hsicCCAfunc: Canonical Correlation Analysis based on the Hilbert-Schmidt...
In hsicCCA: Canonical Correlation Analysis based on Kernel Independence Measures

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Given two multi-dimensional data sets, find a pair of canonical projection pairs that maximizes the HSIC criterion. Called by hsicCCA, and intended for internal use, but users may play with it for potential finer controls.

1	hsicCCAfunc(x, y, Wx = NULL, Wy = NULL, sigmax, sigmay, numiter = 20, reltolstop = 1e-04)

`x`	The x-variable data set. One row per observation.
`y`	The y-variable data set. One row per observation.
`Wx`	Initial projection vector for the x data set. Randomly set if NULL.
`Wy`	Initial projection vector for the y data set. Randomly set if NULL.
`sigmax`	The bandwidth parameter for the Gaussian kernel on the x-variable set. A positive value. The smaller the smoother.
`sigmay`	The bandwidth parameter for the Gaussian kernel on the y-variable set. A positive value. The smaller the smoother.
`numiter`	Maximum number of iterations.
`reltolstop`	Convergence threshold. Algorithm stops when relative changes in cost from consecutive iterations is less than the threshold.

Optimization is done by gradient descent, where Nelder-Mead is used for step-size selection. Nelder Mead may fail to increase the cost at times (when stuck at local minima). User may consider restarting the algorithm when this happens.

A list containing:

`Wx`	The canoncial projection vector for the x-variable set.
`Wy`	The canoncial projection vector for the y-variable set.
`cost`	A vector of (negative) cost values at each iteration.

Current implementation is slow and requires high storage for large sample data. Sample size > 2000 not recommended.

Billy Chang

Chang et. al. (2013) Canonical Correlation Analysis based on Hilbert-Schmidt Independence Criterion and Centered Kernel Target Alignment. ICML 2013.

Gretton et. al. (2005) Measuring statistical dependence with Hilbert-Schmidt Norm. In Algorithmic Learning Theory 2005.

hsicCCA

set.seed(1)
numData <- 100
numDim <- 2
x <- matrix(rnorm(numData*numDim),numData,numDim)
y <- matrix(rnorm(numData*numDim),numData,numDim)
z <- runif(numData,-pi,pi)
y[,1] <- cos(z)+rnorm(numData,sd=0.1); x[,1] <- sin(z)+rnorm(numData,sd=0.1)
x <- scale(x)
y <- scale(y)

fit <- hsicCCAfunc(x,y,sigmax=1,sigmay=1)
plot(x%*%fit$Wx,y%*%fit$Wy)