R: Correlational Measures for Matrices

r1 {MatrixCorrelation}

R Documentation

Correlational Measures for Matrices

Description

Matrix similarity as described by Ramsey et al. (1984).

Usage

r1(X1, X2, center = TRUE)

r2(X1, X2, center = TRUE)

r3(X1, X2, center = TRUE)

r4(X1, X2, center = TRUE)

GCD(X1, X2, ncomp1 = Rank(X1), ncomp2 = Rank(X2), center = TRUE)

Arguments

`X1`	first `matrix` to be compared (`data.frames` are also accepted).
`X2`	second `matrix` to be compared (`data.frames` are also accepted).
`center`	`logical` indicating if input matrices should be centered (default = TRUE).
`ncomp1`	(GCD) number of subspace components from the first `matrix` (default: full subspace).
`ncomp2`	(GCD) number of subspace components from the second `matrix` (default: full subspace).

Details

Details can be found in Ramsey's paper:

r1: inner product correlation
r2: orientation-independent inner product correlation
r3: spectra-independent inner product correlations (including orientation)
r4: Spectra-Independent inner product Correlations
GCD: Yanai's Generalized Coefficient of Determination (GCD) Measure. To reproduce the original GCD, use all components. When X1 and X2 are dummy variables, GCD is proportional with Pillai's criterion: tr(W^-1(B+W)).

Value

A single value measuring the similarity of two matrices.

Author(s)

Kristian Hovde Liland

References

Ramsay, JO; Berg, JT; Styan, GPH; 1984. "Matrix Correlation". Psychometrica 49(3): 403-423.

Examples

X1  <- matrix(rnorm(100*300),100,300)
usv <- svd(X1)
X2  <- usv$u[,-3] %*% diag(usv$d[-3]) %*% t(usv$v[,-3])

r1(X1,X2)
r2(X1,X2)
r3(X1,X2)
r4(X1,X2)
GCD(X1,X2)
GCD(X1,X2, 5,5)

[Package MatrixCorrelation version 0.9.4 Index]