ifrkcca: Influence Function of Robust Kernel Canonical Analysis

Description

##To define the robustness in statistics, different approaches have been pro- posed, for example, the minimax approach, the sensitivity curve, the influence function (IF) and the finite sample breakdown point. Due to its simplic- ity, the IF is the most useful approach in statistical machine learning.

Usage

ifrkcca(X, Y, lossfu = "Huber", kernel = "rbfdot", gamma = 0.00001, ncomps = 10, jth = 1)

Arguments

a data matrix index by row

lossfu

a loss function: square, Hampel's or Huber's loss

kernel

a positive definite kernel

gamma

the hyper-parameters

ncomps

the number of canonical vectors

jth

the influence function of the jth canonical vector

Value

ifrkcor

Influence value of the data by robust kernel canonical correalation

ifrkxcv

Influence value of cnonical vector of X dataset

ifrkycv

Influence value of cnonical vector of Y dataset

References

Md Ashad Alam, Kenji Fukumizu and Yu-Ping Wang (2018), Influence Function and Robust Variant of Kernel Canonical Correlation Analysis, Neurocomputing, Vol. 304 (2018) 12-29.

M. Romanazzi (1992), Influence in canonical correlation analysis, Psychometrika vol 57(2) (1992) 237-259.

Examples

Run this code

# NOT RUN {
##Dummy data:

X <- matrix(rnorm(500),100); Y <- matrix(rnorm(500),100)

ifrkcca(X,Y, lossfu = "Huber", kernel = "rbfdot", gamma = 0.00001, ncomps = 10, jth = 2)
# }