Homework02.Rmd

---
title: "Multivariate Hw02"
author: "Lin Chian Hung"
date: "2018/4/21"
output: 
  html_document:
    toc: true
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---

# Classification tree
```{r}
fish<-read.csv("~/Desktop/碩一下/多變量/Fishdata.csv")
library(rpart)
fish.control<-rpart.control(minisplit=10,minbucket=3,xval=0)
fish.treeorig<-rpart(Species~
Weight+L1+L2+L3+Height+Width,data=fish,method="class",control=fish.control)
```
Let’s now plot the tree:
```{r}
# 第一種畫法
plot(fish.treeorig)
text(fish.treeorig)
# 第二種畫法
require(rpart.plot) 
prp(fish.treeorig,         # 模型
    faclen=0,           # 呈現的變數不要縮寫
    fallen.leaves=TRUE, # 讓樹枝以垂直方式呈現
    shadow.col="gray",  # 最下面的節點塗上陰影
    # number of correct classifications / number of observations in that node
    extra=2) 
```

Also check out the complexity parameter (CP):
```{r}
printcp(fish.treeorig)
```
```{r}
summary(fish.treeorig)
```
```{r}
fish.prunetree<-prune.rpart(fish.treeorig,cp=0.02) 
# 第一種畫法
plot(fish.prunetree)
text(fish.prunetree)
# 第二種畫法
require(rpart.plot) 
prp(fish.prunetree,         # 模型
    faclen=0,           # 呈現的變數不要縮寫
    fallen.leaves=TRUE, # 讓樹枝以垂直方式呈現
    shadow.col="gray",  # 最下面的節點塗上陰影
    # number of correct classifications / number of observations in that node
    extra=2) 
```
```{r}
L21<-fish$L2-fish$L1
L32<-fish$L3-fish$L2
L31<-fish$L3-fish$L1
newfish<-cbind(fish,L21,L32,L31)
newfish.treenew<-rpart(Species~., data=newfish,method="class",parms=list(split="information"),control=fish.control) 
printcp(newfish.treenew)
```
```{r}
# 第一種畫法
plot(newfish.treenew) 
text(newfish.treenew)
# 第二種畫法
require(rpart.plot) 
prp(newfish.treenew,         # 模型
    faclen=0,           # 呈現的變數不要縮寫
    fallen.leaves=TRUE, # 讓樹枝以垂直方式呈現
    shadow.col="gray",  # 最下面的節點塗上陰影
    # number of correct classifications / number of observations in that node
    extra=2) 
```
```{r}
fish.control<-rpart.control(minbucket=3,minsplit=10,xval=148)
newfish.treenewcv<- rpart(Species~., data=newfish,method="class",
parms=list(split='information'),control=fish.control) 
printcp(newfish.treenewcv)
```
```{r}
newfish.test<-read.csv("~/Desktop/碩一下/多變量/Fish_test_data.csv")
L31<-newfish.test$L3- newfish.test$L1
L32<-newfish.test$L3- newfish.test$L2
L21<-newfish.test$L2- newfish.test$L1
newfish.test<-cbind(newfish.test,L21,L32,L31)
newfish.tpred<-predict(newfish.treenewcv,newfish.test)
newfish.tpred
```

# Linear Discriminant Analysis
```{r warning=FALSE}
library(MASS)
newfish.lda<-lda(Species~.,data=newfish)
# 有共線性存在
```
```{r}
newfish.lda<-lda(Species~Weight+L1+Height+Width+L21+L32,data=newfish) 
newfish.lda
```
```{r}
newfish.ldapred<-predict(newfish.lda,newfish[,-1])
table(newfish$Species,newfish.ldapred$class)
```

```{r}
newfish.ldacv<-lda(Species~Weight+L1+Height+Width+L21+L32,data=newfish,CV=T)  
table(newfish$Species,newfish.ldacv$class)
```
```{r}
eqscplot(newfish.ldapred$x,type='n',xlab="1st LD",ylab="2nd LD")
fish.species<-c(rep("B",33),rep("W",5),rep("R",18),rep("Pa",10),rep("S",12),rep("Pi",16),rep("Pe",54))
fish.colors<-c(rep(1,33),rep(2,5),rep(3,18),rep(4,10),rep(5,12),rep(6,16),rep(7,54)) 
text(newfish.ldapred$x[,1:2],fish.species,col=fish.colors)
```

```{r}
newfish.ldatest<-predict(newfish.lda,newfish.test) 
newfish.ldatest$class
```
# Quadratic Discriminant Analysis
Let us examine how to apply QDA to this dataset.
Let us pretend that the multivariate normal assumption is valid (you can check for this by using the R package “MVN”, as shown in the lab of CCA)

Check Normailty
```{r}
library(MVN)
fish1 <- newfish[,2:6]
mvn(fish1,mvnTest = "hz")
```


```{r eval=FALSE}
newfish.qda<-qda(Species~.,data=newfish)
```

```{r}
newfish.q<-read.csv("~/Desktop/碩一下/多變量/QDA.csv")
```
```{r eval = FALSE}
newfish.qda<-qda(Species~.,data=newfish.q)
```
```{r}
newfish.qda<-qda(Species~Weight+L1+Height+Width+L21+L32,data=newfish.q) 
newfish.qdapred<-predict(newfish.qda,newfish.q)
table(newfish.q$Species,newfish.qdapred$class)
```
```{r}
predict(newfish.qda,newfish.test)$class
```
```{r}
newfish.qda<-qda(Species~Weight+L1+Height+Width+L21+L32,data=newfish.q,CV=T) 
table(newfish.q$Species,newfish.qda$class)
```
# Nearest Neighbor Methdos
k = 3
```{r}
library(class)
newfish.knn<-knn(newfish[,2:10],newfish[,2:10],newfish[,"Species"],k=3,prob=T) 
table(newfish$Species,newfish.knn)
```
k = 2
```{r}
newfish.knn<-knn(newfish[,2:10],newfish[,2:10],newfish[,"Species"],k=2,prob=T) 
table(newfish$Species,newfish.knn)
```
k = 1
```{r}
newfish.knn<-knn(newfish[,2:10],newfish[,2:10],newfish[,"Species"],k=1,prob=T) 
table(newfish$Species,newfish.knn)
```
```{r}
newfish1<-newfish[,c(1,2,3,6,8,9)]
newfish.knncv<-knn.cv(newfish1[,2:6],newfish1[,"Species"],k=1,prob=T) 
table(newfish1$Species,newfish.knncv)
```

```{r}
newfish1.test<-newfish.test[,c(1,2,5,7,8)]
newfish.knntest<-knn(newfish1[,2:6],newfish1.test,newfish1[,"Species"],k=1,prob=T) 
newfish.knntest

```

# Logistic Discrimination
Again, let us pretend that all assumptions (including “multivariate normal” and “common covariance matrix” over all classes) are valid (need to check that in practice).
In order to use this method in R, we need another package.
```{r}
library(nnet)
newfish.logd<-multinom(Species~.,data=newfish,maxit=250) 
newfish.logd
```
```{r}
table(newfish$Species,predict(newfish.logd,newfish))
```
Now we examine the true error rate by cross-validation. To do this, we use another package called “glmnet”:
```{r warning=FALSE}
library(glmnet)
x <- as.matrix(newfish[,-1])
y <- newfish$Species
cvfit <- cv.glmnet(x, y, family='multinomial', type.measure='class', nfolds=148) 
predict.value <- predict(cvfit, x, s = "lambda.min", type = "class")
table(predict.value,newfish$Species)
```
```{r}
predict(newfish.logd,newfish.test)
```