DistanceMatrix: Pairwise distance between pairs of objects

In Mthrun/Distances: Functions For Different Distance Measures

Description

computes the distance between objects in the data matrix, X, using the method specified by method

Usage

DistanceMatrix(X, method, dim, outputisvector)

Arguments

X	data matrix [1:n,1:d], n cases d variables
method	Optional, method specified by distance string: 'euclidean','sqEuclidean','binary','cityblock', 'maximum','canberra','cosine','chebychev','jaccard', 'mahalanobis','minkowski','manhattan','braycur','cosine'
dim	Optional: Dimension of X. If method="minkowski", choose p
outputisvector	Optional: should the output be converted to a vector

Details

'binary' (aka asymmetric binary): The vectors are regarded as binary bits, so non-zero elements are 'on' and zero elements are 'off'. The distance is the proportion of bits in which only one is on amongst those in which at least one is on.

'cityblock'==manhattan

'maximum': Maximum distance between two components of x and y (supremum norm)

'cosine' calculates a similarity matrix sim between all column vectors of a matrix x. This matrix might be a document-term matrix, so columns would be expected to be documents and rows to be terms. the distances is than defined with D=max(sim)-sim

'jaccard' Jaccard index is computed as 2B/(1+B), where B is Bray-Curtis dissimilarity: the number of items which occur in both elements divided by the total number of items in the elements (Sneath, 1957). This measure is often also called: binary, asymmetric binary, etc.

'mahalanobis' 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 = (x_i - x_j)' S^-1 (x_i - x_j)

'minkowski':The p norm, the pth root of the sum of the pth powers of the differences of the components.

'manhattan': Absolute distance between the two vectors (1 norm aka L_1).

'chebychev'=max(abs(x-y)),

'canberra'=sum abs(x-y)/sum(abs(x)-abs(y)), Terms with zero numerator and denominator are omitted from the sum and treated as if the values were missing. This is intended for non-negative values (e.g., counts): taking the absolute value of the denominator is a 1998 R modification to avoid negative distances.

'braycur'=sum abs(x -y)/abs(x+y)

'pearson' 1 - r if r>1 and 1 otherwise. r is Pearson's correlation coefficient.

'cosine' s. wiki fuer simuilarity umrchnung: max(S)-S(i,j)

Value

Dmatrix

[1:n,1:n] Distance Marix: Pairwise distance between pairs of objects

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.

Examples

	example 
	## Not run: Dmarix = DistanceMatrix(X,method=euclidean) 
	

Mthrun/Distances documentation built on Feb. 4, 2020, 8:39 p.m.