (knots).

Details

The original data contains daily average wind speeds (in knots) at 12 synoptic meteorological stations in the Republic of Ireland, collected by the Irish Meteorological Service. This is the classic Haslett and Raftery (1989) dataset, one of the most widely used benchmarks in spatial statistics. Following the approach of Teles and Brito (2015), the raw daily data is aggregated to monthly intervals for 5 selected stations: Birr (BIR), Dublin Airport (DUB), Kilkenny (KIL), Shannon Airport (SHA), and Valentia Observatory (VAL). Each monthly interval captures the range of daily wind variability within that month.

Metadata

Source

Derived from the wind dataset in the gstat R package (originally from Haslett and Raftery, 1989). Daily data aggregated to monthly intervals.

References

Haslett, J. and Raftery, A. E. (1989). Space-time modelling with long-memory dependence: Assessing Ireland's wind power resource. Journal of the Royal Statistical Society, Series C (Applied Statistics), 38(1), 1–50.

Teles, P. and Brito, P. (2015). Modeling interval time series with space-time processes. Communications in Statistics – Theory and Methods, 44(17), 3599–3619.

Examples

data(irish_wind.its)
head(irish_wind.its)
# Plot Valentia Observatory wind speed interval
plot(irish_wind.its$date, irish_wind.its$VAL_u, type = "l", col = "red",
     ylab = "Wind speed (knots)", xlab = "Date",
     main = "Valentia Observatory Monthly Wind Speed Interval")
lines(irish_wind.its$date, irish_wind.its$VAL_l, col = "blue")
legend("topright", c("Max", "Min"), col = c("red", "blue"), lty = 1)

Description

Mixed symbolic dataset of 10 jogger groups with one interval-valued variable (pulse rate) and one histogram-valued variable (running time distribution).

Usage

data(joggers.mix)

Format

A symbolic data frame (symbolic_tbl) with 10 observations (jogger groups) and 2 variables:

• pulse_rate: Interval-valued resting pulse rate range (bpm).

• running_time: Histogram-valued distribution of running times (minutes).

Row names are Group_1 through Group_10.

Metadata

Source

Billard, L. and Diday, E. (2020), Table 2-5.

References

Billard, L. and Diday, E. (2020). Clustering Methodology for Symbolic Data. Wiley, Chichester. Table 2-5.

Examples

data(joggers.mix)

Description

Interval-valued ratings from Judge 1 for 6 regions on 4 variables. From a study of generalized principal component analysis for interval-valued data (GPCSIV).

Usage

data(judge1.int)

Format

A symbolic data frame (symbolic_tbl) with 6 observations and 4 interval-valued variables (V1–V4).

Metadata