ncca.rsvd: Nonparametric Canonical Correlation Analysis

In ilariabonavita/NCCApckg:

Description

Compute the Nonparametric canonical correlations between two data matrices

Usage

ncca.rsvd(X, Y, XV = NULL, YV = NULL, XT = NULL, YT = NULL, d, hx = 1,
  hy = 1, nx = 20, ny = 20, PreComputedNNs = NULL,
  verbose = getOption("verbose"), ...)

Arguments

X	The training data set containing n samples and p features
Y	The paired training data set containing n samples and q features
XV	The validation data set containing nv samples and p features
YV	The paired validation data set containing nv samples and q features
XT	The testing data set containing nt samples and p features
YT	The paired testing data set containing nt samples and q features
d	The dimension of the ouput transformed features
hx	The bandwidth parameters for the KDEs of X
hy	The bandwidth parameters for the KDEs of Y
nx	The number of nearest neighbors for the KDEs of X
ny	The number of nearest neighbors for the KDEs of Y
PreComputedNNs	The name of the .Rda file containing two n*nx matrices for the nearest neighbor indice and the nearest neighbor Euclidean distances for X, and two n*ny matrices for the nearest neighbor indice and the nearest neighbor Euclidean distances for Y. It is optional, only for debugging purposes.
...

Value

X_new The d-dimensional projections of the training data X

Y_new The d-dimensional projections of the training data Y

XV_new The d-dimensional projections of the validation data X

YV_new The d-dimensional projections of the validation data Y

XT_new The d-dimensional projections of the testing data X

YT_new The d-dimensional projections of the testing data Y

The canonical correlation between X_new and Y_new

The canonical correlation between XV_new and YV_new

The canonical correlation between XT_new and YT_new

p value for X_new and V_new

p value XV_new and YV_new

p value XT_new and YT_new

Author(s)

Meiwen Jia, [e-mail] Ilaria Bonavita, [e-mail]

References

Michaeli, T., Wang, W., & Livescu, K. (2015). Nonparametric canonical correlation analysis. arXiv preprint arXiv:1511.04839.

Examples

N <- 10000 # Overal number of examples (train+test)
N_paired <- 5000 # Number of training examples
MaxAngle <- 4*pi
MinRadius <-0.3
MaxRadius <- 8
NumNNs_X <- 20
NumNNs_Y <- 20
sx <- 0.5
sy <- 0.5
set.seed(8409)
## Generate data for views 1,2
t <- seq(0, MaxAngle, length.out = N)
r <- seq(MinRadius, MaxRadius, length.out = N) + 2*runif(N)
#### generate X, the noise can be added!
X <- cbind(r*cos(t+0*rnorm(N)*0.05), r*sin(t+0*rnorm(N)*0.05))
X <- X + 0*matrix(rnorm(N*2), ncol = 2)
#### generate Y, the noise can be added!
Y <- cbind(t+0*rnorm(N)*1, 2*rnorm(N))
Y <- Y + 0*cbind(rep(0, N), rnorm(N))
## Training data
PairedIndices <- sample(1:N, N_paired)
## Test (or validation) data
UnpairedIndices <- setdiff(1:N,PairedIndices)
ncca_res <- ncca.rsvd(X[PairedIndices,],Y[PairedIndices,], X[UnpairedIndices,],Y[UnpairedIndices,],
                 d = 2, hx = 0.75, hy = 0.75, nx = NumNNs_X, ny=NumNNs_Y)
cat("The nonparametric canonical correlation between X and Y is ", ncca_res$cor_XY, "\n")

ilariabonavita/NCCApckg documentation built on May 28, 2019, 5:39 a.m.