Definição do problema:

Previsão de occorências de cancer de mama utilizando o dataset do UCI: http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29

Dicionário de dados:

    1. ID number
    1. Diagnosis (M = malignant, B = benign)
  • 3-32) Ten real-valued features are computed for each cell nucleus:
    1. radius (mean of distances from center to points on the perimeter)
    1. texture (standard deviation of gray-scale values)
    1. perimeter
    1. area
    1. smoothness (local variation in radius lengths)
    1. compactness (perimeter^2 / area - 1.0)
    1. concavity (severity of concave portions of the contour)
    1. concave points (number of concave portions of the contour)
    1. symmetry
    1. fractal dimension (“coastline approximation” - 1)

Pacotes Utilizados:

  • library(dplyr)
  • library(tidyr)
  • library(data.table)
  • library(ggplot2)
  • library(caTools)
  • library(gmodels)

Carregando os dados:

setwd("/home/sandro/Documents/4.projetos_DS/machine_learning/prevendo_cancer_de_mama")
getwd()
## [1] "/home/sandro/Documents/4.projetos_DS/machine_learning/prevendo_cancer_de_mama"
df <- read.csv("dataset.csv", stringsAsFactors = FALSE)

Utilizamos StringsAsFactors para que não sejam identificadas nenhuma variável como tipo fator, por tratar-se de um problema de classificaçao.

Vizualizando os dados:

View(df)
str(df)
## 'data.frame':    569 obs. of  32 variables:
##  $ id               : int  87139402 8910251 905520 868871 9012568 906539 925291 87880 862989 89827 ...
##  $ diagnosis        : chr  "B" "B" "B" "B" ...
##  $ radius_mean      : num  12.3 10.6 11 11.3 15.2 ...
##  $ texture_mean     : num  12.4 18.9 16.8 13.4 13.2 ...
##  $ perimeter_mean   : num  78.8 69.3 70.9 73 97.7 ...
##  $ area_mean        : num  464 346 373 385 712 ...
##  $ smoothness_mean  : num  0.1028 0.0969 0.1077 0.1164 0.0796 ...
##  $ compactness_mean : num  0.0698 0.1147 0.078 0.1136 0.0693 ...
##  $ concavity_mean   : num  0.0399 0.0639 0.0305 0.0464 0.0339 ...
##  $ points_mean      : num  0.037 0.0264 0.0248 0.048 0.0266 ...
##  $ symmetry_mean    : num  0.196 0.192 0.171 0.177 0.172 ...
##  $ dimension_mean   : num  0.0595 0.0649 0.0634 0.0607 0.0554 ...
##  $ radius_se        : num  0.236 0.451 0.197 0.338 0.178 ...
##  $ texture_se       : num  0.666 1.197 1.387 1.343 0.412 ...
##  $ perimeter_se     : num  1.67 3.43 1.34 1.85 1.34 ...
##  $ area_se          : num  17.4 27.1 13.5 26.3 17.7 ...
##  $ smoothness_se    : num  0.00805 0.00747 0.00516 0.01127 0.00501 ...
##  $ compactness_se   : num  0.0118 0.03581 0.00936 0.03498 0.01485 ...
##  $ concavity_se     : num  0.0168 0.0335 0.0106 0.0219 0.0155 ...
##  $ points_se        : num  0.01241 0.01365 0.00748 0.01965 0.00915 ...
##  $ symmetry_se      : num  0.0192 0.035 0.0172 0.0158 0.0165 ...
##  $ dimension_se     : num  0.00225 0.00332 0.0022 0.00344 0.00177 ...
##  $ radius_worst     : num  13.5 11.9 12.4 11.9 16.2 ...
##  $ texture_worst    : num  15.6 22.9 26.4 15.8 15.7 ...
##  $ perimeter_worst  : num  87 78.3 79.9 76.5 104.5 ...
##  $ area_worst       : num  549 425 471 434 819 ...
##  $ smoothness_worst : num  0.139 0.121 0.137 0.137 0.113 ...
##  $ compactness_worst: num  0.127 0.252 0.148 0.182 0.174 ...
##  $ concavity_worst  : num  0.1242 0.1916 0.1067 0.0867 0.1362 ...
##  $ points_worst     : num  0.0939 0.0793 0.0743 0.0861 0.0818 ...
##  $ symmetry_worst   : num  0.283 0.294 0.3 0.21 0.249 ...
##  $ dimension_worst  : num  0.0677 0.0759 0.0788 0.0678 0.0677 ...
head(df)
##         id diagnosis radius_mean texture_mean perimeter_mean area_mean
## 1 87139402         B       12.32        12.39          78.85     464.1
## 2  8910251         B       10.60        18.95          69.28     346.4
## 3   905520         B       11.04        16.83          70.92     373.2
## 4   868871         B       11.28        13.39          73.00     384.8
## 5  9012568         B       15.19        13.21          97.65     711.8
## 6   906539         B       11.57        19.04          74.20     409.7
##   smoothness_mean compactness_mean concavity_mean points_mean symmetry_mean
## 1         0.10280          0.06981        0.03987     0.03700        0.1959
## 2         0.09688          0.11470        0.06387     0.02642        0.1922
## 3         0.10770          0.07804        0.03046     0.02480        0.1714
## 4         0.11640          0.11360        0.04635     0.04796        0.1771
## 5         0.07963          0.06934        0.03393     0.02657        0.1721
## 6         0.08546          0.07722        0.05485     0.01428        0.2031
##   dimension_mean radius_se texture_se perimeter_se area_se smoothness_se
## 1        0.05955    0.2360     0.6656        1.670   17.43      0.008045
## 2        0.06491    0.4505     1.1970        3.430   27.10      0.007470
## 3        0.06340    0.1967     1.3870        1.342   13.54      0.005158
## 4        0.06072    0.3384     1.3430        1.851   26.33      0.011270
## 5        0.05544    0.1783     0.4125        1.338   17.72      0.005012
## 6        0.06267    0.2864     1.4400        2.206   20.30      0.007278
##   compactness_se concavity_se points_se symmetry_se dimension_se radius_worst
## 1       0.011800      0.01683  0.012410     0.01924     0.002248        13.50
## 2       0.035810      0.03354  0.013650     0.03504     0.003318        11.88
## 3       0.009355      0.01056  0.007483     0.01718     0.002198        12.41
## 4       0.034980      0.02187  0.019650     0.01580     0.003442        11.92
## 5       0.014850      0.01551  0.009155     0.01647     0.001767        16.20
## 6       0.020470      0.04447  0.008799     0.01868     0.003339        13.07
##   texture_worst perimeter_worst area_worst smoothness_worst compactness_worst
## 1         15.64           86.97      549.1           0.1385            0.1266
## 2         22.94           78.28      424.8           0.1213            0.2515
## 3         26.44           79.93      471.4           0.1369            0.1482
## 4         15.77           76.53      434.0           0.1367            0.1822
## 5         15.73          104.50      819.1           0.1126            0.1737
## 6         26.98           86.43      520.5           0.1249            0.1937
##   concavity_worst points_worst symmetry_worst dimension_worst
## 1         0.12420      0.09391         0.2827         0.06771
## 2         0.19160      0.07926         0.2940         0.07587
## 3         0.10670      0.07431         0.2998         0.07881
## 4         0.08669      0.08611         0.2102         0.06784
## 5         0.13620      0.08178         0.2487         0.06766
## 6         0.25600      0.06664         0.3035         0.08284
summary(df)
##        id             diagnosis          radius_mean      texture_mean  
##  Min.   :     8670   Length:569         Min.   : 6.981   Min.   : 9.71  
##  1st Qu.:   869218   Class :character   1st Qu.:11.700   1st Qu.:16.17  
##  Median :   906024   Mode  :character   Median :13.370   Median :18.84  
##  Mean   : 30371831                      Mean   :14.127   Mean   :19.29  
##  3rd Qu.:  8813129                      3rd Qu.:15.780   3rd Qu.:21.80  
##  Max.   :911320502                      Max.   :28.110   Max.   :39.28  
##  perimeter_mean     area_mean      smoothness_mean   compactness_mean 
##  Min.   : 43.79   Min.   : 143.5   Min.   :0.05263   Min.   :0.01938  
##  1st Qu.: 75.17   1st Qu.: 420.3   1st Qu.:0.08637   1st Qu.:0.06492  
##  Median : 86.24   Median : 551.1   Median :0.09587   Median :0.09263  
##  Mean   : 91.97   Mean   : 654.9   Mean   :0.09636   Mean   :0.10434  
##  3rd Qu.:104.10   3rd Qu.: 782.7   3rd Qu.:0.10530   3rd Qu.:0.13040  
##  Max.   :188.50   Max.   :2501.0   Max.   :0.16340   Max.   :0.34540  
##  concavity_mean     points_mean      symmetry_mean    dimension_mean   
##  Min.   :0.00000   Min.   :0.00000   Min.   :0.1060   Min.   :0.04996  
##  1st Qu.:0.02956   1st Qu.:0.02031   1st Qu.:0.1619   1st Qu.:0.05770  
##  Median :0.06154   Median :0.03350   Median :0.1792   Median :0.06154  
##  Mean   :0.08880   Mean   :0.04892   Mean   :0.1812   Mean   :0.06280  
##  3rd Qu.:0.13070   3rd Qu.:0.07400   3rd Qu.:0.1957   3rd Qu.:0.06612  
##  Max.   :0.42680   Max.   :0.20120   Max.   :0.3040   Max.   :0.09744  
##    radius_se        texture_se      perimeter_se       area_se       
##  Min.   :0.1115   Min.   :0.3602   Min.   : 0.757   Min.   :  6.802  
##  1st Qu.:0.2324   1st Qu.:0.8339   1st Qu.: 1.606   1st Qu.: 17.850  
##  Median :0.3242   Median :1.1080   Median : 2.287   Median : 24.530  
##  Mean   :0.4052   Mean   :1.2169   Mean   : 2.866   Mean   : 40.337  
##  3rd Qu.:0.4789   3rd Qu.:1.4740   3rd Qu.: 3.357   3rd Qu.: 45.190  
##  Max.   :2.8730   Max.   :4.8850   Max.   :21.980   Max.   :542.200  
##  smoothness_se      compactness_se      concavity_se       points_se       
##  Min.   :0.001713   Min.   :0.002252   Min.   :0.00000   Min.   :0.000000  
##  1st Qu.:0.005169   1st Qu.:0.013080   1st Qu.:0.01509   1st Qu.:0.007638  
##  Median :0.006380   Median :0.020450   Median :0.02589   Median :0.010930  
##  Mean   :0.007041   Mean   :0.025478   Mean   :0.03189   Mean   :0.011796  
##  3rd Qu.:0.008146   3rd Qu.:0.032450   3rd Qu.:0.04205   3rd Qu.:0.014710  
##  Max.   :0.031130   Max.   :0.135400   Max.   :0.39600   Max.   :0.052790  
##   symmetry_se        dimension_se        radius_worst   texture_worst  
##  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  
##  perimeter_worst    area_worst     smoothness_worst  compactness_worst
##  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  
##  concavity_worst   points_worst     symmetry_worst   dimension_worst  
##  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.   :0.20750

Vamos dropar a coluna id, e em seguida faremos a normalização:

df$id <- NULL
df$diagnosis <- as.factor(df$diagnosis)
normalizar <- function(x){
  return((x-min(x))/ (max(x)-min(x)))
}

Normalização:

df2 <- as.data.frame(lapply(df[-1], normalizar))
df3 <- as.data.frame(scale(df[-1]))

Verificando proporçao da variável target:

round(prop.table(table(df$diagnosis))*100, digits =2 )
## 
##     B     M 
## 62.74 37.26

Criação do modelo com o KNN:

treino <- df2[1:469, ]
teste <- df2[470:569, ]

Criando o Labels e criando o modelo de KNN

treino_labels <- df[1:469, 1]
teste_labels <- df[470:569, 1]
length(treino_labels)
## [1] 469
length(teste_labels)
## [1] 100
modelo1 <- knn(train = treino,
               test = teste,
               cl = treino_labels,
               k = 21)

Avaliando o modelo:

summary(modelo1)
##  B  M 
## 63 37
CrossTable(x = teste_labels, y = modelo1, prop.chisq = FALSE)
## 
##  
##    Cell Contents
## |-------------------------|
## |                       N |
## |           N / Row Total |
## |           N / Col Total |
## |         N / Table Total |
## |-------------------------|
## 
##  
## Total Observations in Table:  100 
## 
##  
##              | modelo1 
## teste_labels |         B |         M | Row Total | 
## -------------|-----------|-----------|-----------|
##            B |        61 |         0 |        61 | 
##              |     1.000 |     0.000 |     0.610 | 
##              |     0.968 |     0.000 |           | 
##              |     0.610 |     0.000 |           | 
## -------------|-----------|-----------|-----------|
##            M |         2 |        37 |        39 | 
##              |     0.051 |     0.949 |     0.390 | 
##              |     0.032 |     1.000 |           | 
##              |     0.020 |     0.370 |           | 
## -------------|-----------|-----------|-----------|
## Column Total |        63 |        37 |       100 | 
##              |     0.630 |     0.370 |           | 
## -------------|-----------|-----------|-----------|
## 
##

Podemos identificar que, para todos os dados onde foram observados “B”, nosso modelo errou 0.

Já para os dados onde foram observados “M”, nosso modelo teve 2 erros.

Taxa de acerto do modelo1: 98%

Criando outro modelo com a normalização 2:

treino2 <- df3[1:469, ]
teste2 <- df3[470:569, ]
treino_labels <- df[1:469, 1]
teste_labels <- df[470:569, 1]
length(treino_labels)
## [1] 469
length(teste_labels)
## [1] 100
modelo2 <- knn(train = treino2,
               test = teste2,
               cl = treino_labels,
               k = 21)

Avaliando modelo 2:

summary(modelo2)
##  B  M 
## 66 34
CrossTable(x = teste_labels, y = modelo2, prop.chisq = FALSE)
## 
##  
##    Cell Contents
## |-------------------------|
## |                       N |
## |           N / Row Total |
## |           N / Col Total |
## |         N / Table Total |
## |-------------------------|
## 
##  
## Total Observations in Table:  100 
## 
##  
##              | modelo2 
## teste_labels |         B |         M | Row Total | 
## -------------|-----------|-----------|-----------|
##            B |        61 |         0 |        61 | 
##              |     1.000 |     0.000 |     0.610 | 
##              |     0.924 |     0.000 |           | 
##              |     0.610 |     0.000 |           | 
## -------------|-----------|-----------|-----------|
##            M |         5 |        34 |        39 | 
##              |     0.128 |     0.872 |     0.390 | 
##              |     0.076 |     1.000 |           | 
##              |     0.050 |     0.340 |           | 
## -------------|-----------|-----------|-----------|
## Column Total |        66 |        34 |       100 | 
##              |     0.660 |     0.340 |           | 
## -------------|-----------|-----------|-----------|
## 
##

Podemos identificar que, para todos os dados foram observador “B”, nosso modelo errou 0.

Para os dados observados “M”, nosso modelo errou 5.

Taxa de acerto do modelo 2: 95%.