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Predicting Breast Cancer Using Support Vector Machine in R



Breast Cancer Prediction





Installing required package

Importing Libraries

library(devtools)
## Loading required package: usethis
library(readr)
library(knitr)
library(ggplot2)
library(plotly)
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(naniar)
library(tidyverse)
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v tibble  3.1.4     v stringr 1.4.0
## v tidyr   1.1.3     v forcats 0.5.1
## v purrr   0.3.4
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks plotly::filter(), stats::filter()
## x dplyr::lag()    masks stats::lag()
library(ggcorrplot) # finding the correlation with variables 
library(caTools)# splitting data into training set test set 

Importing Data

data_cancer <- read.csv("breastcancer.csv")
head(data_cancer)
##         id diagnosis radius_mean texture_mean perimeter_mean area_mean
## 1   842302         M       17.99        10.38         122.80    1001.0
## 2   842517         M       20.57        17.77         132.90    1326.0
## 3 84300903         M       19.69        21.25         130.00    1203.0
## 4 84348301         M       11.42        20.38          77.58     386.1
## 5 84358402         M       20.29        14.34         135.10    1297.0
## 6   843786         M       12.45        15.70          82.57     477.1
##   smoothness_mean compactness_mean concavity_mean concave.points_mean
## 1         0.11840          0.27760         0.3001             0.14710
## 2         0.08474          0.07864         0.0869             0.07017
## 3         0.10960          0.15990         0.1974             0.12790
## 4         0.14250          0.28390         0.2414             0.10520
## 5         0.10030          0.13280         0.1980             0.10430
## 6         0.12780          0.17000         0.1578             0.08089
##   symmetry_mean fractal_dimension_mean radius_se texture_se perimeter_se
## 1        0.2419                0.07871    1.0950     0.9053        8.589
## 2        0.1812                0.05667    0.5435     0.7339        3.398
## 3        0.2069                0.05999    0.7456     0.7869        4.585
## 4        0.2597                0.09744    0.4956     1.1560        3.445
## 5        0.1809                0.05883    0.7572     0.7813        5.438
## 6        0.2087                0.07613    0.3345     0.8902        2.217
##   area_se smoothness_se compactness_se concavity_se concave.points_se
## 1  153.40      0.006399        0.04904      0.05373           0.01587
## 2   74.08      0.005225        0.01308      0.01860           0.01340
## 3   94.03      0.006150        0.04006      0.03832           0.02058
## 4   27.23      0.009110        0.07458      0.05661           0.01867
## 5   94.44      0.011490        0.02461      0.05688           0.01885
## 6   27.19      0.007510        0.03345      0.03672           0.01137
##   symmetry_se fractal_dimension_se radius_worst texture_worst perimeter_worst
## 1     0.03003             0.006193        25.38         17.33          184.60
## 2     0.01389             0.003532        24.99         23.41          158.80
## 3     0.02250             0.004571        23.57         25.53          152.50
## 4     0.05963             0.009208        14.91         26.50           98.87
## 5     0.01756             0.005115        22.54         16.67          152.20
## 6     0.02165             0.005082        15.47         23.75          103.40
##   area_worst smoothness_worst compactness_worst concavity_worst
## 1     2019.0           0.1622            0.6656          0.7119
## 2     1956.0           0.1238            0.1866          0.2416
## 3     1709.0           0.1444            0.4245          0.4504
## 4      567.7           0.2098            0.8663          0.6869
## 5     1575.0           0.1374            0.2050          0.4000
## 6      741.6           0.1791            0.5249          0.5355
##   concave.points_worst symmetry_worst fractal_dimension_worst
## 1               0.2654         0.4601                 0.11890
## 2               0.1860         0.2750                 0.08902
## 3               0.2430         0.3613                 0.08758
## 4               0.2575         0.6638                 0.17300
## 5               0.1625         0.2364                 0.07678
## 6               0.1741         0.3985                 0.12440
str(data_cancer)
## 'data.frame':    569 obs. of  32 variables:
##  $ id                     : int  842302 842517 84300903 84348301 84358402 843786 844359 84458202 844981 84501001 ...
##  $ diagnosis              : chr  "M" "M" "M" "M" ...
##  $ radius_mean            : num  18 20.6 19.7 11.4 20.3 ...
##  $ texture_mean           : num  10.4 17.8 21.2 20.4 14.3 ...
##  $ perimeter_mean         : num  122.8 132.9 130 77.6 135.1 ...
##  $ area_mean              : num  1001 1326 1203 386 1297 ...
##  $ smoothness_mean        : num  0.1184 0.0847 0.1096 0.1425 0.1003 ...
##  $ compactness_mean       : num  0.2776 0.0786 0.1599 0.2839 0.1328 ...
##  $ concavity_mean         : num  0.3001 0.0869 0.1974 0.2414 0.198 ...
##  $ concave.points_mean    : num  0.1471 0.0702 0.1279 0.1052 0.1043 ...
##  $ symmetry_mean          : num  0.242 0.181 0.207 0.26 0.181 ...
##  $ fractal_dimension_mean : num  0.0787 0.0567 0.06 0.0974 0.0588 ...
##  $ radius_se              : num  1.095 0.543 0.746 0.496 0.757 ...
##  $ texture_se             : num  0.905 0.734 0.787 1.156 0.781 ...
##  $ perimeter_se           : num  8.59 3.4 4.58 3.44 5.44 ...
##  $ area_se                : num  153.4 74.1 94 27.2 94.4 ...
##  $ smoothness_se          : num  0.0064 0.00522 0.00615 0.00911 0.01149 ...
##  $ compactness_se         : num  0.049 0.0131 0.0401 0.0746 0.0246 ...
##  $ concavity_se           : num  0.0537 0.0186 0.0383 0.0566 0.0569 ...
##  $ concave.points_se      : num  0.0159 0.0134 0.0206 0.0187 0.0188 ...
##  $ symmetry_se            : num  0.03 0.0139 0.0225 0.0596 0.0176 ...
##  $ fractal_dimension_se   : num  0.00619 0.00353 0.00457 0.00921 0.00511 ...
##  $ radius_worst           : num  25.4 25 23.6 14.9 22.5 ...
##  $ texture_worst          : num  17.3 23.4 25.5 26.5 16.7 ...
##  $ perimeter_worst        : num  184.6 158.8 152.5 98.9 152.2 ...
##  $ area_worst             : num  2019 1956 1709 568 1575 ...
##  $ smoothness_worst       : num  0.162 0.124 0.144 0.21 0.137 ...
##  $ compactness_worst      : num  0.666 0.187 0.424 0.866 0.205 ...
##  $ concavity_worst        : num  0.712 0.242 0.45 0.687 0.4 ...
##  $ concave.points_worst   : num  0.265 0.186 0.243 0.258 0.163 ...
##  $ symmetry_worst         : num  0.46 0.275 0.361 0.664 0.236 ...
##  $ fractal_dimension_worst: num  0.1189 0.089 0.0876 0.173 0.0768 ...

To visualize all the variable in the data frame

data_1 <- data_cancer %>%
  as.data.frame() %>%
  select_if(is.numeric) %>%
  gather(key = "variable", value = "value")

ggplot(data_1, aes(value)) +
  geom_density() +
  facet_wrap(~variable)

# This visualization reprsent which data require feature scaling : concave points, concave points, fractal dimensiona, #smoothness se,

We have all the data in the numeric form, except diagnosis which is M and B

Lets convert this into numeric only

data_cancer$diagnosis <- factor(data_cancer$diagnosis, levels = c("M","B"), labels = c(0,1))

now converting facrtors to character and then character to numeric, if we convert this directly to numeric it will

give errors

data_cancer$diagnosis <- as.character(data_cancer$diagnosis)

data_cancer$diagnosis <- as.numeric(data_cancer$diagnosis)

str(data_cancer)
## 'data.frame':    569 obs. of  32 variables:
##  $ id                     : int  842302 842517 84300903 84348301 84358402 843786 844359 84458202 844981 84501001 ...
##  $ diagnosis              : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ radius_mean            : num  18 20.6 19.7 11.4 20.3 ...
##  $ texture_mean           : num  10.4 17.8 21.2 20.4 14.3 ...
##  $ perimeter_mean         : num  122.8 132.9 130 77.6 135.1 ...
##  $ area_mean              : num  1001 1326 1203 386 1297 ...
##  $ smoothness_mean        : num  0.1184 0.0847 0.1096 0.1425 0.1003 ...
##  $ compactness_mean       : num  0.2776 0.0786 0.1599 0.2839 0.1328 ...
##  $ concavity_mean         : num  0.3001 0.0869 0.1974 0.2414 0.198 ...
##  $ concave.points_mean    : num  0.1471 0.0702 0.1279 0.1052 0.1043 ...
##  $ symmetry_mean          : num  0.242 0.181 0.207 0.26 0.181 ...
##  $ fractal_dimension_mean : num  0.0787 0.0567 0.06 0.0974 0.0588 ...
##  $ radius_se              : num  1.095 0.543 0.746 0.496 0.757 ...
##  $ texture_se             : num  0.905 0.734 0.787 1.156 0.781 ...
##  $ perimeter_se           : num  8.59 3.4 4.58 3.44 5.44 ...
##  $ area_se                : num  153.4 74.1 94 27.2 94.4 ...
##  $ smoothness_se          : num  0.0064 0.00522 0.00615 0.00911 0.01149 ...
##  $ compactness_se         : num  0.049 0.0131 0.0401 0.0746 0.0246 ...
##  $ concavity_se           : num  0.0537 0.0186 0.0383 0.0566 0.0569 ...
##  $ concave.points_se      : num  0.0159 0.0134 0.0206 0.0187 0.0188 ...
##  $ symmetry_se            : num  0.03 0.0139 0.0225 0.0596 0.0176 ...
##  $ fractal_dimension_se   : num  0.00619 0.00353 0.00457 0.00921 0.00511 ...
##  $ radius_worst           : num  25.4 25 23.6 14.9 22.5 ...
##  $ texture_worst          : num  17.3 23.4 25.5 26.5 16.7 ...
##  $ perimeter_worst        : num  184.6 158.8 152.5 98.9 152.2 ...
##  $ area_worst             : num  2019 1956 1709 568 1575 ...
##  $ smoothness_worst       : num  0.162 0.124 0.144 0.21 0.137 ...
##  $ compactness_worst      : num  0.666 0.187 0.424 0.866 0.205 ...
##  $ concavity_worst        : num  0.712 0.242 0.45 0.687 0.4 ...
##  $ concave.points_worst   : num  0.265 0.186 0.243 0.258 0.163 ...
##  $ symmetry_worst         : num  0.46 0.275 0.361 0.664 0.236 ...
##  $ fractal_dimension_worst: num  0.1189 0.089 0.0876 0.173 0.0768 ...
view(data_cancer)

Changing the postiion of dependent variable ie. diagnosis to the extreme right of the data to avoid confusion

We will use this by uisng tidyverse function relocate() , .after(), .before() these are very handy function while changing

the position of the columns . Here we need to shift diagnosis column after fractal_dimension_worst

data_cancer <- data_cancer %>% relocate(diagnosis,.after= fractal_dimension_worst)

str(data_cancer)
## 'data.frame':    569 obs. of  32 variables:
##  $ id                     : int  842302 842517 84300903 84348301 84358402 843786 844359 84458202 844981 84501001 ...
##  $ radius_mean            : num  18 20.6 19.7 11.4 20.3 ...
##  $ texture_mean           : num  10.4 17.8 21.2 20.4 14.3 ...
##  $ perimeter_mean         : num  122.8 132.9 130 77.6 135.1 ...
##  $ area_mean              : num  1001 1326 1203 386 1297 ...
##  $ smoothness_mean        : num  0.1184 0.0847 0.1096 0.1425 0.1003 ...
##  $ compactness_mean       : num  0.2776 0.0786 0.1599 0.2839 0.1328 ...
##  $ concavity_mean         : num  0.3001 0.0869 0.1974 0.2414 0.198 ...
##  $ concave.points_mean    : num  0.1471 0.0702 0.1279 0.1052 0.1043 ...
##  $ symmetry_mean          : num  0.242 0.181 0.207 0.26 0.181 ...
##  $ fractal_dimension_mean : num  0.0787 0.0567 0.06 0.0974 0.0588 ...
##  $ radius_se              : num  1.095 0.543 0.746 0.496 0.757 ...
##  $ texture_se             : num  0.905 0.734 0.787 1.156 0.781 ...
##  $ perimeter_se           : num  8.59 3.4 4.58 3.44 5.44 ...
##  $ area_se                : num  153.4 74.1 94 27.2 94.4 ...
##  $ smoothness_se          : num  0.0064 0.00522 0.00615 0.00911 0.01149 ...
##  $ compactness_se         : num  0.049 0.0131 0.0401 0.0746 0.0246 ...
##  $ concavity_se           : num  0.0537 0.0186 0.0383 0.0566 0.0569 ...
##  $ concave.points_se      : num  0.0159 0.0134 0.0206 0.0187 0.0188 ...
##  $ symmetry_se            : num  0.03 0.0139 0.0225 0.0596 0.0176 ...
##  $ fractal_dimension_se   : num  0.00619 0.00353 0.00457 0.00921 0.00511 ...
##  $ radius_worst           : num  25.4 25 23.6 14.9 22.5 ...
##  $ texture_worst          : num  17.3 23.4 25.5 26.5 16.7 ...
##  $ perimeter_worst        : num  184.6 158.8 152.5 98.9 152.2 ...
##  $ area_worst             : num  2019 1956 1709 568 1575 ...
##  $ smoothness_worst       : num  0.162 0.124 0.144 0.21 0.137 ...
##  $ compactness_worst      : num  0.666 0.187 0.424 0.866 0.205 ...
##  $ concavity_worst        : num  0.712 0.242 0.45 0.687 0.4 ...
##  $ concave.points_worst   : num  0.265 0.186 0.243 0.258 0.163 ...
##  $ symmetry_worst         : num  0.46 0.275 0.361 0.664 0.236 ...
##  $ fractal_dimension_worst: num  0.1189 0.089 0.0876 0.173 0.0768 ...
##  $ diagnosis              : num  0 0 0 0 0 0 0 0 0 0 ...
str(data_cancer$diagnosis)
##  num [1:569] 0 0 0 0 0 0 0 0 0 0 ...
data_cancer$diagnosis
##   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [38] 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0
##  [75] 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1
## [112] 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1
## [149] 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0
## [186] 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1
## [223] 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0
## [260] 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1
## [297] 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1
## [334] 1 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0
## [371] 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1
## [408] 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1
## [445] 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1
## [482] 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0
## [519] 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [556] 1 1 1 1 1 1 1 0 0 0 0 0 0 1

Visualising the correlation between datasets

r <- cor(data_cancer, use="complete.obs")
round(r,2)
##                            id radius_mean texture_mean perimeter_mean area_mean
## id                       1.00        0.07         0.10           0.07      0.10
## radius_mean              0.07        1.00         0.32           1.00      0.99
## texture_mean             0.10        0.32         1.00           0.33      0.32
## perimeter_mean           0.07        1.00         0.33           1.00      0.99
## area_mean                0.10        0.99         0.32           0.99      1.00
## smoothness_mean         -0.01        0.17        -0.02           0.21      0.18
## compactness_mean         0.00        0.51         0.24           0.56      0.50
## concavity_mean           0.05        0.68         0.30           0.72      0.69
## concave.points_mean      0.04        0.82         0.29           0.85      0.82
## symmetry_mean           -0.02        0.15         0.07           0.18      0.15
## fractal_dimension_mean  -0.05       -0.31        -0.08          -0.26     -0.28
## radius_se                0.14        0.68         0.28           0.69      0.73
## texture_se              -0.01       -0.10         0.39          -0.09     -0.07
## perimeter_se             0.14        0.67         0.28           0.69      0.73
## area_se                  0.18        0.74         0.26           0.74      0.80
## smoothness_se            0.10       -0.22         0.01          -0.20     -0.17
## compactness_se           0.03        0.21         0.19           0.25      0.21
## concavity_se             0.06        0.19         0.14           0.23      0.21
## concave.points_se        0.08        0.38         0.16           0.41      0.37
## symmetry_se             -0.02       -0.10         0.01          -0.08     -0.07
## fractal_dimension_se     0.03       -0.04         0.05          -0.01     -0.02
## radius_worst             0.08        0.97         0.35           0.97      0.96
## texture_worst            0.06        0.30         0.91           0.30      0.29
## perimeter_worst          0.08        0.97         0.36           0.97      0.96
## area_worst               0.11        0.94         0.34           0.94      0.96
## smoothness_worst         0.01        0.12         0.08           0.15      0.12
## compactness_worst        0.00        0.41         0.28           0.46      0.39
## concavity_worst          0.02        0.53         0.30           0.56      0.51
## concave.points_worst     0.04        0.74         0.30           0.77      0.72
## symmetry_worst          -0.04        0.16         0.11           0.19      0.14
## fractal_dimension_worst -0.03        0.01         0.12           0.05      0.00
## diagnosis               -0.04       -0.73        -0.42          -0.74     -0.71
##                         smoothness_mean compactness_mean concavity_mean
## id                                -0.01             0.00           0.05
## radius_mean                        0.17             0.51           0.68
## texture_mean                      -0.02             0.24           0.30
## perimeter_mean                     0.21             0.56           0.72
## area_mean                          0.18             0.50           0.69
## smoothness_mean                    1.00             0.66           0.52
## compactness_mean                   0.66             1.00           0.88
## concavity_mean                     0.52             0.88           1.00
## concave.points_mean                0.55             0.83           0.92
## symmetry_mean                      0.56             0.60           0.50
## fractal_dimension_mean             0.58             0.57           0.34
## radius_se                          0.30             0.50           0.63
## texture_se                         0.07             0.05           0.08
## perimeter_se                       0.30             0.55           0.66
## area_se                            0.25             0.46           0.62
## smoothness_se                      0.33             0.14           0.10
## compactness_se                     0.32             0.74           0.67
## concavity_se                       0.25             0.57           0.69
## concave.points_se                  0.38             0.64           0.68
## symmetry_se                        0.20             0.23           0.18
## fractal_dimension_se               0.28             0.51           0.45
## radius_worst                       0.21             0.54           0.69
## texture_worst                      0.04             0.25           0.30
## perimeter_worst                    0.24             0.59           0.73
## area_worst                         0.21             0.51           0.68
## smoothness_worst                   0.81             0.57           0.45
## compactness_worst                  0.47             0.87           0.75
## concavity_worst                    0.43             0.82           0.88
## concave.points_worst               0.50             0.82           0.86
## symmetry_worst                     0.39             0.51           0.41
## fractal_dimension_worst            0.50             0.69           0.51
## diagnosis                         -0.36            -0.60          -0.70
##                         concave.points_mean symmetry_mean
## id                                     0.04         -0.02
## radius_mean                            0.82          0.15
## texture_mean                           0.29          0.07
## perimeter_mean                         0.85          0.18
## area_mean                              0.82          0.15
## smoothness_mean                        0.55          0.56
## compactness_mean                       0.83          0.60
## concavity_mean                         0.92          0.50
## concave.points_mean                    1.00          0.46
## symmetry_mean                          0.46          1.00
## fractal_dimension_mean                 0.17          0.48
## radius_se                              0.70          0.30
## texture_se                             0.02          0.13
## perimeter_se                           0.71          0.31
## area_se                                0.69          0.22
## smoothness_se                          0.03          0.19
## compactness_se                         0.49          0.42
## concavity_se                           0.44          0.34
## concave.points_se                      0.62          0.39
## symmetry_se                            0.10          0.45
## fractal_dimension_se                   0.26          0.33
## radius_worst                           0.83          0.19
## texture_worst                          0.29          0.09
## perimeter_worst                        0.86          0.22
## area_worst                             0.81          0.18
## smoothness_worst                       0.45          0.43
## compactness_worst                      0.67          0.47
## concavity_worst                        0.75          0.43
## concave.points_worst                   0.91          0.43
## symmetry_worst                         0.38          0.70
## fractal_dimension_worst                0.37          0.44
## diagnosis                             -0.78         -0.33
##                         fractal_dimension_mean radius_se texture_se
## id                                       -0.05      0.14      -0.01
## radius_mean                              -0.31      0.68      -0.10
## texture_mean                             -0.08      0.28       0.39
## perimeter_mean                           -0.26      0.69      -0.09
## area_mean                                -0.28      0.73      -0.07
## smoothness_mean                           0.58      0.30       0.07
## compactness_mean                          0.57      0.50       0.05
## concavity_mean                            0.34      0.63       0.08
## concave.points_mean                       0.17      0.70       0.02
## symmetry_mean                             0.48      0.30       0.13
## fractal_dimension_mean                    1.00      0.00       0.16
## radius_se                                 0.00      1.00       0.21
## texture_se                                0.16      0.21       1.00
## perimeter_se                              0.04      0.97       0.22
## area_se                                  -0.09      0.95       0.11
## smoothness_se                             0.40      0.16       0.40
## compactness_se                            0.56      0.36       0.23
## concavity_se                              0.45      0.33       0.19
## concave.points_se                         0.34      0.51       0.23
## symmetry_se                               0.35      0.24       0.41
## fractal_dimension_se                      0.69      0.23       0.28
## radius_worst                             -0.25      0.72      -0.11
## texture_worst                            -0.05      0.19       0.41
## perimeter_worst                          -0.21      0.72      -0.10
## area_worst                               -0.23      0.75      -0.08
## smoothness_worst                          0.50      0.14      -0.07
## compactness_worst                         0.46      0.29      -0.09
## concavity_worst                           0.35      0.38      -0.07
## concave.points_worst                      0.18      0.53      -0.12
## symmetry_worst                            0.33      0.09      -0.13
## fractal_dimension_worst                   0.77      0.05      -0.05
## diagnosis                                 0.01     -0.57       0.01
##                         perimeter_se area_se smoothness_se compactness_se
## id                              0.14    0.18          0.10           0.03
## radius_mean                     0.67    0.74         -0.22           0.21
## texture_mean                    0.28    0.26          0.01           0.19
## perimeter_mean                  0.69    0.74         -0.20           0.25
## area_mean                       0.73    0.80         -0.17           0.21
## smoothness_mean                 0.30    0.25          0.33           0.32
## compactness_mean                0.55    0.46          0.14           0.74
## concavity_mean                  0.66    0.62          0.10           0.67
## concave.points_mean             0.71    0.69          0.03           0.49
## symmetry_mean                   0.31    0.22          0.19           0.42
## fractal_dimension_mean          0.04   -0.09          0.40           0.56
## radius_se                       0.97    0.95          0.16           0.36
## texture_se                      0.22    0.11          0.40           0.23
## perimeter_se                    1.00    0.94          0.15           0.42
## area_se                         0.94    1.00          0.08           0.28
## smoothness_se                   0.15    0.08          1.00           0.34
## compactness_se                  0.42    0.28          0.34           1.00
## concavity_se                    0.36    0.27          0.27           0.80
## concave.points_se               0.56    0.42          0.33           0.74
## symmetry_se                     0.27    0.13          0.41           0.39
## fractal_dimension_se            0.24    0.13          0.43           0.80
## radius_worst                    0.70    0.76         -0.23           0.20
## texture_worst                   0.20    0.20         -0.07           0.14
## perimeter_worst                 0.72    0.76         -0.22           0.26
## area_worst                      0.73    0.81         -0.18           0.20
## smoothness_worst                0.13    0.13          0.31           0.23
## compactness_worst               0.34    0.28         -0.06           0.68
## concavity_worst                 0.42    0.39         -0.06           0.64
## concave.points_worst            0.55    0.54         -0.10           0.48
## symmetry_worst                  0.11    0.07         -0.11           0.28
## fractal_dimension_worst         0.09    0.02          0.10           0.59
## diagnosis                      -0.56   -0.55          0.07          -0.29
##                         concavity_se concave.points_se symmetry_se
## id                              0.06              0.08       -0.02
## radius_mean                     0.19              0.38       -0.10
## texture_mean                    0.14              0.16        0.01
## perimeter_mean                  0.23              0.41       -0.08
## area_mean                       0.21              0.37       -0.07
## smoothness_mean                 0.25              0.38        0.20
## compactness_mean                0.57              0.64        0.23
## concavity_mean                  0.69              0.68        0.18
## concave.points_mean             0.44              0.62        0.10
## symmetry_mean                   0.34              0.39        0.45
## fractal_dimension_mean          0.45              0.34        0.35
## radius_se                       0.33              0.51        0.24
## texture_se                      0.19              0.23        0.41
## perimeter_se                    0.36              0.56        0.27
## area_se                         0.27              0.42        0.13
## smoothness_se                   0.27              0.33        0.41
## compactness_se                  0.80              0.74        0.39
## concavity_se                    1.00              0.77        0.31
## concave.points_se               0.77              1.00        0.31
## symmetry_se                     0.31              0.31        1.00
## fractal_dimension_se            0.73              0.61        0.37
## radius_worst                    0.19              0.36       -0.13
## texture_worst                   0.10              0.09       -0.08
## perimeter_worst                 0.23              0.39       -0.10
## area_worst                      0.19              0.34       -0.11
## smoothness_worst                0.17              0.22       -0.01
## compactness_worst               0.48              0.45        0.06
## concavity_worst                 0.66              0.55        0.04
## concave.points_worst            0.44              0.60       -0.03
## symmetry_worst                  0.20              0.14        0.39
## fractal_dimension_worst         0.44              0.31        0.08
## diagnosis                      -0.25             -0.41        0.01
##                         fractal_dimension_se radius_worst texture_worst
## id                                      0.03         0.08          0.06
## radius_mean                            -0.04         0.97          0.30
## texture_mean                            0.05         0.35          0.91
## perimeter_mean                         -0.01         0.97          0.30
## area_mean                              -0.02         0.96          0.29
## smoothness_mean                         0.28         0.21          0.04
## compactness_mean                        0.51         0.54          0.25
## concavity_mean                          0.45         0.69          0.30
## concave.points_mean                     0.26         0.83          0.29
## symmetry_mean                           0.33         0.19          0.09
## fractal_dimension_mean                  0.69        -0.25         -0.05
## radius_se                               0.23         0.72          0.19
## texture_se                              0.28        -0.11          0.41
## perimeter_se                            0.24         0.70          0.20
## area_se                                 0.13         0.76          0.20
## smoothness_se                           0.43        -0.23         -0.07
## compactness_se                          0.80         0.20          0.14
## concavity_se                            0.73         0.19          0.10
## concave.points_se                       0.61         0.36          0.09
## symmetry_se                             0.37        -0.13         -0.08
## fractal_dimension_se                    1.00        -0.04          0.00
## radius_worst                           -0.04         1.00          0.36
## texture_worst                           0.00         0.36          1.00
## perimeter_worst                         0.00         0.99          0.37
## area_worst                             -0.02         0.98          0.35
## smoothness_worst                        0.17         0.22          0.23
## compactness_worst                       0.39         0.48          0.36
## concavity_worst                         0.38         0.57          0.37
## concave.points_worst                    0.22         0.79          0.36
## symmetry_worst                          0.11         0.24          0.23
## fractal_dimension_worst                 0.59         0.09          0.22
## diagnosis                              -0.08        -0.78         -0.46
##                         perimeter_worst area_worst smoothness_worst
## id                                 0.08       0.11             0.01
## radius_mean                        0.97       0.94             0.12
## texture_mean                       0.36       0.34             0.08
## perimeter_mean                     0.97       0.94             0.15
## area_mean                          0.96       0.96             0.12
## smoothness_mean                    0.24       0.21             0.81
## compactness_mean                   0.59       0.51             0.57
## concavity_mean                     0.73       0.68             0.45
## concave.points_mean                0.86       0.81             0.45
## symmetry_mean                      0.22       0.18             0.43
## fractal_dimension_mean            -0.21      -0.23             0.50
## radius_se                          0.72       0.75             0.14
## texture_se                        -0.10      -0.08            -0.07
## perimeter_se                       0.72       0.73             0.13
## area_se                            0.76       0.81             0.13
## smoothness_se                     -0.22      -0.18             0.31
## compactness_se                     0.26       0.20             0.23
## concavity_se                       0.23       0.19             0.17
## concave.points_se                  0.39       0.34             0.22
## symmetry_se                       -0.10      -0.11            -0.01
## fractal_dimension_se               0.00      -0.02             0.17
## radius_worst                       0.99       0.98             0.22
## texture_worst                      0.37       0.35             0.23
## perimeter_worst                    1.00       0.98             0.24
## area_worst                         0.98       1.00             0.21
## smoothness_worst                   0.24       0.21             1.00
## compactness_worst                  0.53       0.44             0.57
## concavity_worst                    0.62       0.54             0.52
## concave.points_worst               0.82       0.75             0.55
## symmetry_worst                     0.27       0.21             0.49
## fractal_dimension_worst            0.14       0.08             0.62
## diagnosis                         -0.78      -0.73            -0.42
##                         compactness_worst concavity_worst concave.points_worst
## id                                   0.00            0.02                 0.04
## radius_mean                          0.41            0.53                 0.74
## texture_mean                         0.28            0.30                 0.30
## perimeter_mean                       0.46            0.56                 0.77
## area_mean                            0.39            0.51                 0.72
## smoothness_mean                      0.47            0.43                 0.50
## compactness_mean                     0.87            0.82                 0.82
## concavity_mean                       0.75            0.88                 0.86
## concave.points_mean                  0.67            0.75                 0.91
## symmetry_mean                        0.47            0.43                 0.43
## fractal_dimension_mean               0.46            0.35                 0.18
## radius_se                            0.29            0.38                 0.53
## texture_se                          -0.09           -0.07                -0.12
## perimeter_se                         0.34            0.42                 0.55
## area_se                              0.28            0.39                 0.54
## smoothness_se                       -0.06           -0.06                -0.10
## compactness_se                       0.68            0.64                 0.48
## concavity_se                         0.48            0.66                 0.44
## concave.points_se                    0.45            0.55                 0.60
## symmetry_se                          0.06            0.04                -0.03
## fractal_dimension_se                 0.39            0.38                 0.22
## radius_worst                         0.48            0.57                 0.79
## texture_worst                        0.36            0.37                 0.36
## perimeter_worst                      0.53            0.62                 0.82
## area_worst                           0.44            0.54                 0.75
## smoothness_worst                     0.57            0.52                 0.55
## compactness_worst                    1.00            0.89                 0.80
## concavity_worst                      0.89            1.00                 0.86
## concave.points_worst                 0.80            0.86                 1.00
## symmetry_worst                       0.61            0.53                 0.50
## fractal_dimension_worst              0.81            0.69                 0.51
## diagnosis                           -0.59           -0.66                -0.79
##                         symmetry_worst fractal_dimension_worst diagnosis
## id                               -0.04                   -0.03     -0.04
## radius_mean                       0.16                    0.01     -0.73
## texture_mean                      0.11                    0.12     -0.42
## perimeter_mean                    0.19                    0.05     -0.74
## area_mean                         0.14                    0.00     -0.71
## smoothness_mean                   0.39                    0.50     -0.36
## compactness_mean                  0.51                    0.69     -0.60
## concavity_mean                    0.41                    0.51     -0.70
## concave.points_mean               0.38                    0.37     -0.78
## symmetry_mean                     0.70                    0.44     -0.33
## fractal_dimension_mean            0.33                    0.77      0.01
## radius_se                         0.09                    0.05     -0.57
## texture_se                       -0.13                   -0.05      0.01
## perimeter_se                      0.11                    0.09     -0.56
## area_se                           0.07                    0.02     -0.55
## smoothness_se                    -0.11                    0.10      0.07
## compactness_se                    0.28                    0.59     -0.29
## concavity_se                      0.20                    0.44     -0.25
## concave.points_se                 0.14                    0.31     -0.41
## symmetry_se                       0.39                    0.08      0.01
## fractal_dimension_se              0.11                    0.59     -0.08
## radius_worst                      0.24                    0.09     -0.78
## texture_worst                     0.23                    0.22     -0.46
## perimeter_worst                   0.27                    0.14     -0.78
## area_worst                        0.21                    0.08     -0.73
## smoothness_worst                  0.49                    0.62     -0.42
## compactness_worst                 0.61                    0.81     -0.59
## concavity_worst                   0.53                    0.69     -0.66
## concave.points_worst              0.50                    0.51     -0.79
## symmetry_worst                    1.00                    0.54     -0.42
## fractal_dimension_worst           0.54                    1.00     -0.32
## diagnosis                        -0.42                   -0.32      1.00

It provides a solution for reordering the correlation matrix and displays the significance level on the correlogram.

#It includes also a function for computing a matrix of correlation p-value

ggcorrplot(r)

ggcorrplot(r, hc.order = TRUE, type = "lower",
           outline.col = "white",
           ggtheme = ggplot2::theme_gray,
           colors = c("#6D9EC1", "white", "#E46726"))

Visualising the missing values in the data using naniar

vis_miss(data_cancer)

# as per the above graph there is not missing values lets check this other way

sum(is.na(data_cancer))
## [1] 0

Lets check whther every columns have no missing values


sapply(data_cancer,function(x)sum(is.na(x)))

By using the above three methods it is confirmed that above data has no missing values

Spliting data into training set and test set

split = sample.split(data_cancer$diagnosis, SplitRatio = 0.75)

train_set = subset(data_cancer, split ==TRUE)
test_set = subset(data_cancer, split ==FALSE)

View(train_set)

Feature scaling on few columns : colun 2 to colmn 5

train_set[, 2:5] = scale(train_set[ , 2:5])
test_set[, 2:5] = scale(test_set[ , 2:5])
view(train_set)

data.frame(colnames(data_cancer)) # to know the index number of each colums 
##      colnames.data_cancer.
## 1                       id
## 2              radius_mean
## 3             texture_mean
## 4           perimeter_mean
## 5                area_mean
## 6          smoothness_mean
## 7         compactness_mean
## 8           concavity_mean
## 9      concave.points_mean
## 10           symmetry_mean
## 11  fractal_dimension_mean
## 12               radius_se
## 13              texture_se
## 14            perimeter_se
## 15                 area_se
## 16           smoothness_se
## 17          compactness_se
## 18            concavity_se
## 19       concave.points_se
## 20             symmetry_se
## 21    fractal_dimension_se
## 22            radius_worst
## 23           texture_worst
## 24         perimeter_worst
## 25              area_worst
## 26        smoothness_worst
## 27       compactness_worst
## 28         concavity_worst
## 29    concave.points_worst
## 30          symmetry_worst
## 31 fractal_dimension_worst
## 32               diagnosis

Feature scaling on few columns : colun 14 to colmn 15

train_set[, 14:15] = scale(train_set[ , 14:15]) test_set[, 14:15] = scale(test_set[ , 14:15]) view(train_set)

Feature scaling on few columns : colun 22 to colmn 25

train_set[, 22:25] = scale(train_set[ , 22:25])
test_set[, 22:25] = scale(test_set[ , 22:25])
view(train_set)

view(test_set)

Multiple regresssion model :

regressor = lm(diagnosis~.,data = train_set)

#The visreg package provides tools for visualizing these conditional relationships.

#The visreg function takes (1) the model and (2) the variable of interest and plots the conditional relationship, controlling for the other variables. The option gg = TRUE is used to produce a ggplot2 graph.

conditional plot of diagnosis vs. texture mean , we can compare diagnosis with other variable of the data to check relationship

Logistic Regression Model

regressor_lr <- glm(formula = diagnosis ~ ., 
                    family = binomial , 
                    data=data_cancer)
## Warning: glm.fit: algorithm did not converge
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Predicting the test set results

prob_pred = predict(regressor_lr, type = 'response', newdata = test_set[-32])

y_pred = ifelse(prob_pred > 0.5, 1,0)

Making confusion matrix

cm = table(test_set [ , 32], y_pred)
cm
##    y_pred
##      0
##   0 53
##   1 89

SVM Model

library(e1071)

regressor_svm <- svm(formula = diagnosis ~ ., 
                     data=train_set,
                     type = 'C-classification',
                     kernel = 'linear')

Predicting the test set results

y_pred1 = predict(regressor_svm, newdata = test_set[-32])

Making confusion matrix

cm = table(test_set [ , 32], y_pred1)
cm
##    y_pred1
##      0  1
##   0 51  2
##   1  2 87



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