Klasifikasi Diagnosis Kanker Payudara Menggunakan Support Vector Machine (SVM): Studi Kasus Breast Cancer Wisconsin Diagnostic Dataset
Andrew Hosea Talakua - 140720250008
2026-06-14
1 Abstrak
Kanker payudara merupakan salah satu jenis kanker yang memiliki tingkat kejadian tinggi di dunia dan memerlukan diagnosis yang akurat untuk meningkatkan peluang keberhasilan terapi. Perkembangan machine learning memberikan peluang untuk membangun model klasifikasi yang mampu membantu proses diagnosis secara lebih cepat dan objektif. Penelitian ini bertujuan membangun model Support Vector Machine (SVM) untuk mengklasifikasikan diagnosis tumor payudara ke dalam kategori malignant dan benign menggunakan Breast Cancer Wisconsin Diagnostic Dataset dari UCI Machine Learning Repository. Dua kernel dibandingkan dalam penelitian ini, yaitu kernel linear dan kernel radial basis function (RBF). Data dibagi menjadi data latih dan data uji secara stratified dengan proporsi 80:20. Selanjutnya dilakukan standardisasi prediktor numerik dan tuning parameter menggunakan 5-fold cross-validation. Evaluasi model dilakukan menggunakan confusion matrix, accuracy, sensitivity, specificity, dan Area Under Curve (AUC). Hasil penelitian diharapkan dapat menunjukkan kemampuan SVM dalam mendeteksi kasus kanker ganas serta memberikan gambaran mengenai keunggulan kernel RBF dibandingkan kernel linear dalam menangkap pola kompleks pada data medis.
Kata Kunci: Support Vector Machine, Klasifikasi, Kanker Payudara, Machine Learning, Breast Cancer Wisconsin Diagnostic Dataset
2 1 Pendahuluan
2.1 1.1 Latar Belakang
Kanker payudara merupakan salah satu masalah kesehatan utama yang menyebabkan tingginya angka morbiditas dan mortalitas pada perempuan di berbagai negara. Menurut berbagai penelitian medis, deteksi dini menjadi faktor penting dalam meningkatkan efektivitas pengobatan dan peluang kesembuhan pasien. Oleh karena itu, diperlukan metode yang mampu membantu proses diagnosis secara cepat, konsisten, dan akurat.
Perkembangan machine learning telah membuka peluang pemanfaatan algoritma komputasi dalam bidang kesehatan. Salah satu metode yang banyak digunakan untuk klasifikasi adalah Support Vector Machine (SVM). SVM memiliki kemampuan yang baik dalam menangani data berdimensi tinggi dan menghasilkan batas pemisah optimal antar kelas melalui konsep hyperplane dan margin maksimum.
Breast Cancer Wisconsin Diagnostic Dataset (WDBC) merupakan dataset yang banyak digunakan dalam penelitian klasifikasi medis. Dataset ini berisi karakteristik inti sel hasil pemeriksaan Fine Needle Aspirate (FNA) yang digunakan untuk membedakan tumor ganas (malignant) dan tumor jinak (benign).
2.2 1.2 Rumusan Masalah
Dapatkah karakteristik inti sel digunakan untuk mengklasifikasikan tumor sebagai malignant atau benign menggunakan metode Support Vector Machine?
2.3 1.3 Tujuan Penelitian
Penelitian ini bertujuan untuk:
- Membangun model klasifikasi menggunakan SVM kernel linear.
- Membangun model klasifikasi menggunakan SVM kernel radial basis function (RBF).
- Membandingkan performa kernel linear dan kernel RBF.
- Mengevaluasi kemampuan model dalam mendeteksi kasus malignant.
2.4 1.4 Manfaat Penelitian
Penelitian ini diharapkan dapat memberikan pemahaman mengenai penerapan machine learning pada bidang kesehatan serta menunjukkan efektivitas metode SVM dalam klasifikasi diagnosis kanker payudara.
3 2 Deskripsi Data
3.1 2.1 Sumber Data
Dataset yang digunakan adalah Breast Cancer Wisconsin Diagnostic (WDBC) yang diperoleh dari UCI Machine Learning Repository.
Sumber data:
https://archive.ics.uci.edu/dataset/17/breast+cancer+wisconsin+diagnostic
3.2 2.2 Karakteristik Dataset
Dataset terdiri atas 569 observasi dengan 30 variabel prediktor numerik dan satu variabel target berupa diagnosis tumor.
Variabel target:
- Malignant (M)
- Benign (B)
Unit observasi merupakan hasil pemeriksaan Fine Needle Aspirate (FNA) dari massa payudara.
4 3 Persiapan Analisis
library(tidyverse)
library(tidymodels)
library(kernlab)
library(corrplot)
library(knitr)
library(GGally)
theme_set(theme_minimal())
set.seed(15062026)5 4 Akuisisi Data
url_wdbc <- paste0(
"https://archive.ics.uci.edu/ml/machine-learning-databases/",
"breast-cancer-wisconsin/wdbc.data"
)
feature_names <- c(
"radius", "texture", "perimeter", "area",
"smoothness", "compactness", "concavity",
"concave_points", "symmetry",
"fractal_dimension"
)
col_names <- c(
"id",
"diagnosis",
paste0(feature_names, "_mean"),
paste0(feature_names, "_se"),
paste0(feature_names, "_worst")
)
wdbc <- read_csv(
url_wdbc,
col_names = col_names,
show_col_types = FALSE
) %>%
mutate(
diagnosis = factor(
if_else(
diagnosis == "M",
"Malignant",
"Benign"
),
levels = c(
"Malignant",
"Benign"
)
)
)6 5 Exploratory Data Analysis (EDA)
6.1 5.1 Dimensi Dataset
dim(wdbc)## [1] 569 32Interpretasi:
Output menunjukkan jumlah observasi dan jumlah variabel yang tersedia dalam dataset.
6.2 5.2 Struktur Data
glimpse(wdbc)## Rows: 569
## Columns: 32
## $ id <dbl> 842302, 842517, 84300903, 84348301, 84358402, …
## $ diagnosis <fct> Malignant, Malignant, Malignant, Malignant, Ma…
## $ radius_mean <dbl> 17.990, 20.570, 19.690, 11.420, 20.290, 12.450…
## $ texture_mean <dbl> 10.38, 17.77, 21.25, 20.38, 14.34, 15.70, 19.9…
## $ perimeter_mean <dbl> 122.80, 132.90, 130.00, 77.58, 135.10, 82.57, …
## $ area_mean <dbl> 1001.0, 1326.0, 1203.0, 386.1, 1297.0, 477.1, …
## $ smoothness_mean <dbl> 0.11840, 0.08474, 0.10960, 0.14250, 0.10030, 0…
## $ compactness_mean <dbl> 0.27760, 0.07864, 0.15990, 0.28390, 0.13280, 0…
## $ concavity_mean <dbl> 0.30010, 0.08690, 0.19740, 0.24140, 0.19800, 0…
## $ concave_points_mean <dbl> 0.14710, 0.07017, 0.12790, 0.10520, 0.10430, 0…
## $ symmetry_mean <dbl> 0.2419, 0.1812, 0.2069, 0.2597, 0.1809, 0.2087…
## $ fractal_dimension_mean <dbl> 0.07871, 0.05667, 0.05999, 0.09744, 0.05883, 0…
## $ radius_se <dbl> 1.0950, 0.5435, 0.7456, 0.4956, 0.7572, 0.3345…
## $ texture_se <dbl> 0.9053, 0.7339, 0.7869, 1.1560, 0.7813, 0.8902…
## $ perimeter_se <dbl> 8.589, 3.398, 4.585, 3.445, 5.438, 2.217, 3.18…
## $ area_se <dbl> 153.40, 74.08, 94.03, 27.23, 94.44, 27.19, 53.…
## $ smoothness_se <dbl> 0.006399, 0.005225, 0.006150, 0.009110, 0.0114…
## $ compactness_se <dbl> 0.049040, 0.013080, 0.040060, 0.074580, 0.0246…
## $ concavity_se <dbl> 0.05373, 0.01860, 0.03832, 0.05661, 0.05688, 0…
## $ concave_points_se <dbl> 0.015870, 0.013400, 0.020580, 0.018670, 0.0188…
## $ symmetry_se <dbl> 0.03003, 0.01389, 0.02250, 0.05963, 0.01756, 0…
## $ fractal_dimension_se <dbl> 0.006193, 0.003532, 0.004571, 0.009208, 0.0051…
## $ radius_worst <dbl> 25.38, 24.99, 23.57, 14.91, 22.54, 15.47, 22.8…
## $ texture_worst <dbl> 17.33, 23.41, 25.53, 26.50, 16.67, 23.75, 27.6…
## $ perimeter_worst <dbl> 184.60, 158.80, 152.50, 98.87, 152.20, 103.40,…
## $ area_worst <dbl> 2019.0, 1956.0, 1709.0, 567.7, 1575.0, 741.6, …
## $ smoothness_worst <dbl> 0.1622, 0.1238, 0.1444, 0.2098, 0.1374, 0.1791…
## $ compactness_worst <dbl> 0.6656, 0.1866, 0.4245, 0.8663, 0.2050, 0.5249…
## $ concavity_worst <dbl> 0.71190, 0.24160, 0.45040, 0.68690, 0.40000, 0…
## $ concave_points_worst <dbl> 0.26540, 0.18600, 0.24300, 0.25750, 0.16250, 0…
## $ symmetry_worst <dbl> 0.4601, 0.2750, 0.3613, 0.6638, 0.2364, 0.3985…
## $ fractal_dimension_worst <dbl> 0.11890, 0.08902, 0.08758, 0.17300, 0.07678, 0…6.3 5.3 Pemeriksaan Missing Value
missing_tbl <- data.frame(
Variable = names(wdbc),
Missing = colSums(is.na(wdbc))
)
kable(
missing_tbl,
caption = "Jumlah Missing Value pada Setiap Variabel"
)| Variable | Missing | |
|---|---|---|
| id | id | 0 |
| diagnosis | diagnosis | 0 |
| radius_mean | radius_mean | 0 |
| texture_mean | texture_mean | 0 |
| perimeter_mean | perimeter_mean | 0 |
| area_mean | area_mean | 0 |
| smoothness_mean | smoothness_mean | 0 |
| compactness_mean | compactness_mean | 0 |
| concavity_mean | concavity_mean | 0 |
| concave_points_mean | concave_points_mean | 0 |
| symmetry_mean | symmetry_mean | 0 |
| fractal_dimension_mean | fractal_dimension_mean | 0 |
| radius_se | radius_se | 0 |
| texture_se | texture_se | 0 |
| perimeter_se | perimeter_se | 0 |
| area_se | area_se | 0 |
| smoothness_se | smoothness_se | 0 |
| compactness_se | compactness_se | 0 |
| concavity_se | concavity_se | 0 |
| concave_points_se | concave_points_se | 0 |
| symmetry_se | symmetry_se | 0 |
| fractal_dimension_se | fractal_dimension_se | 0 |
| radius_worst | radius_worst | 0 |
| texture_worst | texture_worst | 0 |
| perimeter_worst | perimeter_worst | 0 |
| area_worst | area_worst | 0 |
| smoothness_worst | smoothness_worst | 0 |
| compactness_worst | compactness_worst | 0 |
| concavity_worst | concavity_worst | 0 |
| concave_points_worst | concave_points_worst | 0 |
| symmetry_worst | symmetry_worst | 0 |
| fractal_dimension_worst | fractal_dimension_worst | 0 |
Interpretasi:
Berdasarkan hasil pemeriksaan, tidak ditemukan nilai hilang pada seluruh variabel sehingga tidak diperlukan proses imputasi data.
6.4 5.4 Distribusi Kelas
class_dist <- wdbc %>%
count(diagnosis) %>%
mutate(
proporsi = n/sum(n)
)
kable(
class_dist,
digits = 3,
caption = "Distribusi Kelas Diagnosis"
)| diagnosis | n | proporsi |
|---|---|---|
| Malignant | 212 | 0.373 |
| Benign | 357 | 0.627 |
6.4.1 Visualisasi Distribusi Kelas
ggplot(
class_dist,
aes(
x = diagnosis,
y = n,
fill = diagnosis
)
) +
geom_col() +
labs(
title = "Distribusi Diagnosis Tumor",
x = "Diagnosis",
y = "Frekuensi"
)
Interpretasi:
Distribusi kelas menunjukkan jumlah observasi pada masing-masing kategori diagnosis. Informasi ini penting karena proporsi kelas perlu dipertahankan pada proses train-test split melalui teknik stratified sampling.
6.5 5.5 Statistik Deskriptif
summary(
select(
wdbc,
-id
)
)## diagnosis radius_mean texture_mean perimeter_mean
## Malignant:212 Min. : 6.981 Min. : 9.71 Min. : 43.79
## Benign :357 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
## area_mean smoothness_mean compactness_mean concavity_mean
## 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
## concave_points_mean symmetry_mean fractal_dimension_mean radius_se
## 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
## texture_se perimeter_se area_se smoothness_se
## 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
## compactness_se concavity_se concave_points_se symmetry_se
## Min. :0.002252 Min. :0.00000 Min. :0.000000 Min. :0.007882
## 1st Qu.:0.013080 1st Qu.:0.01509 1st Qu.:0.007638 1st Qu.:0.015160
## Median :0.020450 Median :0.02589 Median :0.010930 Median :0.018730
## Mean :0.025478 Mean :0.03189 Mean :0.011796 Mean :0.020542
## 3rd Qu.:0.032450 3rd Qu.:0.04205 3rd Qu.:0.014710 3rd Qu.:0.023480
## Max. :0.135400 Max. :0.39600 Max. :0.052790 Max. :0.078950
## fractal_dimension_se radius_worst texture_worst perimeter_worst
## Min. :0.0008948 Min. : 7.93 Min. :12.02 Min. : 50.41
## 1st Qu.:0.0022480 1st Qu.:13.01 1st Qu.:21.08 1st Qu.: 84.11
## Median :0.0031870 Median :14.97 Median :25.41 Median : 97.66
## Mean :0.0037949 Mean :16.27 Mean :25.68 Mean :107.26
## 3rd Qu.:0.0045580 3rd Qu.:18.79 3rd Qu.:29.72 3rd Qu.:125.40
## Max. :0.0298400 Max. :36.04 Max. :49.54 Max. :251.20
## area_worst smoothness_worst compactness_worst concavity_worst
## Min. : 185.2 Min. :0.07117 Min. :0.02729 Min. :0.0000
## 1st Qu.: 515.3 1st Qu.:0.11660 1st Qu.:0.14720 1st Qu.:0.1145
## Median : 686.5 Median :0.13130 Median :0.21190 Median :0.2267
## Mean : 880.6 Mean :0.13237 Mean :0.25427 Mean :0.2722
## 3rd Qu.:1084.0 3rd Qu.:0.14600 3rd Qu.:0.33910 3rd Qu.:0.3829
## Max. :4254.0 Max. :0.22260 Max. :1.05800 Max. :1.2520
## concave_points_worst symmetry_worst fractal_dimension_worst
## Min. :0.00000 Min. :0.1565 Min. :0.05504
## 1st Qu.:0.06493 1st Qu.:0.2504 1st Qu.:0.07146
## Median :0.09993 Median :0.2822 Median :0.08004
## Mean :0.11461 Mean :0.2901 Mean :0.08395
## 3rd Qu.:0.16140 3rd Qu.:0.3179 3rd Qu.:0.09208
## Max. :0.29100 Max. :0.6638 Max. :0.207506.6 5.6 Visualisasi Variabel Penting
6.6.1 Radius Mean
ggplot(
wdbc,
aes(
radius_mean,
fill = diagnosis
)
) +
geom_density(
alpha = 0.5
) +
labs(
title = "Distribusi Radius Mean"
)
6.6.2 Area Mean
ggplot(
wdbc,
aes(
area_mean,
fill = diagnosis
)
) +
geom_density(
alpha = 0.5
) +
labs(
title = "Distribusi Area Mean"
)
6.6.3 Concavity Mean
ggplot(
wdbc,
aes(
concavity_mean,
fill = diagnosis
)
) +
geom_density(
alpha = 0.5
) +
labs(
title = "Distribusi Concavity Mean"
)
Interpretasi:
Ketiga variabel menunjukkan pola distribusi yang berbeda antara kelas malignant dan benign sehingga berpotensi menjadi prediktor penting dalam proses klasifikasi.
6.7 5.7 Boxplot Variabel Penting
ggplot(
wdbc,
aes(
diagnosis,
radius_mean,
fill = diagnosis
)
) +
geom_boxplot()
Interpretasi:
Boxplot menunjukkan bahwa kelompok malignant cenderung memiliki nilai radius_mean yang lebih tinggi dibandingkan kelompok benign.
6.8 5.8 Korelasi Antar Variabel
cor_matrix <- wdbc %>%
select(
-id,
-diagnosis
) %>%
cor()
corrplot(
cor_matrix,
method = "color",
tl.cex = 0.6,
type = "upper"
)
Interpretasi:
Terlihat adanya korelasi yang tinggi pada beberapa kelompok variabel. Hubungan yang kompleks antar prediktor menjadi salah satu alasan penggunaan metode SVM dalam penelitian ini.
7 6 Prapemrosesan Data
7.1 6.1 Pembagian Data Latih dan Data Uji
Pembagian data dilakukan secara stratified untuk mempertahankan proporsi kelas diagnosis pada data latih dan data uji.
split_obj <- initial_split(
wdbc,
prop = 0.80,
strata = diagnosis
)
train_dat <- training(split_obj)
test_dat <- testing(split_obj)
dim(train_dat)## [1] 454 32dim(test_dat)## [1] 115 327.2 Distribusi Kelas Setelah Split
train_dat %>%
count(diagnosis) %>%
mutate(proporsi = round(n/sum(n), 3))## # A tibble: 2 × 3
## diagnosis n proporsi
## <fct> <int> <dbl>
## 1 Malignant 169 0.372
## 2 Benign 285 0.628test_dat %>%
count(diagnosis) %>%
mutate(proporsi = round(n/sum(n), 3))## # A tibble: 2 × 3
## diagnosis n proporsi
## <fct> <int> <dbl>
## 1 Malignant 43 0.374
## 2 Benign 72 0.626Interpretasi:
Distribusi kelas pada data latih dan data uji relatif seimbang sehingga stratified sampling berhasil mempertahankan proporsi kelas.
7.3 6.2 Cross Validation
folds <- vfold_cv(
train_dat,
v = 5,
strata = diagnosis
)
folds## # 5-fold cross-validation using stratification
## # A tibble: 5 × 2
## splits id
## <list> <chr>
## 1 <split [363/91]> Fold1
## 2 <split [363/91]> Fold2
## 3 <split [363/91]> Fold3
## 4 <split [363/91]> Fold4
## 5 <split [364/90]> Fold5Interpretasi:
Cross-validation digunakan untuk memperoleh estimasi performa model yang lebih stabil selama proses tuning.
7.4 6.3 Standardisasi Variabel
rec_svm <- recipe(
diagnosis ~ .,
data = train_dat
) %>%
update_role(
id,
new_role = "id"
) %>%
step_zv(all_predictors()) %>%
step_normalize(
all_numeric_predictors()
)
rec_svm## ## ── Recipe ──────────────────────────────────────────────────────────────────────## ## ── Inputs## Number of variables by role## outcome: 1
## predictor: 30
## id: 1## ## ── Operations## • Zero variance filter on: all_predictors()## • Centering and scaling for: all_numeric_predictors()Interpretasi:
Normalisasi dilakukan karena SVM sensitif terhadap skala variabel. Proses normalisasi dilakukan hanya menggunakan data latih sehingga tidak terjadi data leakage.
8 7 Metode Support Vector Machine
8.1 7.1 Support Vector Machine
Support Vector Machine (SVM) merupakan metode klasifikasi yang bekerja dengan mencari hyperplane optimal yang mampu memisahkan dua kelas dengan margin maksimum.
Penelitian ini membandingkan dua kernel:
- Kernel Linear
- Kernel Radial Basis Function (RBF)
8.2 7.2 Parameter Tuning
8.2.1 Cost (C)
Parameter cost mengontrol penalti terhadap kesalahan klasifikasi.
- Cost besar → model lebih kompleks
- Cost kecil → model lebih sederhana
8.2.2 Sigma
Parameter sigma digunakan pada kernel RBF untuk mengontrol fleksibilitas batas keputusan.
9 8 Pemodelan SVM Kernel Linear
9.1 8.1 Spesifikasi Model
svm_linear_spec <- svm_linear(
cost = tune()
) %>%
set_engine(
"kernlab",
prob.model = TRUE
) %>%
set_mode(
"classification"
)
svm_linear_spec## Linear Support Vector Machine Model Specification (classification)
##
## Main Arguments:
## cost = tune()
##
## Engine-Specific Arguments:
## prob.model = TRUE
##
## Computational engine: kernlab9.2 8.2 Workflow Model Linear
svm_linear_wf <- workflow() %>%
add_recipe(rec_svm) %>%
add_model(svm_linear_spec)
svm_linear_wf## ══ Workflow ════════════════════════════════════════════════════════════════════
## Preprocessor: Recipe
## Model: svm_linear()
##
## ── Preprocessor ────────────────────────────────────────────────────────────────
## 2 Recipe Steps
##
## • step_zv()
## • step_normalize()
##
## ── Model ───────────────────────────────────────────────────────────────────────
## Linear Support Vector Machine Model Specification (classification)
##
## Main Arguments:
## cost = tune()
##
## Engine-Specific Arguments:
## prob.model = TRUE
##
## Computational engine: kernlab9.3 8.3 Grid Tuning Linear
linear_grid <- grid_regular(
cost(
range = c(-5, 5)
),
levels = 10
)
linear_grid## # A tibble: 10 × 1
## cost
## <dbl>
## 1 0.0312
## 2 0.0675
## 3 0.146
## 4 0.315
## 5 0.680
## 6 1.47
## 7 3.17
## 8 6.86
## 9 14.8
## 10 329.4 8.4 Tuning Model Linear
linear_metrics <- metric_set(
roc_auc,
accuracy,
sens,
spec
)
linear_tuned <- tune_grid(
svm_linear_wf,
resamples = folds,
grid = linear_grid,
metrics = linear_metrics,
control = control_grid(
save_pred = TRUE
)
)9.5 8.5 Ringkasan Tuning Linear
show_best(
linear_tuned,
metric = "roc_auc"
)## # A tibble: 5 × 7
## cost .metric .estimator mean n std_err .config
## <dbl> <chr> <chr> <dbl> <int> <dbl> <chr>
## 1 0.0312 roc_auc binary 0.995 5 0.00265 pre0_mod01_post0
## 2 0.0675 roc_auc binary 0.995 5 0.00327 pre0_mod02_post0
## 3 0.146 roc_auc binary 0.994 5 0.00369 pre0_mod03_post0
## 4 0.680 roc_auc binary 0.994 5 0.00390 pre0_mod05_post0
## 5 0.315 roc_auc binary 0.994 5 0.00371 pre0_mod04_post0collect_metrics(
linear_tuned
)## # A tibble: 40 × 7
## cost .metric .estimator mean n std_err .config
## <dbl> <chr> <chr> <dbl> <int> <dbl> <chr>
## 1 0.0312 accuracy binary 0.974 5 0.00438 pre0_mod01_post0
## 2 0.0312 roc_auc binary 0.995 5 0.00265 pre0_mod01_post0
## 3 0.0312 sens binary 0.935 5 0.0110 pre0_mod01_post0
## 4 0.0312 spec binary 0.996 5 0.00351 pre0_mod01_post0
## 5 0.0675 accuracy binary 0.980 5 0.00410 pre0_mod02_post0
## 6 0.0675 roc_auc binary 0.995 5 0.00327 pre0_mod02_post0
## 7 0.0675 sens binary 0.953 5 0.00710 pre0_mod02_post0
## 8 0.0675 spec binary 0.996 5 0.00351 pre0_mod02_post0
## 9 0.146 accuracy binary 0.982 5 0.00560 pre0_mod03_post0
## 10 0.146 roc_auc binary 0.994 5 0.00369 pre0_mod03_post0
## # ℹ 30 more rows9.5.1 Visualisasi Tuning Linear
autoplot(
linear_tuned
) +
labs(
title = "Ringkasan Tuning SVM Linear"
)
Interpretasi:
Visualisasi menunjukkan perubahan performa model pada berbagai nilai cost. Nilai ROC-AUC tertinggi dipilih sebagai parameter terbaik.
9.6 8.6 Parameter Terbaik Linear
best_linear <- select_best(
linear_tuned,
metric = "roc_auc"
)
best_linear## # A tibble: 1 × 2
## cost .config
## <dbl> <chr>
## 1 0.0312 pre0_mod01_post09.7 8.7 Workflow Final Linear
final_linear_wf <- finalize_workflow(
svm_linear_wf,
best_linear
)
final_linear_wf## ══ Workflow ════════════════════════════════════════════════════════════════════
## Preprocessor: Recipe
## Model: svm_linear()
##
## ── Preprocessor ────────────────────────────────────────────────────────────────
## 2 Recipe Steps
##
## • step_zv()
## • step_normalize()
##
## ── Model ───────────────────────────────────────────────────────────────────────
## Linear Support Vector Machine Model Specification (classification)
##
## Main Arguments:
## cost = 0.03125
##
## Engine-Specific Arguments:
## prob.model = TRUE
##
## Computational engine: kernlab10 9 Pemodelan SVM Kernel RBF
10.1 9.1 Spesifikasi Model
svm_rbf_spec <- svm_rbf(
cost = tune(),
rbf_sigma = tune()
) %>%
set_engine(
"kernlab",
prob.model = TRUE
) %>%
set_mode(
"classification"
)
svm_rbf_spec## Radial Basis Function Support Vector Machine Model Specification (classification)
##
## Main Arguments:
## cost = tune()
## rbf_sigma = tune()
##
## Engine-Specific Arguments:
## prob.model = TRUE
##
## Computational engine: kernlab10.2 9.2 Workflow Model RBF
svm_rbf_wf <- workflow() %>%
add_recipe(rec_svm) %>%
add_model(svm_rbf_spec)
svm_rbf_wf## ══ Workflow ════════════════════════════════════════════════════════════════════
## Preprocessor: Recipe
## Model: svm_rbf()
##
## ── Preprocessor ────────────────────────────────────────────────────────────────
## 2 Recipe Steps
##
## • step_zv()
## • step_normalize()
##
## ── Model ───────────────────────────────────────────────────────────────────────
## Radial Basis Function Support Vector Machine Model Specification (classification)
##
## Main Arguments:
## cost = tune()
## rbf_sigma = tune()
##
## Engine-Specific Arguments:
## prob.model = TRUE
##
## Computational engine: kernlab10.3 9.3 Grid Tuning RBF
svm_grid <- grid_regular(
cost(
range = c(-5, 5)
),
rbf_sigma(
range = c(-10, 0)
),
levels = 5
)
svm_grid## # A tibble: 25 × 2
## cost rbf_sigma
## <dbl> <dbl>
## 1 0.0312 0.0000000001
## 2 0.177 0.0000000001
## 3 1 0.0000000001
## 4 5.66 0.0000000001
## 5 32 0.0000000001
## 6 0.0312 0.0000000316
## 7 0.177 0.0000000316
## 8 1 0.0000000316
## 9 5.66 0.0000000316
## 10 32 0.0000000316
## # ℹ 15 more rows10.4 9.4 Tuning Model RBF
svm_metrics <- metric_set(
roc_auc,
accuracy,
sens,
spec
)
svm_tuned <- tune_grid(
svm_rbf_wf,
resamples = folds,
grid = svm_grid,
metrics = svm_metrics,
control = control_grid(
save_pred = TRUE
)
)## maximum number of iterations reached 2.861758e-05 -2.861758e-05maximum number of iterations reached 0.0001599879 -0.000159988maximum number of iterations reached 0.0008895575 -0.0008895568maximum number of iterations reached 0.00023972 -0.0002397193maximum number of iterations reached 0.001362556 -0.00136252maximum number of iterations reached 0.007299979 -0.007287874maximum number of iterations reached 0.01408169 -0.01422563maximum number of iterations reached 0.00177549 -0.001765752maximum number of iterations reached 0.01033313 -0.01037645maximum number of iterations reached 0.0002162732 -0.0002151397maximum number of iterations reached 0.006641301 -0.006235938maximum number of iterations reached 2.810598e-05 -2.810598e-05maximum number of iterations reached 0.0001601492 -0.0001601493maximum number of iterations reached 0.000904895 -0.0009048946maximum number of iterations reached 0.0002379273 -0.0002379266maximum number of iterations reached 0.001336436 -0.001336404maximum number of iterations reached 0.007269128 -0.007257217maximum number of iterations reached 0.01417667 -0.01429472maximum number of iterations reached 0.001947118 -0.001934891maximum number of iterations reached 0.010074 -0.01008327maximum number of iterations reached 0.0002042831 -0.0002031999maximum number of iterations reached 0.004500174 -0.004196676maximum number of iterations reached 2.83372e-05 -2.83372e-05maximum number of iterations reached 0.0001566373 -0.0001566374maximum number of iterations reached 0.0008985434 -0.0008985423maximum number of iterations reached 0.0002340835 -0.000234083maximum number of iterations reached 0.001323663 -0.00132363maximum number of iterations reached 0.00717984 -0.007168409maximum number of iterations reached 0.01421069 -0.01437225maximum number of iterations reached 0.002557738 -0.002540893maximum number of iterations reached 0.01027745 -0.01036685maximum number of iterations reached 0.0001924939 -0.0001914824maximum number of iterations reached 0.003159766 -0.003029883maximum number of iterations reached 2.585456e-05 -2.585457e-05maximum number of iterations reached 0.0001518923 -0.0001518924maximum number of iterations reached 0.0008701417 -0.0008701419maximum number of iterations reached 0.000228507 -0.0002285064maximum number of iterations reached 0.001292729 -0.001292696maximum number of iterations reached 0.006967677 -0.00695739maximum number of iterations reached 0.01426127 -0.01444588maximum number of iterations reached 0.002542626 -0.002529864maximum number of iterations reached 0.01042355 -0.01053881maximum number of iterations reached 0.0002736097 -0.0002722411maximum number of iterations reached 0.002550232 -0.002441856maximum number of iterations reached 2.488812e-05 -2.488813e-05maximum number of iterations reached 0.0001529773 -0.0001529774maximum number of iterations reached 0.0008936505 -0.0008936492maximum number of iterations reached 0.0002268538 -0.0002268532maximum number of iterations reached 0.001278651 -0.001278623maximum number of iterations reached 0.006918786 -0.006908756maximum number of iterations reached 0.01412428 -0.01428327maximum number of iterations reached 0.002111655 -0.002101279maximum number of iterations reached 0.01044433 -0.01051128maximum number of iterations reached 7.161995e-05 -7.130906e-05maximum number of iterations reached 0.005321621 -0.00500175210.5 9.5 Ringkasan Tuning RBF
show_best(
svm_tuned,
metric = "roc_auc"
)## # A tibble: 5 × 8
## cost rbf_sigma .metric .estimator mean n std_err .config
## <dbl> <dbl> <chr> <chr> <dbl> <int> <dbl> <chr>
## 1 5.66 0.00316 roc_auc binary 0.994 5 0.00281 pre0_mod19_post0
## 2 32 0.00316 roc_auc binary 0.993 5 0.00386 pre0_mod24_post0
## 3 1 0.00316 roc_auc binary 0.993 5 0.00347 pre0_mod14_post0
## 4 32 0.00001 roc_auc binary 0.988 5 0.00373 pre0_mod23_post0
## 5 0.177 0.00316 roc_auc binary 0.988 5 0.00369 pre0_mod09_post0collect_metrics(
svm_tuned
)## # A tibble: 100 × 8
## cost rbf_sigma .metric .estimator mean n std_err .config
## <dbl> <dbl> <chr> <chr> <dbl> <int> <dbl> <chr>
## 1 0.0312 0.0000000001 accuracy binary 0.628 5 0.00139 pre0_mod01_post0
## 2 0.0312 0.0000000001 roc_auc binary 0.979 5 0.00465 pre0_mod01_post0
## 3 0.0312 0.0000000001 sens binary 0 5 0 pre0_mod01_post0
## 4 0.0312 0.0000000001 spec binary 1 5 0 pre0_mod01_post0
## 5 0.0312 0.0000000316 accuracy binary 0.628 5 0.00139 pre0_mod02_post0
## 6 0.0312 0.0000000316 roc_auc binary 0.985 5 0.00377 pre0_mod02_post0
## 7 0.0312 0.0000000316 sens binary 0 5 0 pre0_mod02_post0
## 8 0.0312 0.0000000316 spec binary 1 5 0 pre0_mod02_post0
## 9 0.0312 0.00001 accuracy binary 0.628 5 0.00139 pre0_mod03_post0
## 10 0.0312 0.00001 roc_auc binary 0.985 5 0.00370 pre0_mod03_post0
## # ℹ 90 more rows10.5.1 Visualisasi Tuning RBF
autoplot(
svm_tuned
) +
labs(
title = "Ringkasan Tuning SVM RBF"
)
Interpretasi:
Visualisasi tuning menunjukkan pengaruh kombinasi parameter cost dan sigma terhadap performa model.
10.6 9.6 Parameter Terbaik RBF
best_par <- select_best(
svm_tuned,
metric = "roc_auc"
)
best_par## # A tibble: 1 × 3
## cost rbf_sigma .config
## <dbl> <dbl> <chr>
## 1 5.66 0.00316 pre0_mod19_post010.7 9.7 Workflow Final RBF
final_rbf_wf <- finalize_workflow(
svm_rbf_wf,
best_par
)
final_rbf_wf## ══ Workflow ════════════════════════════════════════════════════════════════════
## Preprocessor: Recipe
## Model: svm_rbf()
##
## ── Preprocessor ────────────────────────────────────────────────────────────────
## 2 Recipe Steps
##
## • step_zv()
## • step_normalize()
##
## ── Model ───────────────────────────────────────────────────────────────────────
## Radial Basis Function Support Vector Machine Model Specification (classification)
##
## Main Arguments:
## cost = 5.65685424949238
## rbf_sigma = 0.00316227766016838
##
## Engine-Specific Arguments:
## prob.model = TRUE
##
## Computational engine: kernlab11 10 Model Final untuk Evaluasi Data Uji
11.1 10.1 Model Final Linear
linear_fit <- last_fit(
final_linear_wf,
split_obj,
metrics = svm_metrics
)
linear_fit## # Resampling results
## # Manual resampling
## # A tibble: 1 × 6
## splits id .metrics .notes .predictions .workflow
## <list> <chr> <list> <list> <list> <list>
## 1 <split [454/115]> train/test split <tibble> <tibble> <tibble> <workflow>11.2 10.2 Model Final RBF
rbf_fit <- last_fit(
final_rbf_wf,
split_obj,
metrics = svm_metrics
)
rbf_fit## # Resampling results
## # Manual resampling
## # A tibble: 1 × 6
## splits id .metrics .notes .predictions .workflow
## <list> <chr> <list> <list> <list> <list>
## 1 <split [454/115]> train/test split <tibble> <tibble> <tibble> <workflow>12 11 Evaluasi Model pada Data Uji
Evaluasi dilakukan menggunakan data uji yang tidak digunakan selama proses pelatihan maupun tuning model sehingga memberikan gambaran performa model yang lebih objektif.
12.1 11.1 Metrik Evaluasi SVM Linear
linear_test_metrics <- collect_metrics(
linear_fit
)
kable(
linear_test_metrics,
digits = 4,
caption = "Metrik Evaluasi Data Uji SVM Linear"
)| .metric | .estimator | .estimate | .config |
|---|---|---|---|
| accuracy | binary | 0.9739 | pre0_mod0_post0 |
| sens | binary | 0.9535 | pre0_mod0_post0 |
| spec | binary | 0.9861 | pre0_mod0_post0 |
| roc_auc | binary | 0.9958 | pre0_mod0_post0 |
12.2 11.2 Metrik Evaluasi SVM RBF
rbf_test_metrics <- collect_metrics(
rbf_fit
)
kable(
rbf_test_metrics,
digits = 4,
caption = "Metrik Evaluasi Data Uji SVM RBF"
)| .metric | .estimator | .estimate | .config |
|---|---|---|---|
| accuracy | binary | 0.9739 | pre0_mod0_post0 |
| sens | binary | 0.9535 | pre0_mod0_post0 |
| spec | binary | 0.9861 | pre0_mod0_post0 |
| roc_auc | binary | 0.9958 | pre0_mod0_post0 |
Interpretasi:
Tabel di atas menunjukkan performa kedua model berdasarkan metrik accuracy, sensitivity, specificity, dan ROC-AUC pada data uji.
13 12 Confusion Matrix
13.1 12.1 Prediksi Model Linear
pred_linear <- collect_predictions(
linear_fit
)
head(pred_linear)## # A tibble: 6 × 7
## .pred_class .pred_Malignant .pred_Benign id diagnosis .row .config
## <fct> <dbl> <dbl> <chr> <fct> <int> <chr>
## 1 Malignant 1.000 0.00000164 train/test s… Malignant 3 pre0_m…
## 2 Malignant 1.000 0.000289 train/test s… Malignant 4 pre0_m…
## 3 Malignant 0.997 0.00317 train/test s… Malignant 9 pre0_m…
## 4 Malignant 0.997 0.00318 train/test s… Malignant 12 pre0_m…
## 5 Malignant 1.000 0.0000000572 train/test s… Malignant 19 pre0_m…
## 6 Benign 0.0501 0.950 train/test s… Benign 20 pre0_m…13.2 12.2 Confusion Matrix Linear
cm_linear <- conf_mat(
pred_linear,
truth = diagnosis,
estimate = .pred_class
)
cm_linear## Truth
## Prediction Malignant Benign
## Malignant 41 1
## Benign 2 7113.3 12.3 Prediksi Model RBF
pred_rbf <- collect_predictions(
rbf_fit
)
head(pred_rbf)## # A tibble: 6 × 7
## .pred_class .pred_Malignant .pred_Benign id diagnosis .row .config
## <fct> <dbl> <dbl> <chr> <fct> <int> <chr>
## 1 Malignant 1.000 0.00000185 train/test s… Malignant 3 pre0_m…
## 2 Malignant 0.999 0.000695 train/test s… Malignant 4 pre0_m…
## 3 Malignant 0.999 0.00133 train/test s… Malignant 9 pre0_m…
## 4 Malignant 0.998 0.00206 train/test s… Malignant 12 pre0_m…
## 5 Malignant 1.000 0.000000105 train/test s… Malignant 19 pre0_m…
## 6 Benign 0.0415 0.959 train/test s… Benign 20 pre0_m…13.4 12.4 Confusion Matrix RBF
cm_rbf <- conf_mat(
pred_rbf,
truth = diagnosis,
estimate = .pred_class
)
cm_rbf## Truth
## Prediction Malignant Benign
## Malignant 41 1
## Benign 2 71Interpretasi:
Confusion matrix menunjukkan jumlah observasi yang berhasil maupun gagal diklasifikasikan oleh model.
14 13 ROC Curve dan AUC
14.1 13.1 Identifikasi Nama Kolom Probabilitas
names(pred_rbf)## [1] ".pred_class" ".pred_Malignant" ".pred_Benign" "id"
## [5] "diagnosis" ".row" ".config"Perhatikan output yang muncul.
Biasanya terdapat kolom:
- .pred_Malignant
- .pred_Benign
Jika kolom tersebut muncul, gunakan chunk berikut.
14.2 13.2 ROC Curve SVM Linear
roc_curve(
pred_linear,
truth = diagnosis,
.pred_Malignant
) %>%
autoplot() +
labs(
title = "ROC Curve SVM Linear"
)
14.3 13.3 ROC Curve SVM RBF
roc_curve(
pred_rbf,
truth = diagnosis,
.pred_Malignant
) %>%
autoplot() +
labs(
title = "ROC Curve SVM RBF"
)
Interpretasi:
Semakin dekat kurva ROC ke sudut kiri atas, semakin baik kemampuan model membedakan kelas malignant dan benign.
15 14 Perbandingan Performa Model
comparison_metrics <- bind_rows(
linear_test_metrics %>%
mutate(Model = "Linear"),
rbf_test_metrics %>%
mutate(Model = "RBF")
) %>%
select(
Model,
.metric,
.estimate
)
kable(
comparison_metrics,
digits = 4,
caption = "Perbandingan Metrik Evaluasi Kedua Model"
)| Model | .metric | .estimate |
|---|---|---|
| Linear | accuracy | 0.9739 |
| Linear | sens | 0.9535 |
| Linear | spec | 0.9861 |
| Linear | roc_auc | 0.9958 |
| RBF | accuracy | 0.9739 |
| RBF | sens | 0.9535 |
| RBF | spec | 0.9861 |
| RBF | roc_auc | 0.9958 |
15.1 Visualisasi Perbandingan
comparison_plot <- comparison_metrics %>%
filter(
.metric %in%
c(
"accuracy",
"sens",
"spec",
"roc_auc"
)
)
ggplot(
comparison_plot,
aes(
x = Model,
y = .estimate,
fill = Model
)
) +
geom_col() +
facet_wrap(
~ .metric,
scales = "free_y"
) +
labs(
title = "Perbandingan Kinerja SVM Linear dan RBF",
x = "Model",
y = "Nilai Metrik"
)
16 15 Analisis False Negative
False negative merupakan kasus ketika observasi yang sebenarnya malignant diprediksi sebagai benign.
Kesalahan ini sangat penting dalam konteks diagnosis kanker karena dapat menyebabkan keterlambatan penanganan pasien.
false_negative_rbf <- pred_rbf %>%
filter(
diagnosis == "Malignant",
.pred_class == "Benign"
)
nrow(false_negative_rbf)## [1] 216.1 Daftar Kasus False Negative
false_negative_rbf## # A tibble: 2 × 7
## .pred_class .pred_Malignant .pred_Benign id diagnosis .row .config
## <fct> <dbl> <dbl> <chr> <fct> <int> <chr>
## 1 Benign 0.250 0.750 train/test s… Malignant 39 pre0_m…
## 2 Benign 0.0733 0.927 train/test s… Malignant 74 pre0_m…Interpretasi:
Jumlah observasi pada output di atas menunjukkan banyaknya kasus malignant yang salah diklasifikasikan sebagai benign.
17 16 Diskusi
17.1 Accuracy
Accuracy menunjukkan proporsi keseluruhan observasi yang berhasil diklasifikasikan dengan benar.
17.2 Sensitivity
Sensitivity merupakan metrik terpenting dalam penelitian ini karena menunjukkan kemampuan model mendeteksi kasus malignant.
Semakin tinggi sensitivity maka semakin sedikit kasus kanker yang gagal terdeteksi.
17.3 Specificity
Specificity menunjukkan kemampuan model dalam mengenali kasus benign secara tepat.
17.4 ROC-AUC
ROC-AUC digunakan untuk mengevaluasi kemampuan model dalam membedakan kedua kelas diagnosis.
Nilai yang mendekati 1 menunjukkan kemampuan diskriminasi yang sangat baik.
17.5 Perbandingan Kernel
Bandingkan nilai accuracy, sensitivity, specificity, dan ROC-AUC antara model linear dan model RBF.
Model dengan sensitivity dan ROC-AUC tertinggi dapat dipertimbangkan sebagai model terbaik.
18 17 Keterbatasan Penelitian
Penelitian ini memiliki beberapa keterbatasan:
- Dataset hanya berasal dari satu sumber.
- Tidak dilakukan validasi eksternal.
- Tidak dilakukan perbandingan dengan metode machine learning lainnya.
- Hasil analisis bergantung pada karakteristik dataset WDBC.
19 18 Kesimpulan
Penelitian ini menerapkan Support Vector Machine (SVM) untuk mengklasifikasikan diagnosis kanker payudara menggunakan Breast Cancer Wisconsin Diagnostic Dataset.
Dua kernel dibandingkan yaitu kernel linear dan kernel radial basis function (RBF).
Evaluasi dilakukan menggunakan confusion matrix, accuracy, sensitivity, specificity, dan ROC-AUC.
Model dengan nilai sensitivity dan ROC-AUC tertinggi dapat dipertimbangkan sebagai model terbaik karena lebih mampu mendeteksi kasus malignant dengan baik.
20 Referensi
Breast Cancer Wisconsin (Diagnostic) Dataset. UCI Machine Learning Repository.
https://archive.ics.uci.edu/dataset/17/breast+cancer+wisconsin+diagnostic
Kuhn, M., & Silge, J. (2022). Tidy Modeling with R.
James, G., Witten, D., Hastie, T., & Tibshirani, R. (2021). An Introduction to Statistical Learning.
Vapnik, V. N. (1998). Statistical Learning Theory.
Posit Team. Tidymodels Documentation.