Package {BIDistances}

Type:	Package
Title:	Bioinformatic Distances
Version:	0.1.5
Date:	2026-08-03
Maintainer:	Michael Thrun <m.thrun@gmx.net>
Description:	A collection of high-performance methods for computing distance measures for bioinformatics data. The weighted Euclidean distance can be computed using 'OpenCL' on a GPU or a parallelized implementation on a CPU. Other important distance measures for bioinformatics data are provided by the R package 'parallelDist'. A specialized distance measure for the Gene Ontology is also available.
Depends:	R (≥ 3.5.0)
Imports:	Rcpp (≥ 1.0.8), RcppParallel, parallelDist, parallel, DataVisualizations, diptest, e1071, vegan, methods, pracma, ggplot2
Suggests:	knitr, rmarkdown, remotes, sphet, OpenCL, transport, ineq, memshare, philentropy (≥ 0.10.0), manydist (≥ 0.5.0)
LinkingTo:	Rcpp, RcppParallel, RcppArmadillo
NeedsCompilation:	yes
SystemRequirements:	GNU make, OpenCL library (optional, for GPU acceleration), pandoc (>=1.12.3, needed for vignettes)
License:	GPL-3
LazyLoad:	yes
LazyData:	TRUE
Encoding:	UTF-8
VignetteBuilder:	knitr
BugReports:	https://github.com/Mthrun/BIDistances/issues
Packaged:	2026-08-03 15:14:20 UTC; mct_l
Author:	Quirin Stier [aut, rev, ctb], Michael Thrun [aut, cre], Luca Brinkmann [ctb]
Repository:	CRAN
Date/Publication:	2026-08-04 08:40:20 UTC

Cosine Distance

Description

Calculates the cosine distance

Usage

CosinusDistance(Data)

Arguments

Details

https://en.wikipedia.org/wiki/Cosine_similarity

Value

Note

The cosine distance is calculated by calculating the cosine similarity d(i,j)=\max{s}-s(i,j), where s is the cosine similarity and the d the cosine distance.

Author(s)

Michael Thrun

References

http://stats.stackexchange.com/questions/31565/is-there-an-r-function-that-will-compute-the-cosine-dissimilarity-matrix

Examples

data(Hepta)
distMatrix = CosinusDistance(Hepta$Data)

Distances from One Point to All Rows of a Matrix

Description

Calculates the distance from a numeric vector to every row of a numeric matrix and returns the indices of the nearest rows.

Usage

Dist2All(
  X,
  Data,
  SelectFeatures,
  method = "euclidean",
  p = 2,
  knn = 1,
  GPU = FALSE
)

Arguments

Value

A list with:

Author(s)

Michael Thrun

Examples

data(Hepta)
result <- Dist2All(Hepta$Data[1, ], Hepta$Data)
stopifnot(length(result$distToAll) == nrow(Hepta$Data))

Distance Distribution

Description

Calculates the distribution of the distances between the data points

Usage

DistanceDistributions(Data, DistanceMethods=c('bhjattacharyya', 'bray',
                                                       'canberra', 'chord',
                                                       'divergence', 'euclidean',
                                                       'minkowski', 'geodesic',
                                                       'hellinger', 'kullback',
                                                       'manhattan', 'maximum',
                                                       'soergel', 'wave',
                                                       'whittaker'),
                               CosineNonParallel = TRUE, CorrelationDist = TRUE,
                               Mahalanobis = FALSE, Podani = FALSE,
                               PlotIt = FALSE, PlotSampleSize = 5e3)

Arguments

Value

List with elements

Author(s)

Michael Thrun

Pairwise Distance, Dissimilarity, or Similarity Matrix

Description

Computes pairwise values between the rows of X. BIDistances-specific methods are retained, parallelDist is tried first for ordinary numeric methods, and philentropy is used only when parallelDist reports that the method name is invalid. Mixed-data calculations use an explicit manydist backend.

Usage

DistanceMatrix(
  X,
  method = "euclidean",
  dim = 2,
  outputisvector = FALSE,
  GPU = FALSE,
  ...
)

Arguments

Details

The aliases "cityblock" and "manhatten" map to "manhattan"; "chebychev" and "chebyshev" map to "maximum"; "braycur" and "braycurtis" map to "bray"; and "squared_euclidean" maps to "sqeuclidean".

Plain overlapping names such as "cosine", "hellinger", and "tanimoto" use parallelDist. Plain "gower" uses the numeric philentropy definition; mixed-data Gower is requested with method = "manydist", preset = "gower".

The philentropy registry includes both distances and similarities. Values are returned unchanged. Some methods are asymmetric, and many are intended for non-negative probability or count vectors.

Value

A numeric square matrix with one row and column per row of X, or a numeric vector containing the upper triangle when outputisvector = TRUE.

Rules for additional arguments

Every argument in ... must have a unique, non-empty name. x and method are controlled by DistanceMatrix() and are rejected when supplied through ....

Backend selection happens before the additional arguments are interpreted. In particular, a method name implemented by both parallelDist and philentropy selects parallelDist. Supplying a philentropy-only argument with such a name does not force the philentropy backend; it normally produces a parallelDist argument error. Use threads for parallelDist and num.threads for philentropy; the two names are not interchangeable.

Additional arguments for the GPU backend

When GPU = TRUE and the method is "euclidean" or "sqeuclidean", the following names may be supplied through ...: Weights, Mem, ctx, backend, and threads. They have the meanings documented in EuclideanDistances_GPU. All other names are rejected before dispatch. The square-Euclidean route squares the matrix returned by that function.

Additional arguments for parallelDist

The following arguments apply when the selected method is implemented by parallelDist::parDist():

threads

Number of CPU threads. With NULL, parallelDist uses the maximum number available on the system.

p

Positive Minkowski exponent, used only with method = "minkowski". When omitted, DistanceMatrix() supplies p = dim.

cov

Covariance matrix used only with method = "mahalanobis". When omitted, parallelDist estimates the covariance matrix from X.

inverted

Logical value used only with Mahalanobis distance. If true, cov is interpreted as an inverse covariance matrix.

window.size

Optional integer width of the Sakoe–Chiba window used only with method = "dtw".

norm.method

Optional DTW normalization. Supported values are "path.length", "n", and "n+m".

step.pattern

DTW step pattern. The backend default is "symmetric1". See parDist for the complete set of supported patterns.

func

An external pointer to a compiled C++ distance function, used only with method = "custom". See parDist for the required function signature and a compilation example.

diag, upper

Printing flags attached to the temporary dist object. Because DistanceMatrix() immediately converts that object to a full matrix, these arguments do not change the returned value and should normally be omitted.

The CPU routes method = "sqeuclidean" and method = "fagerdissimilarity" also use this backend. Applicable arguments such as threads are therefore forwarded to the underlying Euclidean or Fager calculation.

All other method-specific semantics, including data-domain restrictions, are those of parallelDist::parDist().

Additional arguments for philentropy

These arguments apply only when parallelDist rejects the method name and the name is present in philentropy::getDistMethods(). For methods that compare probability distributions, rows of X should be non-negative probability vectors, or non-negative count vectors together with est.prob = "empirical".

test.na

Logical value controlling a second missing-value check inside philentropy. If omitted, DistanceMatrix() sets it to FALSE, because X has already been checked.

unit

Logarithm used by log-dependent methods. Valid values are "log" for the natural logarithm, "log2", and "log10". The backend default is "log".

epsilon

Small positive replacement used by applicable methods in otherwise undefined zero-denominator cases. The backend default is 1e-5. Results from zero-heavy distributions can be sensitive to this value, so it should be chosen for the scale and sparsity of the data.

est.prob

Probability estimation from row-wise counts. The default NULL uses rows as supplied. "empirical" divides each row by its row sum before the distance is calculated.

mute.message

Logical value that suppresses messages from philentropy::distance(). If omitted, DistanceMatrix() sets it to TRUE.

num.threads

Number of worker threads used by philentropy. With NULL, the backend uses RCPP_PARALLEL_NUM_THREADS, or two threads when that environment variable is unset.

use.row.names

Controlled by the wrapper and always set to FALSE. The row names of X, when present, are restored on the final matrix.

as.dist.obj

Controlled by the wrapper and always set to FALSE, because DistanceMatrix() requires a full matrix from the backend.

diag, upper

These only control printing when as.dist.obj = TRUE. They therefore do not affect the matrix returned by DistanceMatrix() and should normally be omitted.

The p argument of philentropy::distance() is not normally reachable through this wrapper: "minkowski" is implemented by parallelDist and is therefore dispatched there first.

Additional arguments for manydist

These arguments apply only with method = "manydist" and are forwarded to manydist::mdist(). Character and logical predictor columns are converted to factors before dispatch.

preset

Predefined distance specification. The default is "custom". Current choices include "gower", "unbiased_dependent", "u_dep", "u_indep", "u_mix", "hl", "gudmm", "dkss", "mod_gower", and "euclidean". With a non-custom preset, the preset controls method_cat, method_num, commensurable, and interaction; values supplied for those arguments are ignored by manydist.

response

Optional response column for response-aware categorical dissimilarities. In this wrapper it must be supplied as a character column name, for example response = "class", because the contents of ... are evaluated before manydist::mdist() is called. manydist removes the response column from the predictor set.

method_cat

Categorical-variable dissimilarity used with preset = "custom". Common choices are "matching" and "tvd". Depending on the selected specification, this can be one method for all categorical variables or a method vector aligned with the categorical columns. Use manydist::all_dist_method_specs() to inspect the methods in the installed package.

method_num

Numerical preprocessing used with preset = "custom". Choices are "none" for no preprocessing, "std" for standard-deviation scaling, "range" for range scaling, "robust" for interquartile-range scaling, and "pc_scores" for principal-component score scaling. The default is "std".

commensurable

Logical value. When true and supported by the selected specification, variable-wise dissimilarities are scaled so that their average contributions to the overall dissimilarity are equal to one. The default is TRUE for the custom specification.

ncomp

Positive integer or NULL; number of principal components retained when method_num = "pc_scores". With NULL, all available components are used unless threshold is supplied and supported.

threshold

Numeric value between zero and one, or NULL; optional cumulative-variance threshold used with method_num = "pc_scores".

interaction

Logical value. If true, add an interaction-aware continuous–categorical component based on local predictive separability. The default is FALSE.

prop_nn

Proportion between zero and one giving the nearest-neighbour fraction used only when interaction = TRUE. The default is 0.1.

score

Interaction score used only when interaction = TRUE. Available values include "ba" for balanced accuracy and "logloss". The default is "ba".

decision

Decision rule used when interaction = TRUE and score = "ba". The default is "prior_corrected"; consult mdist for supported rules.

gower_average

Used only with preset = "gower". The default TRUE averages over active variables and matches the usual Gower scale. FALSE returns the sum of the variable-wise Gower contributions.

new_data

Not supported by DistanceMatrix(). Although manydist::mdist() can calculate rectangular new-data-to-training dissimilarities, this wrapper always returns a square within-X matrix.

The installed manydist documentation is authoritative for preset and method registries, which may grow in later releases.

Author(s)

Michael Thrun

References

Sneath, P. H. A. (1957) Some thoughts on bacterial classification. Journal of General Microbiology 17, pages 184-200.

Leydesdorff, L. (2005) Similarity Measures, Author Cocitation Analysis,and Information Theory. In: JASIST 56(7), pp.769-772.

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. Academic Press.

Borg, I. and Groenen, P. (1997) Modern Multidimensional Scaling. Theory and Applications. Springer.

Mahalanobis, P. C. (1936) On the generalized distance in statistics. Proceedings of The National Institute of Sciences of India, 12:49-55.

van de Velden, M., Iodice D’Enza, A., Markos, A., & Cavicchia, C. (2026). Unbiased Mixed-Variable Distance. Journal of Computational and Graphical Statistics, 1–12. DOI, 10.1080/10618600.2026.2680181

See Also

parDist, getDistMethods, distance, and mdist.

Examples

X <- rbind(a = c(1, 2, 3), b = c(2, 2, 4), c = c(4, 1, 2))
DistanceMatrix(X, method = "euclidean")
DistanceMatrix(X, method = "minkowski", p = 3)

# Method-specific parallelDist arguments
DistanceMatrix(X, method = "mahalanobis", cov = diag(ncol(X)))
DistanceMatrix(X, method = "dtw", window.size = 1,
               norm.method = "path.length")

if (requireNamespace("philentropy", quietly = TRUE)) {
  counts <- rbind(a = c(1, 4, 5), b = c(2, 3, 5), c = c(6, 2, 2))
  DistanceMatrix(
    counts,
    method = "jensen-shannon",
    est.prob = "empirical",
    unit = "log2",
    epsilon = 1e-8
  )
}

if (requireNamespace("manydist", quietly = TRUE)) {
  mixed <- data.frame(
    value = c(1, 3, 2),
    group = factor(c("a", "b", "a"))
  )
  DistanceMatrix(
    mixed,
    method = "manydist",
    preset = "gower",
    gower_average = TRUE
  )
  DistanceMatrix(
    mixed,
    method = "manydist",
    preset = "custom",
    method_cat = "matching",
    method_num = "robust",
    commensurable = TRUE
  )

  # In this wrapper, response must be a character column name:
  # DistanceMatrix(mixed_with_class, method = "manydist",
  #                preset = "custom", method_cat = "tvd",
  #                response = "class")
}

Weighted Euclidean Distances with an Optional OpenCL Backend

Description

Computes all pairwise weighted Euclidean distances between rows of a numeric matrix. An optional OpenCL backend can use an available accelerator; a CPU implementation is always available.

Usage

EuclideanDistances_GPU(
  Data,
  Weights,
  Mem = 2,
  OutputType = "mat",
  ctx = NULL,
  backend = c("auto", "opencl", "cpu"),
  threads = 2L
)

Arguments

Details

For rows x_i and x_j, the returned value is

\left(\sum_k w_k (x_{ik} - x_{jk})^2\right)^{1/2}.

The OpenCL package is suggested rather than imported, so BIDistances can be installed and checked on systems without OpenCL headers, drivers, or hardware. Depending on the memory budget, the OpenCL path uses a full-matrix, output-batched, or input-blocked implementation.

With precision = "best", OpenCL may use single precision on devices without double-precision support. Small numerical differences from the CPU result are therefore possible.

Value

A square numeric matrix, a dist object, or a full column-major numeric vector, according to OutputType.

Author(s)

Quirin Stier, Michael Thrun, Luca Brinkmann

See Also

calculateMemoryDemandGPU, DistanceMatrix, as.dist

Examples

Data <- as.matrix(iris[1:8, 1:4])
Weights <- c(1, 2, 0.5, 1)

D <- EuclideanDistances_GPU(
  Data,
  Weights,
  backend = "cpu",
  OutputType = "mat"
)
reference <- as.matrix(stats::dist(sweep(Data, 2, sqrt(Weights), "*")))
dimnames(reference) <- dimnames(D)
stopifnot(isTRUE(all.equal(D, reference)))

## Not run: 
## This block requires an installed OpenCL implementation and usable device.
Dgpu <- EuclideanDistances_GPU(
  Data,
  Weights,
  backend = "opencl",
  OutputType = "mat"
)
stopifnot(isTRUE(all.equal(Dgpu, reference, tolerance = 1e-5)))

## End(Not run)

Calculates fractional distances

Description

Calculates distance matrix, through \left( \sum_{i=1}^{n} |x_i - y_i|^p \right)^{1/p}

Usage

FractionalDistance(Data, p)

Arguments

Details

Values of p < 1 can be used, which can be useful for high-dimensional data, see references.

Value

Author(s)

Michael Thrun

References

Aggrawal, C. C., Hinneburg, A., Keim, D. (2001), On the Suprising Behavior of Distance Metrics in High Dimensional Space.

Examples

data(Hepta)
distMatrix = FractionalDistance(Hepta$Data, p = 1/2)

Gini Distance Between Features

Description

Computes a distance matrix between the columns of a data matrix based on differences in their Gini coefficients.

Usage

GiniDist(Data)

Arguments

Details

For each feature (column) in Data, the Gini coefficient is computed using the ineq package. The distance between two features i and j is defined as the absolute difference of their Gini coefficients:

d(i,j) = | Gini(x_i) - Gini(x_j) |

The result is returned as a symmetric distance matrix.

Value

A symmetric d \times d distance matrix of class dist.

Author(s)

Michael Thrun (December 2023)

See Also

ineq from the ineq package for computing Gini coefficients.

Examples

# Example with simulated data
set.seed(123)
X <- matrix(runif(50), nrow = 10, ncol = 5)
GiniDist(X)

Hearingloss data

Description

Hearingloss data, with Gene2GoTerm matrix.

Usage

data('Hearingloss_N109')

Details

FeatureMarix_Gene2Term contains the dataset, NCBI are the row names for the genes and GoTerm_Header contains the column names for the GoTerms. Size of data matrix is 109 with dimension 829.

Source

NCBI OtoGenome Test for Hearing Loss, accessed 24 June 2022.

References

GeneTestingRegistry (2018). OtoGenome Test for Hearing Loss Retrieved 2017

Examples

data(Hearingloss_N109)
str(Hearingloss_N109)

Hellinger4ConditionalPDF

Description

Hellinger4ConditionalPDF

Usage

Hellinger4ConditionalPDF(Data, Cls)

Arguments

Value

Matrix with index integer vector and a numeric vector containing hellinger distance between conditional probability density estimation for both classes of the binary classification vector.

Author(s)

Quirin Stier

Examples

Data = iris[1:100, 1:4]
Cls  = as.numeric(iris[1:100, 5])
Hellinger4ConditionalPDF(Data, Cls)

Hepta introduced in [Ultsch, 2003]

Description

Clearly defined clusters, different variances. Detailed description of dataset and its clustering challenge is provided in [Thrun/Ultsch, 2020].

Usage

data('Hepta')

Details

Size 212, Dimensions 3, stored in Hepta$Data

Classes 7, stored in Hepta$Cls

References

[Ultsch, 2003] Ultsch, A.: Maps for the visualization of high-dimensional data spaces, Proc. Workshop on Self organizing Maps (WSOM), pp. 225-230, Kyushu, Japan, 2003.

[Thrun/Ultsch, 2020] Thrun, M. C., & Ultsch, A.: Clustering Benchmark Datasets Exploiting the Fundamental Clustering Problems, Data in Brief, Vol. 30(C), pp. 105501, doi:10.1016/j.dib.2020.105501, 2020.

Examples

data(Hepta)
str(Hepta)

Kullback-Leibler divergence

Description

Kullback-Leibler divergence KLD of discrete distributions or their pdfs

Usage

Kullback_Leibler_div(P, Q, sym = 1, PDF = FALSE, Eps = 1/10000)

Arguments

Details

If P and Q are pdfs they have to have the same length and we assume that they have the same kernels.

NaN in the distributions are ignored. not defined for zero probabilities, replace with very small values.

Value

Author(s)

Michael Thrun

Pairwise Squared Generalized Mahalanobis Distances

Description

Function to calculate the squared generalized Mahalanobis distance between all pairs of rows in a data frame with respect to a covariance matrix. The element of the i-th row and j-th column of the distance matrix is defined as

D_{ij}^2 = (\bold{x}_i - \bold{x}_j)' \bold{\Sigma}^{-1} (\bold{x}_i - \bold{x}_j)

Usage

Mahalanobis(X, cov, inverted = FALSE)

Arguments

Value

Distances[1:n,1:n]

Note

copy of function in biotools package, because this packages doesnt work under mac os

Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

References

Mahalanobis, P. C. (1936) On the generalized distance in statistics. Proceedings of The National Institute of Sciences of India, 12:49-55.

See Also

dist

Examples

# Manly (2004, p.65-66)
x1 <- c(131.37, 132.37, 134.47, 135.50, 136.17)
x2 <- c(133.60, 132.70, 133.80, 132.30, 130.33)
x3 <- c(99.17, 99.07, 96.03, 94.53, 93.50)
x4 <- c(50.53, 50.23, 50.57, 51.97, 51.37)
x <- cbind(x1, x2, x3, x4)
Cov <- matrix(c(21.112,0.038,0.078,2.01, 0.038,23.486,5.2,2.844,
	0.078,5.2,24.18,1.134, 2.01,2.844,1.134,10.154), 4, 4)
Mahalanobis(x, Cov)

# End (not run)

Shared Neighbor Distance

Description

Calculates the Shared Neighbor Distance

Usage

SharedNeighborDistance(Data, k = 5, NThreads = NULL, ComputationInR = FALSE)

Arguments

Value

Author(s)

Quirin Stier

References

https://github.com/albert-espin/snn-clustering/blob/master/SNN/snn.py

Examples

data(Hepta)
distMatrix = SharedNeighborDistance(Hepta$Data, NThreads = 1, ComputationInR=TRUE)

Term frequency-inverse document frequency distance

Description

Computes the term frequency inverse document frequency (tfidf) distance for a FeatureMatrix_Gene2GoTerm. In case of genes with annotated GOterms from gene ontology genes can be interpreted as documents and GOterms as terms.

Usage

Tfidf_dist(FeatureMatrix_Gene2GoTerm, tf_fun = mean)

Arguments

Details

For the FeatureMatrix_Gene2GoTerm it is:
FeatureMatrix_Gene2GoTerm[i,j] > 0 iff GOterm j is relevant for gene i. The FeatureMatrix_Gene2GoTerm[i,j] > 1 if the specific gene is annotated by in a specific GO-Term with more than one evidence code FeatureMatrix_Gene2GoTerm[i,j] is the frequency of term js occurance in document i.

Value

List with

Author(s)

Michael Thrun

References

Stier, Q. and Thrun, M., C.: Deriving homogeneous subsets from gene sets by exploiting the Gene Ontology, Informatica, in review, 2023

Examples

data(Hearingloss_N109)
V = Tfidf_dist(Hearingloss_N109$FeatureMatrix_Gene2Term)
dist = V$dist
TfidfWeights = V$TfidfWeights

Calculate Toroidal Euclidean Distances

Description

Computes the Euclidean distances between one two-dimensional position and a collection of positions on a rectangular toroidal grid. A toroidal grid uses periodic boundary conditions, so positions near opposite grid edges may be close to one another.

Usage

ToroidDist2All(positionxy, AllPositions, Lines, Columns)

Arguments

Details

For each row of AllPositions, the function first calculates the absolute coordinate differences

d_x = |x_i - x|

and

d_y = |y_i - y|.

Periodic boundary conditions are then applied separately to both coordinates. The distances used by the implementation are

d_x^* = \min(d_x, \mathrm{Lines} - d_x + 1)

and

d_y^* = \min(d_y, \mathrm{Columns} - d_y + 1).

The resulting toroidal Euclidean distance is

D_i = \sqrt{(d_x^*)^2 + (d_y^*)^2}.

The computation is vectorized over the rows of AllPositions.

Coordinates should use the same coordinate system and indexing convention as the grid dimensions supplied through Lines and Columns. The function does not check whether coordinates lie within the stated grid dimensions.

Value

A numeric vector with one element for each row of AllPositions. The i-th element is the toroidal Euclidean distance between positionxy and row i of AllPositions.

Author(s)

Michael Thrun

See Also

dist for ordinary distance calculations.

Examples

## Distances to positions away from the grid boundaries
positionxy <- c(1, 1)
AllPositions <- rbind(
  c(2, 3),
  c(5, 2)
)

ToroidDist2All(
  positionxy = positionxy,
  AllPositions = AllPositions,
  Lines = 40,
  Columns = 80
)

## Positions on opposite sides of the grid can be close because
## distances may wrap around the grid boundaries
edgePositions <- rbind(
  c(40, 1),
  c(1, 80),
  c(40, 80)
)

ToroidDist2All(
  positionxy = c(1, 1),
  AllPositions = edgePositions,
  Lines = 40,
  Columns = 80
)

TransformSimilarity2MetricDistance

Description

TransformSimilarity2MetricDistance

Usage

TransformSimilarity2MetricDistance(Similarity)

Arguments

Value

Similarity

Author(s)

Michael Thrun

VariablePrecision

Description

Computes the variable precision

Usage

VariablePrecision(Variable)

Arguments

Value

matrix of distances, symmetric

Author(s)

Michael Thrun

Examples

data(Hepta)
distMat = VariablePrecision(as.matrix(iris[, 1]))

distMat = VariablePrecision(as.matrix(iris[, 1:4]))

Wasserstein Distance

Description

Computes the Wasserstein distance for a data matrix

Usage

WassersteinDist(Data, p = 1, InverseWeighting = FALSE)

Arguments

Details

Wasserstein distance, also known as Earth Mover’s Distance (EMD) is the distance between two probability distributions over a region D. The Wasserstein distance of order p is defined as the p-th root of the total cost incurred when transporting measure a to measure b in an optimal way, where the cost of transporting a unit of mass from x to y is given as the p-th power of the Euclidean distance.

It is claimed to be useful for distributions that do not align well with traditional measures like Euclidean distance.

Value

matrix of distances, symmetric

Author(s)

Michae Thrun

References

...

See Also

wasserstein1d

Examples

data(Hepta)
distMat=WassersteinDist(Hepta$Data)

Plan Device-Memory Batches for Weighted Euclidean Distances

Description

Selects one of three OpenCL execution layouts and calculates the corresponding batch sizes from the number of rows, number of columns, and a device-memory budget.

Usage

calculateMemoryDemandGPU(n, d, mem = 2)

Arguments

Details

The estimate conservatively uses eight bytes per input, weight, and output value.

Version 0

The complete input and output matrix fit in the budget.

Version 1

The complete input fits, while output columns are processed in batches.

Version 2

Two input blocks and their output block are processed at a time.

The calculation is a planning estimate. Device-specific limits, driver memory, and other allocations can still prevent an OpenCL allocation. With backend = "auto", EuclideanDistances_GPU() catches such failures and uses its CPU backend.

Value

A list with components:

Author(s)

Luca Brinkmann, with portability revisions by Michael Thrun

See Also

EuclideanDistances_GPU

Examples

info <- calculateMemoryDemandGPU(70000, 784, 6)

fastPdist

Description

calculates pairwise euclidean distances

Usage

fastPdist(X)

Arguments

Value

dist[1:n,1:n] distances

Author(s)

Michael Thrun

fastPdist

Description

calculates pairwise euclidean distances

Usage

fastPdistC(Ar,Br)

Arguments

Value

dist[1:n,1:n] distances

Author(s)

Felix Riede

Computes dissimilarity indices Jaccard

Description

The function computes dissimilarity indices Jaccard, which index is computed as 2B/(1+B), where B is Bray-Curtis dissimilarity

Usage

jaccard(X)

Arguments

Value

Kosinusdistanz der beiden Vektoren x,y

Author(s)

MT

Find Nearest Neighbors from a Distance Matrix

Description

For every point, finds the k nearest other points represented by a square distance matrix. The point itself is excluded explicitly rather than by assuming that the diagonal is the unique smallest value.

Usage

knneighborDistances(k, Distances)

Arguments

Details

Missing values are not accepted. Infinite distances are allowed. Equal finite or infinite distances are ordered by the point index, with the smaller index first.

Value

A list with two components:

Author(s)

Michael Thrun

Examples

Distances <- matrix(
  c(
    0, 1, 4, 1,
    1, 0, 2, 3,
    4, 2, 0, 5,
    1, 3, 5, 0
  ),
  nrow = 4,
  byrow = TRUE
)

knneighborDistances(2, Distances)

msmd

Description

msmd

Usage

msmd(Values1, Values2, ParameterC)

Arguments

Value

List with elements

Author(s)

Quirin Stier

Nearest

Description

returns the index of the nearest neighbour of a given data point.

Usage

nearest(Data, i, defined)

Arguments

Value

Author(s)

Michael Thrun, Raphael Paebst

Calculate toroid Euclidean Distances

Description

Calculate toroid Euclidean Distances

Usage

pdistToroid(X,Y,Lines,Columns,Points)

Arguments

Value

distance(s) between row(s) of x and y in MATHLBs pdist form

Author(s)

MT

twed

Description

twed

Usage

twed(Values1, Values2, Time1, Time2, Nu = 1, Lambda = 1, Degree = 2)

Arguments

Value

List with elements

Author(s)

Quirin Stier