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###  BMTRY 790: MACHINE LEARNING AND DATA MINING, Spring 2023  		###
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###  Lecture 8: Linear Classifiers, Part I					###
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###  Breast Cancer Tissue Example                    				###
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###  Looking at linear classification using ordinary least squares,	###
###  regression, logistic regression, linear discriminant analysis, and	###
###  quadratic discriminant analysis using the breast tissue data		###	         		
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#### 3-Class Example ####
btis<-read.csv("H:\\public_html\\BMTRY790_Spring2023\\Datasets\\BreastTissue.csv")
btis<-btis[-which(btis$Class=="adipose"),]
btis$Iclass<-ifelse(btis$Class=="nonmalig", 1, ifelse(btis$Class=="connective", 2, 3))
y1<-ifelse(btis$Class=="nonmalig", 1, 0)
y2<-ifelse(btis$Class=="connective", 1, 0)
y3<-ifelse(btis$Class=="carcinoma", 1, 0)
Y<-cbind(y1,y2,y3)

### Linear Classifier ###
X<-as.matrix(btis[,6:7])
mvmod<-lm(Y ~ X)
summary(mvmod)
bhat<-coef(mvmod)
yhat<-predict(mvmod)

### Fitting linear model with cross-product
X<-as.matrix(cbind(btis[,6:7], btis[,6]*btis[,7]))
colnames(X)<-c("normArea","MaxIP","CrossProd")
mvmodq<-lm(Y ~ X)
bhat<-coef(mvmodq)
round(bhat, 4)
summary(mvmodq)
yhat<-predict(mvmodq)


### Multinomial Logistic Model: Breast Tissue Classification ###
library(nnet)
mnlogit<-multinom(Iclass~normArea + MaxIP, data=btis)
bhat<-coef(mnlogit)
round(bhat, 4)

### Multinomial Logistic Model With Quadratic Term
mnlogit<-multinom(Iclass~normArea + MaxIP + normArea*MaxIP, data=btis)
bhat<-coef(mnlogit)
round(bhat, 4)





### Linear Discriminant and Quadratic Discriminant Analysis
library(MASS)

mnlda<-lda(Iclass ~ normArea + MaxIP, data=btis, CV=FALSE)   
mnlda  
plot(mnlda, dimen=1)
plot(mnlda, type="density", dimen=1)     
predict(mnlda)$class     

### QDA model ###
mnqda<-qda(Iclass ~ normArea + MaxIP, data=btis, CV=FALSE)