binaryDistance {Mercator}

Binary Distance Definitions Across Methods

Description

The binaryDistance function defines various similarity or distance measures between binary vectors, which represent the first step in the algorithm underlying the Mercator visualizations.

Usage

binaryDistance(X, metric)

Arguments

X

An object of class matrix.

metric

An object of class character limited to the names of 10 selected distance metrics: jaccard, sokalMichener, hamming, russellRao, pearson, goodmanKruskal, manhattan, canberra, binary, or euclid.

Details

Similarity or difference between binary vectors can be calculated using a variety of distance measures. In the main reference (below), Choi and colleagues reviewed 76 different measures of similarity of distance between binary vectors. They also produced a hierarchical clustering of these measures, based on the correlation between their distance values on multiple simulated data sets. For metrics that are highly similar, we chose a single representative.

Cluster 1, represented by the jaccard distance, contains Dice & Sorenson, Ochiai, Kulcyznski, Bray & Curtis, Baroni-Urbani & Buser, and Jaccard.

Cluster 2, represented by the sokalMichener distance, contains Sokal & Sneath, Gilbert & Wells, Gower & Legendre, Pearson & Heron, Hamming, and Sokal & Michener. Also within this cluster are 4 distances represented independently within this function: hamming, manhattan, canberra, and euclidean distances

Cluster 3, represented by the russellRao distance, contains Driver & Kroeber, Forbes, Fossum, and Russell & Rao.

The remaining metrics are more isolated, without strong clustering. We considered a few examples, including the Pearson distance (pearson) and the Goodman & Kruskal distance (goodmanKruskal). The binary distance is also included.

Value

Returns an object of class dist corresponding to the distance metric provided.

Note

Although the distance metrics provided in the binaryDistance function are explicitly offered for use on matrices of binary vectors, some metrics may return useful distances when applied to non-binary matrices.

Author(s)

Kevin R. Coombes <[e-mail]>, Caitlin E. Coombes

References

Choi SS, Cha SH, Tappert CC, A Survey of Binary Similarity and Distance Measures. Systemics, Cybernetics, and Informatics. 2010; 8(1):43-48.

See Also

This set includes all of the metrics from the dist function.

Examples

my.matrix <- matrix(rbinom(50*100, 1, 0.15), ncol=50)
my.dist <- binaryDistance(my.matrix, "jaccard")