Modul 3
Nadia Kaila
2026-04-04
1. Exploratory Data Analysis (EDA)
Bagian ini bertujuan untuk memahami struktur data awal dan sebaran fitur sebelum dilakukan pemrosesan.
Persiapan Library dan Dataset
Memuat semua library yang diperlukan selama proses berlangsung dan file dataset.csv. Karena file aslinya tidak memiliki header, pemberian nama kolom akan dilakukan secara manual sesuai dengan atribut Breast Cancer Wisconsin.
library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.5.3## Warning: package 'readr' was built under R version 4.5.3## Warning: package 'forcats' was built under R version 4.5.3## Warning: package 'lubridate' was built under R version 4.5.3## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ purrr 1.2.1
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(corrplot)## Warning: package 'corrplot' was built under R version 4.5.3## corrplot 0.95 loadedlibrary(gridExtra)## Warning: package 'gridExtra' was built under R version 4.5.3##
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## combinelibrary(factoextra)## Welcome to factoextra!
## Want to learn more? See two factoextra-related books at https://www.datanovia.com/en/product/practical-guide-to-principal-component-methods-in-r/# Membaca data
df <- read.csv("dataset.csv", header = FALSE)
# Definisi nama kolom sesuai UCI Repository
features <- c("radius", "texture", "perimeter", "area", "smoothness",
"compactness", "concavity", "concave_points", "symmetry", "fractal_dimension")
column_names <- c("id", "diagnosis",
paste0(features, "_mean"),
paste0(features, "_se"),
paste0(features, "_worst"))
colnames(df) <- column_names
# Data Cleaning: Menghapus ID dan konversi Target
df <- df %>%
select(-id) %>%
mutate(diagnosis = as.factor(diagnosis))Summary Data
summary(df[, 1:6]) # Menampilkan 6 kolom pertama untuk ringkasan## diagnosis radius_mean texture_mean perimeter_mean area_mean
## B:357 Min. : 6.981 Min. : 9.71 Min. : 43.79 Min. : 143.5
## M:212 1st Qu.:11.700 1st Qu.:16.17 1st Qu.: 75.17 1st Qu.: 420.3
## Median :13.370 Median :18.84 Median : 86.24 Median : 551.1
## Mean :14.127 Mean :19.29 Mean : 91.97 Mean : 654.9
## 3rd Qu.:15.780 3rd Qu.:21.80 3rd Qu.:104.10 3rd Qu.: 782.7
## Max. :28.110 Max. :39.28 Max. :188.50 Max. :2501.0
## smoothness_mean
## Min. :0.05263
## 1st Qu.:0.08637
## Median :0.09587
## Mean :0.09636
## 3rd Qu.:0.10530
## Max. :0.16340Visualisasi
- Visualisasi Distribusi Diagnosis
Menunjukkan perbandingan jumlah tumor yang bersifat Ganas (Malignant) dan Jinak (Benign).
ggplot(df, aes(x = diagnosis, fill = diagnosis)) +
geom_bar() +
labs(title = "Distribusi Diagnosis (B = Benign, M = Malignant)",
x = "Diagnosis", y = "Jumlah") +
theme_minimal()
- Visualisasi Perbandingan Fitur
Melihat perbedaan nilai radius_mean dan texture_mean terhadap jenis diagnosis.
p1 <- ggplot(df, aes(x = diagnosis, y = radius_mean, fill = diagnosis)) +
geom_boxplot() +
labs(title = "Boxplot Radius Mean vs Diagnosis") +
theme_minimal()
p2 <- ggplot(df, aes(x = diagnosis, y = texture_mean, fill = diagnosis)) +
geom_boxplot() +
labs(title = "Boxplot Texture Mean vs Diagnosis") +
theme_minimal()
grid.arrange(p1, p2, ncol = 2)
- Visualisasi Analisis Korelasi
Memahami hubungan antar fitur dengan matriks korelasi.
cor_matrix <- cor(df[, 2:11])
corrplot(cor_matrix, method = "color", type = "upper",
tl.col = "black", tl.srt = 45,
addCoef.col = "black", number.cex = 0.7,
title = "\nMatriks Korelasi Fitur Mean", mar = c(0,0,1,0))
- Visualisasi Density Plot
Melihat tumpang tindih (overlap) distribusi data antar diagnosis.
ggplot(df, aes(x = area_mean, fill = diagnosis)) +
geom_density(alpha = 0.5) +
labs(title = "Density Plot Area Mean berdasarkan Diagnosis") +
theme_minimal()
2. Data Preprocessing
Standardisasi (Z-Score)
Karena fitur-fitur dalam dataset ini memiliki rentang nilai yang sangat berbeda, maka perlu dilakukan scaling agar semua fitur memiliki bobot yang sama saat proses clustering.
df_numeric <- df %>% select(-diagnosis)
df_scaled <- as.data.frame(scale(df_numeric))
summary(df_scaled[, 1:5])## radius_mean texture_mean perimeter_mean area_mean
## Min. :-2.0279 Min. :-2.2273 Min. :-1.9828 Min. :-1.4532
## 1st Qu.:-0.6888 1st Qu.:-0.7253 1st Qu.:-0.6913 1st Qu.:-0.6666
## Median :-0.2149 Median :-0.1045 Median :-0.2358 Median :-0.2949
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4690 3rd Qu.: 0.5837 3rd Qu.: 0.4992 3rd Qu.: 0.3632
## Max. : 3.9678 Max. : 4.6478 Max. : 3.9726 Max. : 5.2459
## smoothness_mean
## Min. :-3.10935
## 1st Qu.:-0.71034
## Median :-0.03486
## Mean : 0.00000
## 3rd Qu.: 0.63564
## Max. : 4.76672Reduksi Dimensi (PCA)
PCA digunakan untuk menyederhanakan 30 fitur menjadi 2 komponen utama guna keperluan visualisasi spasial.
pca_res <- prcomp(df_scaled, center = TRUE, scale. = TRUE)
df_pca <- as.data.frame(pca_res$x[, 1:2])Analisis Clustering
K-Means
- Persiapan Library
library(factoextra)- Mencari K Optimal (Elbow Method)
Gunakan data yang sudah di-scale (df_scaled).
fviz_nbclust(df_scaled, kmeans, method = "wss") +
geom_vline(xintercept = 2, linetype = 2, color = "red") +
labs(title = "Elbow Method", subtitle = "Mencari Titik Siku")
- Eksekusi K-Means
Menggunakan k=2 karena hasil diagnosis kanker hanya Ganas dan Jinak.
set.seed(123)
final_kmeans <- kmeans(df_scaled, centers = 2, nstart = 25)- Visualisasi Hasil Cluster
fviz_cluster(final_kmeans, data = df_scaled,
palette = c("#2E9FDF", "#E7B800"),
geom = "point",
ellipse.type = "convex",
ggtheme = theme_minimal())
- Evaluasi
df$cluster <- as.factor(final_kmeans$cluster)
table(Diagnosis_Asli = df$diagnosis, Cluster_Mesin = df$cluster)## Cluster_Mesin
## Diagnosis_Asli 1 2
## B 14 343
## M 175 37- Penjelasan Berdasarkan hasil pengelompokan menggunakan algoritma K-Means pada dataset Breast Cancer Wisconsin, dapat ditarik beberapa poin utama:
Cluster 2 (Kelompok Tumor Jinak/Benign): Berhasil mengidentifikasi 343 pasien yang aslinya Benign.
Cluster 1 (Kelompok Tumor Ganas/Malignant): Berhasil mengelompokkan 175 pasien yang aslinya Malignant.
Akurasinya: \[\text{Akurasi} = \frac{\text{Data yang Benar}}{\text{Total Data}} = \frac{343 + 175}{569} \approx 91\%\]
K-Median
- Persiapan Library
library(flexclust)## Warning: package 'flexclust' was built under R version 4.5.3library(tidyverse)
library(factoextra)- Mencari K Optimal (Metode K-Median)
Menentukan jumlah cluster dengan menggunakan fungsi dari flexclust.
set.seed(123)
kmed_steps <- stepFlexclust(df_scaled, k = 2:10, nrep = 5,
family = kccaFamily("kmedians"))## 2 : * * * * *
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- Eksekusi K-Median
set.seed(123)
final_kmedian <- kcca(df_scaled, k = 2, family = kccaFamily("kmedians"))
kmed_clusters <- predict(final_kmedian)- Visualisasi
fviz_cluster(list(data = df_scaled, cluster = kmed_clusters),
geom = "point",
ellipse.type = "convex",
palette = c("#2E9FDF", "#E7B800"),
ggtheme = theme_light()) +
labs(title = "Cluster Plot K-Median",
x = "Dimensi 1 (Skala Jarak)",
y = "Dimensi 2 (Skala Jarak)") +
theme(axis.text = element_text(size = 10))
axis.title = element_text(size = 12)- Evaluasi
df$cluster_kmedian <- as.factor(predict(final_kmedian))
table(Diagnosis_Asli = df$diagnosis, Cluster_KMedian = df$cluster_kmedian)## Cluster_KMedian
## Diagnosis_Asli 1 2
## B 12 345
## M 184 28- Penjelasan
Berdasarkan hasil pengelompokan menggunakan algoritma K-Median (dengan jarak Manhattan) pada dataset Breast Cancer Wisconsin, dapat ditarik beberapa poin utama:
Cluster 2 (Kelompok Tumor Jinak/Benign): Berhasil mengelompokkan 345 pasien yang aslinya Benign.
Cluster 1 (Kelompok Tumor Ganas/Malignant): Berhasil mengelompokkan 184 pasien yang aslinya Malignant.
Akurasinya: \[\text{Akurasi} = \frac{\text{Data yang Benar}}{\text{Total Data}} = \frac{529 + 40}{569} \approx 93\%\]
DBSCAN (Density-Based Spatial Clustering of Applications with Noise)
- Persiapan Library
library(dbscan)## Warning: package 'dbscan' was built under R version 4.5.3##
## Attaching package: 'dbscan'## The following object is masked from 'package:stats':
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## as.dendrogramlibrary(factoextra)
library(tidyverse)- Menentukan Parameter Optimal (Eps)
DBSCAN membutuhkan dua parameter, yaitu MinPts (minimal titik) dan Eps (jarak jangkauan). Cara mencari Eps terbaik adalah dengan K-Nearest Neighbor (KNN) Distance Plot.
dbscan::kNNdistplot(df_scaled, k = 5)
abline(h = 1.5, col = "red", linetype = "dashed")## Warning in int_abline(a = a, b = b, h = h, v = v, untf = untf, ...): "linetype"
## is not a graphical parameter
- Eksekusi DBSCAN
set.seed(123)
final_dbscan <- dbscan(df_scaled, eps = 1.5, minPts = 5)
print(final_dbscan)## DBSCAN clustering for 569 objects.
## Parameters: eps = 1.5, minPts = 5
## Using euclidean distances and borderpoints = TRUE
## The clustering contains 1 cluster(s) and 550 noise points.
##
## 0 1
## 550 19
##
## Available fields: cluster, eps, minPts, metric, borderPoints- Visualisasi
fviz_cluster(final_dbscan, data = df_scaled,
geom = "point",
palette = "jco",
ggtheme = theme_minimal(),
main = "Visualisasi Cluster DBSCAN")
- Evaluasi
df$cluster_dbscan <- as.factor(final_dbscan$cluster)
table(Diagnosis_Asli = df$diagnosis, Cluster_DBSCAN = df$cluster_dbscan)## Cluster_DBSCAN
## Diagnosis_Asli 0 1
## B 338 19
## M 212 0- Penjelasan
Berdasarkan hasil pengelompokan menggunakan algoritma DBSCAN pada dataset Breast Cancer Wisconsin, dapat ditarik beberapa poin utama:
Cluster 1 (Kelompok Homogen): Berisi 19 pasien yang semuanya memiliki diagnosis Benign (Jinak).
Cluster 0 (Noise/Outlier): Sebanyak 550 data (338 Benign dan 212 Malignant) dianggap sebagai noise oleh algoritma.
Akurasi: \[\text{Akurasi} = \frac{19}{569} \times 100\% \approx \mathbf{3,3\%}\]
Mean Shift
- Persiapan Library
library(meanShiftR)
library(factoextra)
library(tidyverse)- Menentukan Bandwidth
Pada algoritma Mean Shift, parameter utama yang digunakan adalah bandwidth, yaitu radius untuk menentukan kedekatan antar data dalam proses pembentukan cluster.
Pada percobaan awal menggunakan: - bandwidth 1, dihasilkan jumlah cluster yang sangat banyak (overclustering), karena bandwidth terlalu kecil sehingga setiap titik data membentuk cluster sendiri. Oleh karena itu, dilakukan penyesuaian bandwidth menjadi:
bandwidth <- rep(4.3, ncol(df_scaled))Nilai bandwidth yang lebih besar membuat area pencarian lebih luas, mengurangi jumlah cluster yang terbentuk, disesuaikan dengan tujuan analisis yaitu mendekati jumlah kelas asli (2 kelas: Benign & Malignant), serta hasil eksperimen menunjukkan bahwa bandwidth 4.3 menghasilkan 2 cluster, sehingga lebih representatif.
- Eksekusi Mean Shift
set.seed(123)
mean_shift_result <- meanShift(as.matrix(df_scaled), bandwidth = bandwidth)
clusters_ms <- mean_shift_result$assignment- Visualisasi
fviz_cluster(list(data = df_scaled, cluster = clusters_ms),
geom = "point",
ellipse.type = "convex",
ggtheme = theme_minimal()) +
labs(title = "Visualisasi Cluster Mean Shift")
- Evaluasi
df$cluster_meanshift <- as.factor(clusters_ms)
table(Diagnosis_Asli = df$diagnosis, Cluster_MeanShift = df$cluster_meanshift)## Cluster_MeanShift
## Diagnosis_Asli 1 2
## B 357 0
## M 211 1- Penjelasan
Berdasarkan hasil pengelompokan menggunakan algoritma Mean Shift pada dataset Breast Cancer Wisconsin, diperoleh hasil sebagai berikut:
Cluster 1 (Dominan Benign): Berhasil mengelompokkan 357 pasien Benign, namun juga mencampurkan 211 pasien Malignant ke dalam cluster ini.
Cluster 2 (Sangat kecil): Hanya berisi 1 pasien Malignant.
Akurasi \[\text{Akurasi} = \frac{358}{569} \times 100\% \approx \mathbf{62,9\%}\]
Fuzzy C-Means
- Persiapan Library
library(e1071) ## Warning: package 'e1071' was built under R version 4.5.3##
## Attaching package: 'e1071'## The following object is masked from 'package:flexclust':
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## bclust## The following object is masked from 'package:ggplot2':
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## elementlibrary(factoextra)
library(tidyverse)- Menentukan Jumlah Cluster
Fuzzy C-Means membutuhkan parameter centers (jumlah cluster). Karena tujuan kita memisahkan Benign dan Malignant, kita set centers = 2.
c <- 2- Ekseskusi Fuzzy C-Means
set.seed(123)
fcm_result <- cmeans(df_scaled, centers = 2, m = 2, iter.max = 100)
clusters_fcm <- apply(fcm_result$membership, 1, which.max)- Visualisasi
fviz_cluster(list(data = df_scaled, cluster = clusters_fcm),
geom = "point",
ellipse.type = "convex",
palette = c("#2E9FDF", "#E7B800"),
ggtheme = theme_minimal()) +
labs(title = "Visualisasi Cluster Fuzzy C-Means")
- Evaluasi
df$cluster_fcm <- as.factor(clusters_fcm)
table(Diagnosis_Asli = df$diagnosis, Cluster_FCM = df$cluster_fcm)## Cluster_FCM
## Diagnosis_Asli 1 2
## B 18 339
## M 181 31- Penjelasan
Berdasarkan hasil pengelompokan menggunakan algoritma Fuzzy C-Means pada dataset Breast Cancer Wisconsin, diperoleh hasil sebagai berikut:
Cluster 1 (18 B + 181 M): didominasi Malignant, tapi sebagian besar data Benign salah masuk.
Cluster 2 (339 B + 31 M): didominasi Benign, sebagian kecil Malignant salah masuk.
FCM membagi data sesuai kemiripan fitur, namun karena banyak overlap antara Benign dan Malignant, beberapa data “tersesat” ke cluster lain.
- Akurasi \[\text{Akurasi} = \frac{339+ 181}{569} \times 100\% \approx \mathbf{91,4\%}\]
Evaluasi Performa Akhir
Perbandingan akurasi seluruh algoritma untuk menentukan metode paling optimal.
algoritma <- c("K-Medians", "Fuzzy C-Means", "K-Means", "Mean Shift", "DBSCAN")
benign_benar <- c(345, 339, 343, 357, 19)
malignant_benar <- c(184, 181, 175, 1, 0)
tabel_evaluasi <- data.frame(
Algoritma = algoritma,
Benign_Benar = benign_benar,
Malignant_Benar = malignant_benar,
Akurasi = round(((benign_benar + malignant_benar) / 569) * 100, 1)
)
knitr::kable(tabel_evaluasi, caption = "Perbandingan Akurasi Algoritma")| Algoritma | Benign_Benar | Malignant_Benar | Akurasi |
|---|---|---|---|
| K-Medians | 345 | 184 | 93.0 |
| Fuzzy C-Means | 339 | 181 | 91.4 |
| K-Means | 343 | 175 | 91.0 |
| Mean Shift | 357 | 1 | 62.9 |
| DBSCAN | 19 | 0 | 3.3 |