Classification in R
Dữ liệu thị trường chứng khoán
library(ISLR)
names(Smarket)
## [1] "Year" "Lag1" "Lag2" "Lag3" "Lag4" "Lag5"
## [7] "Volume" "Today" "Direction"
dim(Smarket)
## [1] 1250 9
summary(Smarket)
## Year Lag1 Lag2 Lag3
## Min. :2001 Min. :-4.9 Min. :-4.9 Min. :-4.9
## 1st Qu.:2002 1st Qu.:-0.6 1st Qu.:-0.6 1st Qu.:-0.6
## Median :2003 Median : 0.0 Median : 0.0 Median : 0.0
## Mean :2003 Mean : 0.0 Mean : 0.0 Mean : 0.0
## 3rd Qu.:2004 3rd Qu.: 0.6 3rd Qu.: 0.6 3rd Qu.: 0.6
## Max. :2005 Max. : 5.7 Max. : 5.7 Max. : 5.7
## Lag4 Lag5 Volume Today Direction
## Min. :-4.9 Min. :-4.9 Min. :0.36 Min. :-4.9 Down:602
## 1st Qu.:-0.6 1st Qu.:-0.6 1st Qu.:1.26 1st Qu.:-0.6 Up :648
## Median : 0.0 Median : 0.0 Median :1.42 Median : 0.0
## Mean : 0.0 Mean : 0.0 Mean :1.48 Mean : 0.0
## 3rd Qu.: 0.6 3rd Qu.: 0.6 3rd Qu.:1.64 3rd Qu.: 0.6
## Max. : 5.7 Max. : 5.7 Max. :3.15 Max. : 5.7
pairs(Smarket)
cor(Smarket[,-9])
## Year Lag1 Lag2 Lag3 Lag4 Lag5 Volume Today
## Year 1.000 0.0297 0.0306 0.0332 0.0357 0.0298 0.539 0.0301
## Lag1 0.030 1.0000 -0.0263 -0.0108 -0.0030 -0.0057 0.041 -0.0262
## Lag2 0.031 -0.0263 1.0000 -0.0259 -0.0109 -0.0036 -0.043 -0.0103
## Lag3 0.033 -0.0108 -0.0259 1.0000 -0.0241 -0.0188 -0.042 -0.0024
## Lag4 0.036 -0.0030 -0.0109 -0.0241 1.0000 -0.0271 -0.048 -0.0069
## Lag5 0.030 -0.0057 -0.0036 -0.0188 -0.0271 1.0000 -0.022 -0.0349
## Volume 0.539 0.0409 -0.0434 -0.0418 -0.0484 -0.0220 1.000 0.0146
## Today 0.030 -0.0262 -0.0103 -0.0024 -0.0069 -0.0349 0.015 1.0000
attach(Smarket)
plot(Volume)
Hồi quy logistic
glm.fit=glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume,data=Smarket,family=binomial)
summary(glm.fit)
##
## Call:
## glm(formula = Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 +
## Volume, family = binomial, data = Smarket)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.45 -1.20 1.07 1.15 1.33
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.12600 0.24074 -0.52 0.60
## Lag1 -0.07307 0.05017 -1.46 0.15
## Lag2 -0.04230 0.05009 -0.84 0.40
## Lag3 0.01109 0.04994 0.22 0.82
## Lag4 0.00936 0.04997 0.19 0.85
## Lag5 0.01031 0.04951 0.21 0.83
## Volume 0.13544 0.15836 0.86 0.39
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1731.2 on 1249 degrees of freedom
## Residual deviance: 1727.6 on 1243 degrees of freedom
## AIC: 1742
##
## Number of Fisher Scoring iterations: 3
coef(glm.fit)
## (Intercept) Lag1 Lag2 Lag3 Lag4 Lag5
## -0.1260 -0.0731 -0.0423 0.0111 0.0094 0.0103
## Volume
## 0.1354
summary(glm.fit)$coef
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.1260 0.24 -0.52 0.60
## Lag1 -0.0731 0.05 -1.46 0.15
## Lag2 -0.0423 0.05 -0.84 0.40
## Lag3 0.0111 0.05 0.22 0.82
## Lag4 0.0094 0.05 0.19 0.85
## Lag5 0.0103 0.05 0.21 0.83
## Volume 0.1354 0.16 0.86 0.39
summary(glm.fit)$coef[,4]
## (Intercept) Lag1 Lag2 Lag3 Lag4 Lag5
## 0.60 0.15 0.40 0.82 0.85 0.83
## Volume
## 0.39
glm.probs=predict(glm.fit,type="response")
glm.probs[1:10]
## 1 2 3 4 5 6 7 8 9 10
## 0.51 0.48 0.48 0.52 0.51 0.51 0.49 0.51 0.52 0.49
contrasts(Direction)
## Up
## Down 0
## Up 1
glm.pred=rep("Down",1250)
glm.pred[glm.probs>.5]="Up"
table(glm.pred,Direction)
## Direction
## glm.pred Down Up
## Down 145 141
## Up 457 507
(507+145)/1250
## [1] 0.52
mean(glm.pred==Direction)
## [1] 0.52
train=(Year<2005)
Smarket.2005=Smarket[!train,]
dim(Smarket.2005)
## [1] 252 9
Direction.2005=Direction[!train]
glm.fit=glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume,data=Smarket,family=binomial,subset=train)
glm.probs=predict(glm.fit,Smarket.2005,type="response")
glm.pred=rep("Down",252)
glm.pred[glm.probs>.5]="Up"
table(glm.pred,Direction.2005)
## Direction.2005
## glm.pred Down Up
## Down 77 97
## Up 34 44
mean(glm.pred==Direction.2005)
## [1] 0.48
mean(glm.pred!=Direction.2005)
## [1] 0.52
glm.fit=glm(Direction~Lag1+Lag2,data=Smarket,family=binomial,subset=train)
glm.probs=predict(glm.fit,Smarket.2005,type="response")
glm.pred=rep("Down",252)
glm.pred[glm.probs>.5]="Up"
table(glm.pred,Direction.2005)
## Direction.2005
## glm.pred Down Up
## Down 35 35
## Up 76 106
mean(glm.pred==Direction.2005)
## [1] 0.56
106/(106+76)
## [1] 0.58
predict(glm.fit,newdata=data.frame(Lag1=c(1.2,1.5),Lag2=c(1.1,-0.8)),type="response")
## 1 2
## 0.48 0.50
Phân tích biệt thức tuyến tính
library(MASS)
lda.fit=lda(Direction~Lag1+Lag2,data=Smarket,subset=train)
lda.fit
## Call:
## lda(Direction ~ Lag1 + Lag2, data = Smarket, subset = train)
##
## Prior probabilities of groups:
## Down Up
## 0.49 0.51
##
## Group means:
## Lag1 Lag2
## Down 0.043 0.034
## Up -0.040 -0.031
##
## Coefficients of linear discriminants:
## LD1
## Lag1 -0.64
## Lag2 -0.51
plot(lda.fit)
lda.pred=predict(lda.fit, Smarket.2005)
names(lda.pred)
## [1] "class" "posterior" "x"
lda.class=lda.pred$class
table(lda.class,Direction.2005)
## Direction.2005
## lda.class Down Up
## Down 35 35
## Up 76 106
mean(lda.class==Direction.2005)
## [1] 0.56
sum(lda.pred$posterior[,1]>=.5)
## [1] 70
sum(lda.pred$posterior[,1]<.5)
## [1] 182
lda.pred$posterior[1:20,1]
## 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013
## 0.49 0.48 0.47 0.47 0.49 0.49 0.50 0.49 0.49 0.48 0.49 0.51 0.49 0.47 0.47
## 1014 1015 1016 1017 1018
## 0.48 0.49 0.50 0.50 0.49
lda.class[1:20]
## [1] Up Up Up Up Up Up Up Up Up Up Up Down Up Up
## [15] Up Up Up Down Up Up
## Levels: Down Up
sum(lda.pred$posterior[,1]>.9)
## [1] 0
Phân tích biệt thức toàn phương
qda.fit=qda(Direction~Lag1+Lag2,data=Smarket,subset=train)
qda.fit
## Call:
## qda(Direction ~ Lag1 + Lag2, data = Smarket, subset = train)
##
## Prior probabilities of groups:
## Down Up
## 0.49 0.51
##
## Group means:
## Lag1 Lag2
## Down 0.043 0.034
## Up -0.040 -0.031
qda.class=predict(qda.fit,Smarket.2005)$class
table(qda.class,Direction.2005)
## Direction.2005
## qda.class Down Up
## Down 30 20
## Up 81 121
mean(qda.class==Direction.2005)
## [1] 0.6
K-Nearest Neighbors (K láng giềng gần nhất)
library(class)
train.X=cbind(Lag1,Lag2)[train,]
test.X=cbind(Lag1,Lag2)[!train,]
train.Direction=Direction[train]
set.seed(1)
knn.pred=knn(train.X,test.X,train.Direction,k=1)
table(knn.pred,Direction.2005)
## Direction.2005
## knn.pred Down Up
## Down 43 58
## Up 68 83
(83+43)/252
## [1] 0.5
knn.pred=knn(train.X,test.X,train.Direction,k=3)
table(knn.pred,Direction.2005)
## Direction.2005
## knn.pred Down Up
## Down 48 54
## Up 63 87
mean(knn.pred==Direction.2005)
## [1] 0.54
Một ứng dụng trong ngành bảo hiểm
dim(Caravan)
## [1] 5822 86
attach(Caravan)
summary(Purchase)
## No Yes
## 5474 348
348/5822
## [1] 0.06
standardized.X=scale(Caravan[,-86])
var(Caravan[,1])
## [1] 165
var(Caravan[,2])
## [1] 0.16
var(standardized.X[,1])
## [1] 1
var(standardized.X[,2])
## [1] 1
test=1:1000
train.X=standardized.X[-test,]
test.X=standardized.X[test,]
train.Y=Purchase[-test]
test.Y=Purchase[test]
set.seed(1)
knn.pred=knn(train.X,test.X,train.Y,k=1)
mean(test.Y!=knn.pred)
## [1] 0.12
mean(test.Y!="No")
## [1] 0.059
table(knn.pred,test.Y)
## test.Y
## knn.pred No Yes
## No 873 50
## Yes 68 9
9/(68+9)
## [1] 0.12
knn.pred=knn(train.X,test.X,train.Y,k=3)
table(knn.pred,test.Y)
## test.Y
## knn.pred No Yes
## No 920 54
## Yes 21 5
5/26
## [1] 0.19
knn.pred=knn(train.X,test.X,train.Y,k=5)
table(knn.pred,test.Y)
## test.Y
## knn.pred No Yes
## No 930 55
## Yes 11 4
4/15
## [1] 0.27
# Comparision to logistic regression
glm.fit=glm(Purchase~.,data=Caravan,family=binomial,subset=-test)
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
glm.probs=predict(glm.fit,Caravan[test,],type="response")
glm.pred=rep("No",1000)
glm.pred[glm.probs>.5]="Yes"
table(glm.pred,test.Y)
## test.Y
## glm.pred No Yes
## No 934 59
## Yes 7 0
glm.pred=rep("No",1000)
glm.pred[glm.probs>.25]="Yes"
table(glm.pred,test.Y)
## test.Y
## glm.pred No Yes
## No 919 48
## Yes 22 11
11/(22+11)
## [1] 0.33