---
title: "Introduction to GMC Package"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to GMC Package}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(GMC)
```

## Introduction

The GMC package provides tools to compute the Generalized Measure of Correlation (GMC), a dependence measure that accounts for nonlinearity and asymmetry in the relationship between variables. This measure was proposed by Zheng, Shi, and Zhang (2012).

## Basic Usage

### Computing GMC(Y|X)

```{r}
# Generate sample data with linear relationship
set.seed(123)
n <- 1000
X <- rnorm(n)
Y <- 2 * X + rnorm(n, sd = 0.5)

# Calculate GMC(Y|X)
gmc_y_given_x <- GMC_Y_given_X(X, Y)
print(paste("GMC(Y|X) =", round(gmc_y_given_x, 3)))
```

### Computing GMC(X|Y)

```{r}
# Generate sample data with nonlinear relationship
set.seed(123)
X <- rnorm(n)
Y <- X^2 + rnorm(n, sd = 0.5)

# Calculate GMC(X|Y)
gmc_x_given_y <- GMC_X_given_Y(X, Y)
print(paste("GMC(X|Y) =", round(gmc_x_given_y, 3)))
```

### Feature Ranking

```{r}
# Generate sample data with multiple predictors
set.seed(123)
n <- 500
X1 <- rnorm(n)
X2 <- rnorm(n)
X3 <- rnorm(n)
Y <- 2 * X1 + X2^2 + rnorm(n, sd = 0.5)
X <- cbind(X1, X2, X3)

# Rank features by GMC
ranking <- GMC_feature_ranking(X, Y)
print(ranking)
```

## References

Zheng, S., Shi, N.Z., & Zhang, Z. (2012). Generalized Measures of Correlation for Asymmetry, Nonlinearity, and Beyond. Journal of the American Statistical Association, 107(499), 1239-1252.