CovDist {CovTools} | R Documentation |

## Compute Pairwise Distance for Symmetric Positive-Definite Matrices

### Description

For a given 3-dimensional array where symmetric positive definite (SPD) matrices are stacked slice
by slice, it computes pairwise distance using various popular measures. Some of measures
are *metric* as they suffice 3 conditions in mathematical context; nonnegative definiteness,
symmetry, and triangle inequalities. Other non-metric measures represent *dissimilarities* between
two SPD objects.

### Usage

```
CovDist(
A,
method = c("AIRM", "Bhattacharyya", "Cholesky", "Euclidean", "Hellinger", "JBLD",
"KLDM", "LERM", "Procrustes.SS", "Procrustes.Full", "PowerEuclidean",
"RootEuclidean"),
power = 1
)
```

### Arguments

`A` |
a |

`method` |
the type of distance measures to be used; |

`power` |
a non-zero number for PowerEuclidean distance. |

### Value

an `(N\times N)`

symmetric matrix of pairwise distances.

### References

Arsigny V, Fillard P, Pennec X, Ayache N (2006).
“Log-Euclidean metrics for fast and simple calculus on diffusion tensors.”
*Magnetic Resonance in Medicine*, **56**(2), 411–421.
ISSN 0740-3194, 1522-2594.

Dryden IL, Koloydenko A, Zhou D (2009).
“Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging.”
*The Annals of Applied Statistics*, **3**(3), 1102–1123.
ISSN 1932-6157.

### Examples

```
## generate 100 SPD matrices of size (5-by-5)
samples = samplecovs(100,5)
## get pairwise distance for "AIRM"
distAIRM = CovDist(samples, method="AIRM")
## dimension reduction using MDS
ss = cmdscale(distAIRM)
## visualize
opar <- par(no.readonly=TRUE)
plot(ss[,1],ss[,2],main="2d projection")
par(opar)
```

*CovTools*version 0.5.4 Index]