Partial Least Squares

Given two data sets, Partial Least Squares (PLS) aims at maximizing cross-covariance of latent variables for each data matrix, therefore it can be considered as supervised methods. As we have two input matrices, do.pls generates two sets of outputs. Though it is widely used for regression problem, we used it in dimension reduction setting. For algorithm aspects, we used recursive gram-schmidt orthogonalization in conjunction with extracting projection vectors under eigen-decomposition formulation, as the problem dimension matters only up to original dimensionality. For more details, see Wikipedia entry on PLS.

do.pls(data1, data2, ndim = 2)

Arguments

data1

an \((n\times N)\) data matrix whose rows are observations

data2

an \((n\times M)\) data matrix whose rows are observations

ndim

an integer-valued target dimension.

Value

a named list containing

Y1

an \((n\times ndim)\) matrix of projected observations from data1.

Y2

an \((n\times ndim)\) matrix of projected observations from data2.

projection1

an \((N\times ndim)\) whose columns are loadings for data1.

projection2

an \((M\times ndim)\) whose columns are loadings for data2.

trfinfo1

a list containing information for out-of-sample prediction for data1.

trfinfo2

a list containing information for out-of-sample prediction for data2.

eigvals

a vector of eigenvalues for iterative decomposition.

References

Wold H (1975). “Path Models with Latent Variables: The NIPALS Approach.” In Quantitative Sociology, 307--357. Elsevier. ISBN 978-0-12-103950-9.

Rosipal R, Krämer N (2006). “Overview and Recent Advances in Partial Least Squares.” In Saunders C, Grobelnik M, Gunn S, Shawe-Taylor J (eds.), Subspace, Latent Structure and Feature Selection: Statistical and Optimization Perspectives Workshop, SLSFS 2005, Bohinj, Slovenia, February 23-25, 2005, Revised Selected Papers, 34--51. Springer Berlin Heidelberg, Berlin, Heidelberg. ISBN 978-3-540-34138-3.

See also

do.cca

Author

Kisung You

Examples

## generate 2 normal data matrices
mat1 = matrix(rnorm(100*12),nrow=100)+10 # 12-dim normal
mat2 = matrix(rnorm(100*6), nrow=100)-10 # 6-dim normal

## project onto 2 dimensional space for each data
output = do.pls(mat1, mat2, ndim=2)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(output$Y1, main="proj(mat1)")
plot(output$Y2, main="proj(mat2)")

par(opar)