mahalanobis.dist {flowMatch} | R Documentation

## Mahanalobis Distance

### Description

Compute the Mahalanobis distance between a pair of normally distributed clusters.

### Usage

    mahalanobis.dist(mean1, mean2, cov1, cov2, n1, n2)

### Arguments

`mean1` | mean vector of length `p` for cluster 1, where `p` is the dimension of the clusters.
`mean2` | mean vector of length `p` for cluster 2.
`cov1` | `pxp` covariance matrix for cluster 1.
`cov2` | `pxp` covariance matrix for cluster 2.
`n1` | number of cells (points) in cluster 1.
`n2` | number of cells (points) in cluster 2.

### Details

Consider two `p`-dimensional, normally distributed clusters with centers μ1, μ2 and covariance matrices Σ1, Σ2. Assume the size of the clusters are `n1` and `n2` respectively. We compute the Mahalanobis distance `d12` between the clusters as follows:

Σ = ( (n1-1) * Σ1 + (n2-1) * Σ2) / (n1+n2-2)

d12 = sqrt( t(μ1-μ2) * Σ^(-1) * (μ1-μ2))

The dimension of the clusters must be same.

### Value

`mahalanobis.dist` returns a numeric value measuring the Mahalanobis distance between a pair of normally distributed clusters.

### Author(s)

Ariful Azad

### References

McLachlan, GJ (1999) Mahalanobis distance; Journal of Resonance 4(6), 20–26.

### See Also

`symmetric.KL`, `dist.cluster`

### Examples

    ## ------------------------------------------------
    ## load data and retrieve a sample
    ## ------------------------------------------------

    library(healthyFlowData)
    data(hd)
    sample = exprs(hd.flowSet[[1]])

    ## ------------------------------------------------
    ## cluster sample using kmeans algorithm
    ## ------------------------------------------------

    km = kmeans(sample, centers=4, nstart=20)
    cluster.labels = km$cluster

    ## ------------------------------------------------
    ## Create ClusteredSample object
    ## and compute mahalanobis distance between two clsuters
    ## ------------------------------------------------

    clustSample = ClusteredSample(labels=cluster.labels, sample=sample)
    mean1 = get.center(get.clusters(clustSample)[[1]])
    mean2 = get.center(get.clusters(clustSample)[[2]])
    cov1 = get.cov(get.clusters(clustSample)[[1]])
    cov2 = get.cov(get.clusters(clustSample)[[2]])
    n1 = get.size(get.clusters(clustSample)[[1]])
    n2 = get.size(get.clusters(clustSample)[[2]])
    mahalanobis.dist(mean1, mean2, cov1, cov2, n1, n2)

[Package flowMatch version 1.16.0 Index]