#KNN Algorithm
iris
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
## 7 4.6 3.4 1.4 0.3 setosa
## 8 5.0 3.4 1.5 0.2 setosa
## 9 4.4 2.9 1.4 0.2 setosa
## 10 4.9 3.1 1.5 0.1 setosa
## 11 5.4 3.7 1.5 0.2 setosa
## 12 4.8 3.4 1.6 0.2 setosa
## 13 4.8 3.0 1.4 0.1 setosa
## 14 4.3 3.0 1.1 0.1 setosa
## 15 5.8 4.0 1.2 0.2 setosa
## 16 5.7 4.4 1.5 0.4 setosa
## 17 5.4 3.9 1.3 0.4 setosa
## 18 5.1 3.5 1.4 0.3 setosa
## 19 5.7 3.8 1.7 0.3 setosa
## 20 5.1 3.8 1.5 0.3 setosa
## 21 5.4 3.4 1.7 0.2 setosa
## 22 5.1 3.7 1.5 0.4 setosa
## 23 4.6 3.6 1.0 0.2 setosa
## 24 5.1 3.3 1.7 0.5 setosa
## 25 4.8 3.4 1.9 0.2 setosa
## 26 5.0 3.0 1.6 0.2 setosa
## 27 5.0 3.4 1.6 0.4 setosa
## 28 5.2 3.5 1.5 0.2 setosa
## 29 5.2 3.4 1.4 0.2 setosa
## 30 4.7 3.2 1.6 0.2 setosa
## 31 4.8 3.1 1.6 0.2 setosa
## 32 5.4 3.4 1.5 0.4 setosa
## 33 5.2 4.1 1.5 0.1 setosa
## 34 5.5 4.2 1.4 0.2 setosa
## 35 4.9 3.1 1.5 0.2 setosa
## 36 5.0 3.2 1.2 0.2 setosa
## 37 5.5 3.5 1.3 0.2 setosa
## 38 4.9 3.6 1.4 0.1 setosa
## 39 4.4 3.0 1.3 0.2 setosa
## 40 5.1 3.4 1.5 0.2 setosa
## 41 5.0 3.5 1.3 0.3 setosa
## 42 4.5 2.3 1.3 0.3 setosa
## 43 4.4 3.2 1.3 0.2 setosa
## 44 5.0 3.5 1.6 0.6 setosa
## 45 5.1 3.8 1.9 0.4 setosa
## 46 4.8 3.0 1.4 0.3 setosa
## 47 5.1 3.8 1.6 0.2 setosa
## 48 4.6 3.2 1.4 0.2 setosa
## 49 5.3 3.7 1.5 0.2 setosa
## 50 5.0 3.3 1.4 0.2 setosa
## 51 7.0 3.2 4.7 1.4 versicolor
## 52 6.4 3.2 4.5 1.5 versicolor
## 53 6.9 3.1 4.9 1.5 versicolor
## 54 5.5 2.3 4.0 1.3 versicolor
## 55 6.5 2.8 4.6 1.5 versicolor
## 56 5.7 2.8 4.5 1.3 versicolor
## 57 6.3 3.3 4.7 1.6 versicolor
## 58 4.9 2.4 3.3 1.0 versicolor
## 59 6.6 2.9 4.6 1.3 versicolor
## 60 5.2 2.7 3.9 1.4 versicolor
## 61 5.0 2.0 3.5 1.0 versicolor
## 62 5.9 3.0 4.2 1.5 versicolor
## 63 6.0 2.2 4.0 1.0 versicolor
## 64 6.1 2.9 4.7 1.4 versicolor
## 65 5.6 2.9 3.6 1.3 versicolor
## 66 6.7 3.1 4.4 1.4 versicolor
## 67 5.6 3.0 4.5 1.5 versicolor
## 68 5.8 2.7 4.1 1.0 versicolor
## 69 6.2 2.2 4.5 1.5 versicolor
## 70 5.6 2.5 3.9 1.1 versicolor
## 71 5.9 3.2 4.8 1.8 versicolor
## 72 6.1 2.8 4.0 1.3 versicolor
## 73 6.3 2.5 4.9 1.5 versicolor
## 74 6.1 2.8 4.7 1.2 versicolor
## 75 6.4 2.9 4.3 1.3 versicolor
## 76 6.6 3.0 4.4 1.4 versicolor
## 77 6.8 2.8 4.8 1.4 versicolor
## 78 6.7 3.0 5.0 1.7 versicolor
## 79 6.0 2.9 4.5 1.5 versicolor
## 80 5.7 2.6 3.5 1.0 versicolor
## 81 5.5 2.4 3.8 1.1 versicolor
## 82 5.5 2.4 3.7 1.0 versicolor
## 83 5.8 2.7 3.9 1.2 versicolor
## 84 6.0 2.7 5.1 1.6 versicolor
## 85 5.4 3.0 4.5 1.5 versicolor
## 86 6.0 3.4 4.5 1.6 versicolor
## 87 6.7 3.1 4.7 1.5 versicolor
## 88 6.3 2.3 4.4 1.3 versicolor
## 89 5.6 3.0 4.1 1.3 versicolor
## 90 5.5 2.5 4.0 1.3 versicolor
## 91 5.5 2.6 4.4 1.2 versicolor
## 92 6.1 3.0 4.6 1.4 versicolor
## 93 5.8 2.6 4.0 1.2 versicolor
## 94 5.0 2.3 3.3 1.0 versicolor
## 95 5.6 2.7 4.2 1.3 versicolor
## 96 5.7 3.0 4.2 1.2 versicolor
## 97 5.7 2.9 4.2 1.3 versicolor
## 98 6.2 2.9 4.3 1.3 versicolor
## 99 5.1 2.5 3.0 1.1 versicolor
## 100 5.7 2.8 4.1 1.3 versicolor
## 101 6.3 3.3 6.0 2.5 virginica
## 102 5.8 2.7 5.1 1.9 virginica
## 103 7.1 3.0 5.9 2.1 virginica
## 104 6.3 2.9 5.6 1.8 virginica
## 105 6.5 3.0 5.8 2.2 virginica
## 106 7.6 3.0 6.6 2.1 virginica
## 107 4.9 2.5 4.5 1.7 virginica
## 108 7.3 2.9 6.3 1.8 virginica
## 109 6.7 2.5 5.8 1.8 virginica
## 110 7.2 3.6 6.1 2.5 virginica
## 111 6.5 3.2 5.1 2.0 virginica
## 112 6.4 2.7 5.3 1.9 virginica
## 113 6.8 3.0 5.5 2.1 virginica
## 114 5.7 2.5 5.0 2.0 virginica
## 115 5.8 2.8 5.1 2.4 virginica
## 116 6.4 3.2 5.3 2.3 virginica
## 117 6.5 3.0 5.5 1.8 virginica
## 118 7.7 3.8 6.7 2.2 virginica
## 119 7.7 2.6 6.9 2.3 virginica
## 120 6.0 2.2 5.0 1.5 virginica
## 121 6.9 3.2 5.7 2.3 virginica
## 122 5.6 2.8 4.9 2.0 virginica
## 123 7.7 2.8 6.7 2.0 virginica
## 124 6.3 2.7 4.9 1.8 virginica
## 125 6.7 3.3 5.7 2.1 virginica
## 126 7.2 3.2 6.0 1.8 virginica
## 127 6.2 2.8 4.8 1.8 virginica
## 128 6.1 3.0 4.9 1.8 virginica
## 129 6.4 2.8 5.6 2.1 virginica
## 130 7.2 3.0 5.8 1.6 virginica
## 131 7.4 2.8 6.1 1.9 virginica
## 132 7.9 3.8 6.4 2.0 virginica
## 133 6.4 2.8 5.6 2.2 virginica
## 134 6.3 2.8 5.1 1.5 virginica
## 135 6.1 2.6 5.6 1.4 virginica
## 136 7.7 3.0 6.1 2.3 virginica
## 137 6.3 3.4 5.6 2.4 virginica
## 138 6.4 3.1 5.5 1.8 virginica
## 139 6.0 3.0 4.8 1.8 virginica
## 140 6.9 3.1 5.4 2.1 virginica
## 141 6.7 3.1 5.6 2.4 virginica
## 142 6.9 3.1 5.1 2.3 virginica
## 143 5.8 2.7 5.1 1.9 virginica
## 144 6.8 3.2 5.9 2.3 virginica
## 145 6.7 3.3 5.7 2.5 virginica
## 146 6.7 3.0 5.2 2.3 virginica
## 147 6.3 2.5 5.0 1.9 virginica
## 148 6.5 3.0 5.2 2.0 virginica
## 149 6.2 3.4 5.4 2.3 virginica
## 150 5.9 3.0 5.1 1.8 virginica
head(iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
str(iris)
## 'data.frame': 150 obs. of 5 variables:
## $ Sepal.Length: num 5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
## $ Sepal.Width : num 3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
## $ Petal.Length: num 1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
## $ Petal.Width : num 0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
## $ Species : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...
summary(iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100
## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300
## Median :5.800 Median :3.000 Median :4.350 Median :1.300
## Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199
## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800
## Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500
## Species
## setosa :50
## versicolor:50
## virginica :50
##
##
##
#visualization
library(ggvis)
iris %>% ggvis(~Petal.Length, ~Petal.Width, fill = ~factor(Species)) %>%layer_points()
library(ggvis)
iris %>% ggvis(~Sepal.Width, ~Sepal.Length, fill = ~factor(Species)) %>%layer_points()
#min max normalization
min_max_normalizer <- function(x)
{
num <- x - min(x)
denom <- max(x) - min(x)
return (num/denom)
}
normalized_iris <- as.data.frame(lapply(iris[1:4], min_max_normalizer))
summary(normalized_iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.2222 1st Qu.:0.3333 1st Qu.:0.1017 1st Qu.:0.08333
## Median :0.4167 Median :0.4167 Median :0.5678 Median :0.50000
## Mean :0.4287 Mean :0.4406 Mean :0.4675 Mean :0.45806
## 3rd Qu.:0.5833 3rd Qu.:0.5417 3rd Qu.:0.6949 3rd Qu.:0.70833
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.00000
#outcome distribution
table(iris$Species)
##
## setosa versicolor virginica
## 50 50 50
#random splitting
set.seed(1234)
random_samples <- sample(2, nrow(iris), replace=TRUE, prob=c(0.67, 0.33))
#train data
iris.training <- iris[random_samples ==1, 1:4]
#train label
iris.trainLabels <- iris[random_samples ==1, 5]
#test data
iris.test <- iris[random_samples ==2, 1:4]
#test label
iris.testLabels <- iris[random_samples ==2, 5]
#training
library(class)
iris_model <- knn(train = iris.training, test = iris.test, cl = iris.trainLabels, k=3)
iris_model
## [1] setosa setosa setosa setosa setosa setosa
## [7] setosa setosa setosa setosa setosa setosa
## [13] versicolor versicolor versicolor versicolor versicolor versicolor
## [19] versicolor versicolor versicolor versicolor versicolor versicolor
## [25] virginica virginica virginica virginica versicolor virginica
## [31] virginica virginica virginica virginica virginica virginica
## [37] virginica virginica virginica virginica
## Levels: setosa versicolor virginica
#evaluation
library(gmodels)
CrossTable(x = iris.testLabels, y = iris_model, prop.chisq=FALSE)
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 40
##
##
## | iris_model
## iris.testLabels | setosa | versicolor | virginica | Row Total |
## ----------------|------------|------------|------------|------------|
## setosa | 12 | 0 | 0 | 12 |
## | 1.000 | 0.000 | 0.000 | 0.300 |
## | 1.000 | 0.000 | 0.000 | |
## | 0.300 | 0.000 | 0.000 | |
## ----------------|------------|------------|------------|------------|
## versicolor | 0 | 12 | 0 | 12 |
## | 0.000 | 1.000 | 0.000 | 0.300 |
## | 0.000 | 0.923 | 0.000 | |
## | 0.000 | 0.300 | 0.000 | |
## ----------------|------------|------------|------------|------------|
## virginica | 0 | 1 | 15 | 16 |
## | 0.000 | 0.062 | 0.938 | 0.400 |
## | 0.000 | 0.077 | 1.000 | |
## | 0.000 | 0.025 | 0.375 | |
## ----------------|------------|------------|------------|------------|
## Column Total | 12 | 13 | 15 | 40 |
## | 0.300 | 0.325 | 0.375 | |
## ----------------|------------|------------|------------|------------|
##
##
#Apriori Algorithm
library(arules)
## Loading required package: Matrix
##
## Attaching package: 'Matrix'
## The following object is masked from 'package:ggvis':
##
## band
##
## Attaching package: 'arules'
## The following objects are masked from 'package:base':
##
## abbreviate, write
data(Adult)
summary(Adult)
## transactions as itemMatrix in sparse format with
## 48842 rows (elements/itemsets/transactions) and
## 115 columns (items) and a density of 0.1089939
##
## most frequent items:
## capital-loss=None capital-gain=None
## 46560 44807
## native-country=United-States race=White
## 43832 41762
## workclass=Private (Other)
## 33906 401333
##
## element (itemset/transaction) length distribution:
## sizes
## 9 10 11 12 13
## 19 971 2067 15623 30162
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 9.00 12.00 13.00 12.53 13.00 13.00
##
## includes extended item information - examples:
## labels variables levels
## 1 age=Young age Young
## 2 age=Middle-aged age Middle-aged
## 3 age=Senior age Senior
##
## includes extended transaction information - examples:
## transactionID
## 1 1
## 2 2
## 3 3
inspect(Adult[0:5])
## items transactionID
## [1] {age=Middle-aged,
## workclass=State-gov,
## education=Bachelors,
## marital-status=Never-married,
## occupation=Adm-clerical,
## relationship=Not-in-family,
## race=White,
## sex=Male,
## capital-gain=Low,
## capital-loss=None,
## hours-per-week=Full-time,
## native-country=United-States,
## income=small} 1
## [2] {age=Senior,
## workclass=Self-emp-not-inc,
## education=Bachelors,
## marital-status=Married-civ-spouse,
## occupation=Exec-managerial,
## relationship=Husband,
## race=White,
## sex=Male,
## capital-gain=None,
## capital-loss=None,
## hours-per-week=Part-time,
## native-country=United-States,
## income=small} 2
## [3] {age=Middle-aged,
## workclass=Private,
## education=HS-grad,
## marital-status=Divorced,
## occupation=Handlers-cleaners,
## relationship=Not-in-family,
## race=White,
## sex=Male,
## capital-gain=None,
## capital-loss=None,
## hours-per-week=Full-time,
## native-country=United-States,
## income=small} 3
## [4] {age=Senior,
## workclass=Private,
## education=11th,
## marital-status=Married-civ-spouse,
## occupation=Handlers-cleaners,
## relationship=Husband,
## race=Black,
## sex=Male,
## capital-gain=None,
## capital-loss=None,
## hours-per-week=Full-time,
## native-country=United-States,
## income=small} 4
## [5] {age=Middle-aged,
## workclass=Private,
## education=Bachelors,
## marital-status=Married-civ-spouse,
## occupation=Prof-specialty,
## relationship=Wife,
## race=Black,
## sex=Female,
## capital-gain=None,
## capital-loss=None,
## hours-per-week=Full-time,
## native-country=Cuba,
## income=small} 5
#Apriori with support=50% confidence =80%
rules <- apriori(Adult, parameter=list(support=0.5, confidence=0.8,target ="rules"))
## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 0.5 1
## maxlen target ext
## 10 rules FALSE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 24421
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[115 item(s), 48842 transaction(s)] done [0.03s].
## sorting and recoding items ... [9 item(s)] done [0.00s].
## creating transaction tree ... done [0.03s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [84 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].
summary(rules)
## set of 84 rules
##
## rule length distribution (lhs + rhs):sizes
## 1 2 3 4
## 4 23 38 19
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 2.000 3.000 2.857 3.000 4.000
##
## summary of quality measures:
## support confidence lift count
## Min. :0.5084 Min. :0.8504 Min. :0.9789 Min. :24832
## 1st Qu.:0.5415 1st Qu.:0.8888 1st Qu.:0.9943 1st Qu.:26447
## Median :0.5897 Median :0.9132 Median :0.9988 Median :28803
## Mean :0.6433 Mean :0.9110 Mean :1.0034 Mean :31422
## 3rd Qu.:0.7490 3rd Qu.:0.9422 3rd Qu.:1.0077 3rd Qu.:36585
## Max. :0.9533 Max. :0.9583 Max. :1.0586 Max. :46560
##
## mining info:
## data ntransactions support confidence
## Adult 48842 0.5 0.8
#top five rules
as(head(sort(rules, by = c("confidence", "support")), n=3), "data.frame")
## rules
## 7 {hours-per-week=Full-time} => {capital-loss=None}
## 15 {workclass=Private} => {capital-loss=None}
## 50 {workclass=Private,native-country=United-States} => {capital-loss=None}
## support confidence lift count
## 7 0.5606650 0.9582531 1.005219 27384
## 15 0.6639982 0.9564974 1.003377 32431
## 50 0.5897179 0.9554818 1.002312 28803
#k-means clustering
kmean_iris <- iris
kmean_iris$Species <- NULL
(clusters <- kmeans(kmean_iris, 3))
## K-means clustering with 3 clusters of sizes 38, 50, 62
##
## Cluster means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1 6.850000 3.073684 5.742105 2.071053
## 2 5.006000 3.428000 1.462000 0.246000
## 3 5.901613 2.748387 4.393548 1.433871
##
## Clustering vector:
## [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [36] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [71] 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 1 1
## [106] 1 3 1 1 1 1 1 1 3 3 1 1 1 1 3 1 3 1 3 1 1 3 3 1 1 1 1 1 3 1 1 1 1 3 1
## [141] 1 1 3 1 1 1 3 1 1 3
##
## Within cluster sum of squares by cluster:
## [1] 23.87947 15.15100 39.82097
## (between_SS / total_SS = 88.4 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss"
## [5] "tot.withinss" "betweenss" "size" "iter"
## [9] "ifault"
table(iris$Species, clusters$cluster)
##
## 1 2 3
## setosa 0 50 0
## versicolor 2 0 48
## virginica 36 0 14
plot(kmean_iris[c("Sepal.Length", "Sepal.Width")],
col=clusters$cluster,pch = c(15,16,17)[as.numeric(clusters$cluster)])
points(clusters$centers[,c("Sepal.Length", "Sepal.Width")], col=1:3,
pch=8, cex=2)
