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.

### See Also

`SMI`, `RV` (RV2/RVadj).

### 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 0.9.5 Index]