---
title: "K-Fold"
author: "D. Renard"
date: "9 juillet 2020"
output:
  pdf_document: default
  html_document: default
---

# Introduction

This paper is to demonstrate the K-Fold option for the Cross-Validation

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(RGeostats)
rm(list=ls())
constant.define("asp",1)
```

We create the data set (by non conditional simulation)

```{r}
db = db.point.init(nech=100,coormax=c(100,100))
model = model.create(vartype="Cubic",range=50)
db = simtub(,db,model)
db = db.rename(db,"Simu*","Data")
plot(db,pch=19,title="Données")
neigh = neigh.create(radius=30,nmaxi=10)
```

# Cross Validation

## Traiditional method

The traditional method consists in suppressing in turn each datum and in re-estimating it from its neighboring samples. This option is called **Leave One Point Out**.

This cross-validation is performed next. The normalized error is displayed at each datum.

```{r}
res = xvalid(db,model,neigh)
plot(res,name="*stderr*",pch=19,title="Normalized Error")
```

## K-Fold method

Each datum is now attributed a code. For simplicity sake, the code values are assigned randomly, using values ranging from 1 to 5 (*ncode*).

```{r}
ncode = 5
db = db.add(db,code=ceiling(ncode * runif(db$nech)))
db = db.locate(db,"Data","z")
db = db.locate(db,"code","code")
plot(db,name.color="code",title="Code")
```

We perform the cross-validation with K-Fold option

```{r}
res = xvalid(db,model,neigh,flag.code=TRUE)
plot(res,name="*stderr*",pch=19,title="Normalized Error")
```

Let us check the results by selecting a target sample specifically. The first trial is performed using the Leave-One-Point-Out algorithm whereas the second trial uses the K-Fold option.

```{r}
debug.reference(17)
res = xvalid(db,model,neigh)
res = xvalid(db,model,neigh,flag.code=TRUE)
debug.reference(0)
```