Using K-NN ( K Nearest Neighbour Classification ) to detect Prostate Cancer on the basis of sample data provided by UCI Machine Learning repository.
Step 1 : Data collection
# Read data from hyperlink and remove 1st column
http.path = "https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data"
cancer <- read.csv(http.path,header = FALSE)Step 2 : Prepare data and exploring data
# Remove 1st column (Patient ID) it does not contain any classification specific data
cancer <- cancer[-1]
# Check for missing value and distribution of data
summary(cancer)## V2 V3 V4 V5
## B:357 Min. : 6.981 Min. : 9.71 Min. : 43.79
## M:212 1st Qu.:11.700 1st Qu.:16.17 1st Qu.: 75.17
## Median :13.370 Median :18.84 Median : 86.24
## Mean :14.127 Mean :19.29 Mean : 91.97
## 3rd Qu.:15.780 3rd Qu.:21.80 3rd Qu.:104.10
## Max. :28.110 Max. :39.28 Max. :188.50
## V6 V7 V8 V9
## Min. : 143.5 Min. :0.05263 Min. :0.01938 Min. :0.00000
## 1st Qu.: 420.3 1st Qu.:0.08637 1st Qu.:0.06492 1st Qu.:0.02956
## Median : 551.1 Median :0.09587 Median :0.09263 Median :0.06154
## Mean : 654.9 Mean :0.09636 Mean :0.10434 Mean :0.08880
## 3rd Qu.: 782.7 3rd Qu.:0.10530 3rd Qu.:0.13040 3rd Qu.:0.13070
## Max. :2501.0 Max. :0.16340 Max. :0.34540 Max. :0.42680
## V10 V11 V12 V13
## Min. :0.00000 Min. :0.1060 Min. :0.04996 Min. :0.1115
## 1st Qu.:0.02031 1st Qu.:0.1619 1st Qu.:0.05770 1st Qu.:0.2324
## Median :0.03350 Median :0.1792 Median :0.06154 Median :0.3242
## Mean :0.04892 Mean :0.1812 Mean :0.06280 Mean :0.4052
## 3rd Qu.:0.07400 3rd Qu.:0.1957 3rd Qu.:0.06612 3rd Qu.:0.4789
## Max. :0.20120 Max. :0.3040 Max. :0.09744 Max. :2.8730
## V14 V15 V16 V17
## Min. :0.3602 Min. : 0.757 Min. : 6.802 Min. :0.001713
## 1st Qu.:0.8339 1st Qu.: 1.606 1st Qu.: 17.850 1st Qu.:0.005169
## Median :1.1080 Median : 2.287 Median : 24.530 Median :0.006380
## Mean :1.2169 Mean : 2.866 Mean : 40.337 Mean :0.007041
## 3rd Qu.:1.4740 3rd Qu.: 3.357 3rd Qu.: 45.190 3rd Qu.:0.008146
## Max. :4.8850 Max. :21.980 Max. :542.200 Max. :0.031130
## V18 V19 V20
## Min. :0.002252 Min. :0.00000 Min. :0.000000
## 1st Qu.:0.013080 1st Qu.:0.01509 1st Qu.:0.007638
## Median :0.020450 Median :0.02589 Median :0.010930
## Mean :0.025478 Mean :0.03189 Mean :0.011796
## 3rd Qu.:0.032450 3rd Qu.:0.04205 3rd Qu.:0.014710
## Max. :0.135400 Max. :0.39600 Max. :0.052790
## V21 V22 V23 V24
## Min. :0.007882 Min. :0.0008948 Min. : 7.93 Min. :12.02
## 1st Qu.:0.015160 1st Qu.:0.0022480 1st Qu.:13.01 1st Qu.:21.08
## Median :0.018730 Median :0.0031870 Median :14.97 Median :25.41
## Mean :0.020542 Mean :0.0037949 Mean :16.27 Mean :25.68
## 3rd Qu.:0.023480 3rd Qu.:0.0045580 3rd Qu.:18.79 3rd Qu.:29.72
## Max. :0.078950 Max. :0.0298400 Max. :36.04 Max. :49.54
## V25 V26 V27 V28
## Min. : 50.41 Min. : 185.2 Min. :0.07117 Min. :0.02729
## 1st Qu.: 84.11 1st Qu.: 515.3 1st Qu.:0.11660 1st Qu.:0.14720
## Median : 97.66 Median : 686.5 Median :0.13130 Median :0.21190
## Mean :107.26 Mean : 880.6 Mean :0.13237 Mean :0.25427
## 3rd Qu.:125.40 3rd Qu.:1084.0 3rd Qu.:0.14600 3rd Qu.:0.33910
## Max. :251.20 Max. :4254.0 Max. :0.22260 Max. :1.05800
## V29 V30 V31 V32
## Min. :0.0000 Min. :0.00000 Min. :0.1565 Min. :0.05504
## 1st Qu.:0.1145 1st Qu.:0.06493 1st Qu.:0.2504 1st Qu.:0.07146
## Median :0.2267 Median :0.09993 Median :0.2822 Median :0.08004
## Mean :0.2722 Mean :0.11461 Mean :0.2901 Mean :0.08395
## 3rd Qu.:0.3829 3rd Qu.:0.16140 3rd Qu.:0.3179 3rd Qu.:0.09208
## Max. :1.2520 Max. :0.29100 Max. :0.6638 Max. :0.20750Step 3A : Normalize Numeric data
Since the data in different scale, best practice advices to normalize the data by transforming to comman scale.
Using Min-Max Normalization of Numeric Data
normalize <- function(x){
return (( x - min(x))/(max(x) - min(x)))
}
cancer_n <- as.data.frame(lapply(cancer[2:31],normalize))
cancer_n$diagnosis <- cancer$V2
# summary(cancer_n)Step 4A : Split data into training and validation set
Using 80% data as training set data and remaining 20% data as validation set of data
library(caTools)
set.seed(2017)
SplitRatio <- 0.8
split = sample.split(cancer_n$diagnosis, SplitRatio = 0.8)
train.sample_n <- subset(cancer_n, split == TRUE)
valid.sample_n <- subset(cancer_n, split == FALSE)Step 5A : Training a KNN Model on training dataset
# Include classification package
library(class)
# Calclulate K value. sqrt of no of observation in training set
k.value <- round(sqrt(nrow(train.sample_n)))
# Predict the cancer data
cancer_predict_n <- knn(
train = train.sample_n[,1:30],
test = valid.sample_n[,1:30],
cl = train.sample_n[,31],
k = k.value
)Step 6A : Evaluate Model Performance
library(gmodels)
CrossTable( x = valid.sample_n[,31] ,
y = cancer_predict_n,
prop.chisq = FALSE,
addmargins = FALSE
)##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
## Actual case of B - 71 but predicted cases are 75. There are 113 cases out of which 4 cases are wrongcly classified. hence accuracy of the model is ((113-4)/113) = 96.4%
Evaluate model Performance by transforming z-score standarization.
Step 3B : Z-Score standardization
cancer_z <- as.data.frame(scale(cancer[2:31]))
cancer_z$diagnosis <- cancer$V2
summary(cancer_z)## V3 V4 V5 V6
## Min. :-2.0279 Min. :-2.2273 Min. :-1.9828 Min. :-1.4532
## 1st Qu.:-0.6888 1st Qu.:-0.7253 1st Qu.:-0.6913 1st Qu.:-0.6666
## Median :-0.2149 Median :-0.1045 Median :-0.2358 Median :-0.2949
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4690 3rd Qu.: 0.5837 3rd Qu.: 0.4992 3rd Qu.: 0.3632
## Max. : 3.9678 Max. : 4.6478 Max. : 3.9726 Max. : 5.2459
## V7 V8 V9 V10
## Min. :-3.10935 Min. :-1.6087 Min. :-1.1139 Min. :-1.2607
## 1st Qu.:-0.71034 1st Qu.:-0.7464 1st Qu.:-0.7431 1st Qu.:-0.7373
## Median :-0.03486 Median :-0.2217 Median :-0.3419 Median :-0.3974
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.63564 3rd Qu.: 0.4934 3rd Qu.: 0.5256 3rd Qu.: 0.6464
## Max. : 4.76672 Max. : 4.5644 Max. : 4.2399 Max. : 3.9245
## V11 V12 V13 V14
## Min. :-2.74171 Min. :-1.8183 Min. :-1.0590 Min. :-1.5529
## 1st Qu.:-0.70262 1st Qu.:-0.7220 1st Qu.:-0.6230 1st Qu.:-0.6942
## Median :-0.07156 Median :-0.1781 Median :-0.2920 Median :-0.1973
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.53031 3rd Qu.: 0.4706 3rd Qu.: 0.2659 3rd Qu.: 0.4661
## Max. : 4.48081 Max. : 4.9066 Max. : 8.8991 Max. : 6.6494
## V15 V16 V17 V18
## Min. :-1.0431 Min. :-0.7372 Min. :-1.7745 Min. :-1.2970
## 1st Qu.:-0.6232 1st Qu.:-0.4943 1st Qu.:-0.6235 1st Qu.:-0.6923
## Median :-0.2864 Median :-0.3475 Median :-0.2201 Median :-0.2808
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.2428 3rd Qu.: 0.1067 3rd Qu.: 0.3680 3rd Qu.: 0.3893
## Max. : 9.4537 Max. :11.0321 Max. : 8.0229 Max. : 6.1381
## V19 V20 V21 V22
## Min. :-1.0566 Min. :-1.9118 Min. :-1.5315 Min. :-1.0960
## 1st Qu.:-0.5567 1st Qu.:-0.6739 1st Qu.:-0.6511 1st Qu.:-0.5846
## Median :-0.1989 Median :-0.1404 Median :-0.2192 Median :-0.2297
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.3365 3rd Qu.: 0.4722 3rd Qu.: 0.3554 3rd Qu.: 0.2884
## Max. :12.0621 Max. : 6.6438 Max. : 7.0657 Max. : 9.8429
## V23 V24 V25 V26
## Min. :-1.7254 Min. :-2.22204 Min. :-1.6919 Min. :-1.2213
## 1st Qu.:-0.6743 1st Qu.:-0.74797 1st Qu.:-0.6890 1st Qu.:-0.6416
## Median :-0.2688 Median :-0.04348 Median :-0.2857 Median :-0.3409
## Mean : 0.0000 Mean : 0.00000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.5216 3rd Qu.: 0.65776 3rd Qu.: 0.5398 3rd Qu.: 0.3573
## Max. : 4.0906 Max. : 3.88249 Max. : 4.2836 Max. : 5.9250
## V27 V28 V29 V30
## Min. :-2.6803 Min. :-1.4426 Min. :-1.3047 Min. :-1.7435
## 1st Qu.:-0.6906 1st Qu.:-0.6805 1st Qu.:-0.7558 1st Qu.:-0.7557
## Median :-0.0468 Median :-0.2693 Median :-0.2180 Median :-0.2233
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.5970 3rd Qu.: 0.5392 3rd Qu.: 0.5307 3rd Qu.: 0.7119
## Max. : 3.9519 Max. : 5.1084 Max. : 4.6965 Max. : 2.6835
## V31 V32 diagnosis
## Min. :-2.1591 Min. :-1.6004 B:357
## 1st Qu.:-0.6413 1st Qu.:-0.6913 M:212
## Median :-0.1273 Median :-0.2163
## Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4497 3rd Qu.: 0.4504
## Max. : 6.0407 Max. : 6.8408Step 4B : Split data into training and validation set
Using 80% data as training set data and remaining 20% data as validation set of data
# library(caTools)
set.seed(2017)
SplitRatio <- 0.8
split = sample.split(cancer_z$diagnosis, SplitRatio = 0.8)
train.sample_z <- subset(cancer_z, split == TRUE)
valid.sample_z <- subset(cancer_z, split == FALSE)Step 5B : Training a KNN Model on training dataset
k.value <- round(sqrt(nrow(train.sample_z)))
# Predict the cancer data
cancer_predict_z <- knn(
train = train.sample_z[,1:30],
test = valid.sample_z[,1:30],
cl = train.sample_z[,31],
k = k.value
)Step 6A : Evaluate Model Performance
CrossTable(
x = valid.sample_z[,31] ,
y = cancer_predict_z,
prop.chisq = FALSE,
addmargins = FALSE)##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_z
## valid.sample_z[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 70 | 1 | 71 |
## | 0.986 | 0.014 | 0.628 |
## | 0.921 | 0.027 | |
## | 0.619 | 0.009 | |
## ---------------------|-----------|-----------|-----------|
## M | 6 | 36 | 42 |
## | 0.143 | 0.857 | 0.372 |
## | 0.079 | 0.973 | |
## | 0.053 | 0.319 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 76 | 37 | 113 |
## | 0.673 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
##
## Unfortunately classification is decline, it predited 7 observation incorrectly ( 113 - 7)/113 = 93.8 Model performance can be improve by chaging the K value
Test Alternate K values (1..30)
k_test_n <- function(k.val){
print(paste("Model for K value", k.val))
cancer_predict_n <- knn(
train = train.sample_n[,1:30],
test = valid.sample_n[,1:30],
cl = train.sample_n[,31],
k = k.val
)
t <- CrossTable( x = valid.sample_n[,31] , y = cancer_predict_n, prop.chisq = FALSE)
t$t
}
# K = 1 to 30 ( Normalized transformation )
for ( k.val in 1:30 ){
k_test_n(k.val)
}## [1] "Model for K value 1"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 68 | 3 | 71 |
## | 0.958 | 0.042 | 0.628 |
## | 0.958 | 0.071 | |
## | 0.602 | 0.027 | |
## ---------------------|-----------|-----------|-----------|
## M | 3 | 39 | 42 |
## | 0.071 | 0.929 | 0.372 |
## | 0.042 | 0.929 | |
## | 0.027 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 71 | 42 | 113 |
## | 0.628 | 0.372 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 2"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 69 | 2 | 71 |
## | 0.972 | 0.028 | 0.628 |
## | 0.945 | 0.050 | |
## | 0.611 | 0.018 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.055 | 0.950 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 73 | 40 | 113 |
## | 0.646 | 0.354 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 3"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 67 | 4 | 71 |
## | 0.944 | 0.056 | 0.628 |
## | 0.957 | 0.093 | |
## | 0.593 | 0.035 | |
## ---------------------|-----------|-----------|-----------|
## M | 3 | 39 | 42 |
## | 0.071 | 0.929 | 0.372 |
## | 0.043 | 0.907 | |
## | 0.027 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 70 | 43 | 113 |
## | 0.619 | 0.381 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 4"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 66 | 5 | 71 |
## | 0.930 | 0.070 | 0.628 |
## | 0.957 | 0.114 | |
## | 0.584 | 0.044 | |
## ---------------------|-----------|-----------|-----------|
## M | 3 | 39 | 42 |
## | 0.071 | 0.929 | 0.372 |
## | 0.043 | 0.886 | |
## | 0.027 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 69 | 44 | 113 |
## | 0.611 | 0.389 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 5"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 68 | 3 | 71 |
## | 0.958 | 0.042 | 0.628 |
## | 0.958 | 0.071 | |
## | 0.602 | 0.027 | |
## ---------------------|-----------|-----------|-----------|
## M | 3 | 39 | 42 |
## | 0.071 | 0.929 | 0.372 |
## | 0.042 | 0.929 | |
## | 0.027 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 71 | 42 | 113 |
## | 0.628 | 0.372 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 6"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 68 | 3 | 71 |
## | 0.958 | 0.042 | 0.628 |
## | 0.958 | 0.071 | |
## | 0.602 | 0.027 | |
## ---------------------|-----------|-----------|-----------|
## M | 3 | 39 | 42 |
## | 0.071 | 0.929 | 0.372 |
## | 0.042 | 0.929 | |
## | 0.027 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 71 | 42 | 113 |
## | 0.628 | 0.372 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 7"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 69 | 2 | 71 |
## | 0.972 | 0.028 | 0.628 |
## | 0.958 | 0.049 | |
## | 0.611 | 0.018 | |
## ---------------------|-----------|-----------|-----------|
## M | 3 | 39 | 42 |
## | 0.071 | 0.929 | 0.372 |
## | 0.042 | 0.951 | |
## | 0.027 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 72 | 41 | 113 |
## | 0.637 | 0.363 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 8"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 69 | 2 | 71 |
## | 0.972 | 0.028 | 0.628 |
## | 0.958 | 0.049 | |
## | 0.611 | 0.018 | |
## ---------------------|-----------|-----------|-----------|
## M | 3 | 39 | 42 |
## | 0.071 | 0.929 | 0.372 |
## | 0.042 | 0.951 | |
## | 0.027 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 72 | 41 | 113 |
## | 0.637 | 0.363 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 9"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 68 | 3 | 71 |
## | 0.958 | 0.042 | 0.628 |
## | 0.958 | 0.071 | |
## | 0.602 | 0.027 | |
## ---------------------|-----------|-----------|-----------|
## M | 3 | 39 | 42 |
## | 0.071 | 0.929 | 0.372 |
## | 0.042 | 0.929 | |
## | 0.027 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 71 | 42 | 113 |
## | 0.628 | 0.372 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 10"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 70 | 1 | 71 |
## | 0.986 | 0.014 | 0.628 |
## | 0.946 | 0.026 | |
## | 0.619 | 0.009 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.054 | 0.974 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 74 | 39 | 113 |
## | 0.655 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 11"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 68 | 3 | 71 |
## | 0.958 | 0.042 | 0.628 |
## | 0.958 | 0.071 | |
## | 0.602 | 0.027 | |
## ---------------------|-----------|-----------|-----------|
## M | 3 | 39 | 42 |
## | 0.071 | 0.929 | 0.372 |
## | 0.042 | 0.929 | |
## | 0.027 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 71 | 42 | 113 |
## | 0.628 | 0.372 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 12"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 69 | 2 | 71 |
## | 0.972 | 0.028 | 0.628 |
## | 0.945 | 0.050 | |
## | 0.611 | 0.018 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.055 | 0.950 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 73 | 40 | 113 |
## | 0.646 | 0.354 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 13"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 69 | 2 | 71 |
## | 0.972 | 0.028 | 0.628 |
## | 0.945 | 0.050 | |
## | 0.611 | 0.018 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.055 | 0.950 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 73 | 40 | 113 |
## | 0.646 | 0.354 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 14"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 15"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 16"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 70 | 1 | 71 |
## | 0.986 | 0.014 | 0.628 |
## | 0.946 | 0.026 | |
## | 0.619 | 0.009 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.054 | 0.974 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 74 | 39 | 113 |
## | 0.655 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 17"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 18"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 70 | 1 | 71 |
## | 0.986 | 0.014 | 0.628 |
## | 0.946 | 0.026 | |
## | 0.619 | 0.009 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.054 | 0.974 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 74 | 39 | 113 |
## | 0.655 | 0.345 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 19"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 20"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 21"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 22"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 23"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 24"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.934 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 5 | 37 | 42 |
## | 0.119 | 0.881 | 0.372 |
## | 0.066 | 1.000 | |
## | 0.044 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 76 | 37 | 113 |
## | 0.673 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 25"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 26"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.947 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 4 | 38 | 42 |
## | 0.095 | 0.905 | 0.372 |
## | 0.053 | 1.000 | |
## | 0.035 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 75 | 38 | 113 |
## | 0.664 | 0.336 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 27"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.934 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 5 | 37 | 42 |
## | 0.119 | 0.881 | 0.372 |
## | 0.066 | 1.000 | |
## | 0.044 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 76 | 37 | 113 |
## | 0.673 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 28"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.934 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 5 | 37 | 42 |
## | 0.119 | 0.881 | 0.372 |
## | 0.066 | 1.000 | |
## | 0.044 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 76 | 37 | 113 |
## | 0.673 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 29"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.934 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 5 | 37 | 42 |
## | 0.119 | 0.881 | 0.372 |
## | 0.066 | 1.000 | |
## | 0.044 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 76 | 37 | 113 |
## | 0.673 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
##
##
## [1] "Model for K value 30"
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 113
##
##
## | cancer_predict_n
## valid.sample_n[, 31] | B | M | Row Total |
## ---------------------|-----------|-----------|-----------|
## B | 71 | 0 | 71 |
## | 1.000 | 0.000 | 0.628 |
## | 0.934 | 0.000 | |
## | 0.628 | 0.000 | |
## ---------------------|-----------|-----------|-----------|
## M | 5 | 37 | 42 |
## | 0.119 | 0.881 | 0.372 |
## | 0.066 | 1.000 | |
## | 0.044 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
## Column Total | 76 | 37 | 113 |
## | 0.673 | 0.327 | |
## ---------------------|-----------|-----------|-----------|
##
## K Value test Concusion : K value 14,17,19,20,21, 22,23,25 and 26 are giving almost similar good result.
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