r1 | R Documentation |
Matrix similarity as described by Ramsey et al. (1984).
r1(X1, X2, center = TRUE, impute = FALSE) r2( X1, X2, center = TRUE, impute = FALSE, impute_par = list(max_iter = 20, tol = 10^-5) ) r3( X1, X2, center = TRUE, impute = FALSE, impute_par = list(max_iter = 20, tol = 10^-5) ) r4( X1, X2, center = TRUE, impute = FALSE, impute_par = list(max_iter = 20, tol = 10^-5) ) GCD( X1, X2, ncomp1 = min(dim(X1)), ncomp2 = min(dim(X2)), center = TRUE, impute = FALSE, impute_par = list(max_iter = 20, tol = 10^-5) )
X1 |
first |
X2 |
second |
center |
|
impute |
|
impute_par |
named |
ncomp1 |
(GCD) number of subspace components from the first |
ncomp2 |
(GCD) number of subspace components from the second |
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)).
A single value measuring the similarity of two matrices.
Kristian Hovde Liland
Ramsay, JO; Berg, JT; Styan, GPH; 1984. "Matrix Correlation". Psychometrica 49(3): 403-423.
SMI
, RV
(RV2/RVadj), Rozeboom
, Coxhead
,
allCorrelations
(matrix correlation comparison), PCAcv (cross-validated PCA)
, PCAimpute (PCA based imputation)
.
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) # Missing data X1[c(1, 50, 400, 900)] <- NA X2[c(10, 200, 450, 1200)] <- NA r1(X1,X2, impute = TRUE) r2(X1,X2, impute = TRUE) r3(X1,X2, impute = TRUE) r4(X1,X2, impute = TRUE) GCD(X1,X2, impute = TRUE) GCD(X1,X2, 5,5, impute = TRUE)
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