# KgCov: Kernel Gini Distance Covariance Statistics In GiniDistance: A New Gini Correlation Between Quantitative and Qualitative Variables

## Description

Computes Kernel Gini distance covariance statistics, in which Xs are quantitative, Y are categorical, sigma is kernel standard deviation and returns the kernel Gini covariance.

## Usage

 1  KgCov(x, y, sigma) 

## Arguments

 x data y label of data or univariate response variable sigma kernel standard deviation

## Details

Kgcov compute kernel Gini distance covariance statistics for data. It is a self-contained R function dealing with both univariate and multivariate data. The sample size (number of rows) of the data must agree with the length of the label vector, and samples must not contain missing values. Arguments x, y are treated as data and labels.

Gini distance covariance are generalized to reproducing kernel Hilbert space (RKHS), \mathcal{H}_κ, as

\mathrm{gCov}_κ(X,Y) = ∑_{k=1}^{K} p_k ≤ft[ 2 {E}d_κ(X_k,X) - {E}d_κ(X_k,{X_k}') - {E}d_κ(X,X')\right],\label{gCovk}

In this case, we use the default Gaussian distance function

d_κ(x,x') = √{1-e^{-\frac{|x-x'|_q^2}{σ^2}}},

induced by a weighted Gaussian kernel, κ(x,x') = \frac{1}{2}e^{-\frac{|x-x'|_q^2}{σ^2}}.

## Value

KgCov returns the sample Kernel Gini distance covariance of x and y.

## References

Zhang, S., Dang, X., Nguyen, D. and Chen, Y. (2019). Estimating feature - label dependence using Gini distance statistics. IEEE Transactions on Pattern Analysis and Machine Intelligence (submitted), https://arXiv.org/pdf/1906.02171.pdf

gCov gCor dCor
 1 2 3  x<-iris[,1:4] y<-unclass(iris[,5]) KgCov(x, y, sigma=1)