Data Summary

This report analyzes the Breast Cancer Wisconsin (Diagnostic) Dataset to build a data-driven framework for cancer diagnosis. We examined 569 patients with 30 different cell measurements to answer one critical question: Which features matter most for detecting cancer?

Dataset Source: Breast Cancer Wisconsin (Diagnostic) Dataset (Kaggle)

Aim

To Predict breast Cancer from FNA cell measurements using machine learning to help doctors make faster, more accurate diagnosis

Research Questions

Do we have a balaanced dataset so the model can learn Properly?
Do cancerous(malignant) cells look different from non-cancerous(benign) cells in the measurements?
Are some of our 30 features giving the same information more than once?
Can machine learning pick out the most important features auutomatically?
Which model predicts cancer best while using the fewest features?
Can we make a simpler diagnostic tool that works as well as real clinical tests?

Project Description

Breast cancer remains one of the most prevalent cancers affecting women globally. Early detection is paramount 5-year survival rates reach 99% when caught in Stage I, compared to 28% in Stage IV.

Fine Needle Aspirate (FNA) biopsies provide a minimally invasive method for diagnosis. Medical imaging software extracts 30 quantitative features from cell nuclei, including:

Size metrics: radius, perimeter, area
Shape characteristics: compactness, concavity, concave points
Texture properties: grayscale variation
Smoothness and symmetry
Fractal dimension (complexity measure)

The Challenge

Hospitals collect 30 measurements per biopsy, creating several problems:

Cognitive overload for radiologists analyzing multi-dimensional data
Redundancy in measurements (e.g., radius, perimeter, area are mathematically related)
Increased costs from unnecessary computations
Model overfitting when training with correlated features

Method Used

This study employs automated feature selection using LASSO (Least Absolute Shrinkage and Selection Operator) regression to:

Identify the top 10 independent predictors
Compare three machine learning models: Logistic Regression, Random Forest, and Support Vector Machines
Validate performance on held-out test data
Achieve clinical-grade accuracy (>95%) with 67% fewer features

Expected Impact

Simplified diagnostics: Reduce from 30 to 10 measurements
Cost reduction: Lower computational and analysis overhead
Faster decisions: Enable rapid triage in clinical settings
Improved interpretability: Clear focus on biologically meaningful features

Data Preparation

Load Required Packages

library(readr)
library(dplyr)
library(ggplot2)
library(corrplot)
library(caret)
library(glmnet)
library(randomForest)
library(e1071)
library(pROC)
library(skimr)

Load data

breast_cancer <- read_csv("C:/Users/PC/Downloads/data (2).csv")

Drop ID and empty column

breast_cancer <- breast_cancer[, -1]
breast_cancer <- breast_cancer[, -ncol(breast_cancer)]

names(breast_cancer) <- gsub(" ", "_", names(breast_cancer))
names(breast_cancer) <- make.names(names(breast_cancer))

Convert diagnosis to factors

if(all(breast_cancer$diagnosis %in% c("M", "B"))) {
  breast_cancer <- breast_cancer %>% 
    mutate(diagnosis = factor(diagnosis, 
                              levels = c("B", "M"), 
                              labels = c("Benign", "Malignant")))
} else {
  breast_cancer <- breast_cancer %>% 
    mutate(diagnosis = factor(diagnosis, 
                              levels = c("Benign", "Malignant")))
}

Quick Check

skim(breast_cancer)

Data summary
Name	breast_cancer
Number of rows	568
Number of columns	31
_______________________
Column type frequency:
factor	1
numeric	30
________________________
Group variables	None

Variable type: factor

skim_variable	n_missing	complete_rate	ordered	n_unique	top_counts
diagnosis	0	1	FALSE	2	Ben: 356, Mal: 212

Variable type: numeric

skim_variable	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
radius_mean	1	14.14	3.52	6.98	11.71	13.38	15.80	28.11	<U+2582><U+2587><U+2583><U+2581><U+2581>
texture_mean	1	19.28	4.30	9.71	16.17	18.84	21.78	39.28	<U+2583><U+2587><U+2583><U+2581><U+2581>
perimeter_mean	1	92.05	24.25	43.79	75.20	86.29	104.15	188.50	<U+2583><U+2587><U+2583><U+2581><U+2581>
area_mean	1	655.72	351.66	143.50	420.30	551.40	784.15	2501.00	<U+2587><U+2583><U+2582><U+2581><U+2581>
smoothness_mean	1	0.10	0.01	0.06	0.09	0.10	0.11	0.16	<U+2582><U+2587><U+2585><U+2581><U+2581>
compactness_mean	1	0.10	0.05	0.02	0.07	0.09	0.13	0.35	<U+2587><U+2587><U+2582><U+2581><U+2581>
concavity_mean	1	0.09	0.08	0.00	0.03	0.06	0.13	0.43	<U+2587><U+2583><U+2582><U+2581><U+2581>
concave_points_mean	1	0.05	0.04	0.00	0.02	0.03	0.07	0.20	<U+2587><U+2583><U+2582><U+2581><U+2581>
symmetry_mean	1	0.18	0.03	0.11	0.16	0.18	0.20	0.30	<U+2581><U+2587><U+2585><U+2581><U+2581>
fractal_dimension_mean	1	0.06	0.01	0.05	0.06	0.06	0.07	0.10	<U+2586><U+2587><U+2582><U+2581><U+2581>
radius_se	1	0.41	0.28	0.11	0.23	0.32	0.48	2.87	<U+2587><U+2581><U+2581><U+2581><U+2581>
texture_se	1	1.22	0.55	0.36	0.83	1.11	1.47	4.88	<U+2587><U+2585><U+2581><U+2581><U+2581>
perimeter_se	1	2.87	2.02	0.76	1.61	2.29	3.36	21.98	<U+2587><U+2581><U+2581><U+2581><U+2581>
area_se	1	40.37	45.52	6.80	17.85	24.57	45.24	542.20	<U+2587><U+2581><U+2581><U+2581><U+2581>
smoothness_se	1	0.01	0.00	0.00	0.01	0.01	0.01	0.03	<U+2587><U+2583><U+2581><U+2581><U+2581>
compactness_se	1	0.03	0.02	0.00	0.01	0.02	0.03	0.14	<U+2587><U+2583><U+2581><U+2581><U+2581>
concavity_se	1	0.03	0.03	0.00	0.02	0.03	0.04	0.40	<U+2587><U+2581><U+2581><U+2581><U+2581>
concave_points_se	1	0.01	0.01	0.00	0.01	0.01	0.01	0.05	<U+2587><U+2587><U+2581><U+2581><U+2581>
symmetry_se	1	0.02	0.01	0.01	0.02	0.02	0.02	0.08	<U+2587><U+2583><U+2581><U+2581><U+2581>
fractal_dimension_se	1	0.00	0.00	0.00	0.00	0.00	0.00	0.03	<U+2587><U+2581><U+2581><U+2581><U+2581>
radius_worst	1	16.28	4.83	7.93	13.02	14.97	18.79	36.04	<U+2586><U+2587><U+2583><U+2581><U+2581>
texture_worst	1	25.67	6.15	12.02	21.08	25.41	29.68	49.54	<U+2583><U+2587><U+2586><U+2581><U+2581>
perimeter_worst	1	107.35	33.57	50.41	84.15	97.66	125.53	251.20	<U+2587><U+2587><U+2583><U+2581><U+2581>
area_worst	1	881.66	569.28	185.20	515.68	686.55	1085.00	4254.00	<U+2587><U+2582><U+2581><U+2581><U+2581>
smoothness_worst	1	0.13	0.02	0.07	0.12	0.13	0.15	0.22	<U+2582><U+2587><U+2587><U+2582><U+2581>
compactness_worst	1	0.25	0.16	0.03	0.15	0.21	0.34	1.06	<U+2587><U+2585><U+2581><U+2581><U+2581>
concavity_worst	1	0.27	0.21	0.00	0.12	0.23	0.38	1.25	<U+2587><U+2585><U+2582><U+2581><U+2581>
concave_points_worst	1	0.11	0.07	0.00	0.06	0.10	0.16	0.29	<U+2585><U+2587><U+2585><U+2583><U+2581>
symmetry_worst	1	0.29	0.06	0.16	0.25	0.28	0.32	0.66	<U+2585><U+2587><U+2581><U+2581><U+2581>
fractal_dimension_worst	1	0.08	0.02	0.06	0.07	0.08	0.09	0.21	<U+2587><U+2583><U+2581><U+2581><U+2581>

table(breast_cancer$diagnosis)

## 
##    Benign Malignant 
##       356       212

=====Visualizatiion====

Diagnosis Distribution

breast_cancer %>%
  count(diagnosis) %>%
  mutate(percentage = n / sum(n)) %>%
  ggplot(aes(x = diagnosis, y = n, fill = diagnosis)) +
  geom_col(width = 0.6) +
  geom_text(aes(label = scales::percent(percentage)), 
            vjust = -0.5, size = 5, fontface = "bold") +
  scale_fill_manual(values = c("Benign" = "#2E86AB", "Malignant" = "#A23B72")) +
  labs(title = "Diagnosis Distribution", x = "Diagnosis", y = "Count") +
  theme_minimal() +
  theme(legend.position = "none")

** What It Tells Us:

looking at the first bar chart, we can see the distribution of our dataset. Out of 569 patients, 357 were diagnosed as Benign (that’s 63%) and 212 as Malignant (37%). This is actually pretty good for machine learning - it’s not perfectly balanced, but it’s not severely skewed either. We have enough cancer cases to train our models properly without needing to do any special balancing techniques.

Distribution Of cell Radius

ggplot(breast_cancer, aes(x = radius_mean)) +
  geom_histogram(aes(y = after_stat(density)), 
                 binwidth = 1.0, 
                 fill = "#4ECDC4", 
                 color = "black", 
                 alpha = 0.7) +
  geom_density(color = "#2E4057", size = 1.5) +
  geom_vline(xintercept = mean(breast_cancer$radius_mean),
             color = "#FF6B6B",
             linetype = "dashed",
             size = 1) +
  labs(title = "Distribution of Cell Radius",
       x = "Mean Radius",
       y = "Density") +
  theme_minimal()

** What I noticed:

The smooth density curve helps us see the underlying pattern better than the bars alone. The skewness suggests we might have two different populations here - which the next graph will confirm.

Radius Distribution by Diagnosis

ggplot(breast_cancer, aes(x = radius_mean, fill = diagnosis)) +
  geom_density(alpha = 0.5) +
  scale_fill_manual(values = c("Benign" = "#2E86AB", "Malignant" = "#D62828")) +
  labs(title = "Tumor Size: Cancer vs Healthy", x = "Mean Radius", fill = "Diagnosis") +
  theme_minimal()

**What this means:

Cancerous tumors are noticeably larger on average. If a tumor has cells with radius below 12 μm, it’s most likely benign. Above 17 μm, it’s probably malignant. But in that overlap zone, we’d need other features to make the call. This confirms that cell size matters, but it can’t be our only predictor.

All mean features distributions

library(tidyr)
breast_cancer %>%
  select(ends_with("_mean"), -diagnosis) %>%
  pivot_longer(everything(), names_to = "feature", values_to = "value") %>%
  ggplot(aes(x = value)) +
  geom_histogram(bins = 30, fill = "#0072B2", color = "white") +
  facet_wrap(~ feature, scales = "free", ncol = 4) +
  labs(title = "Distribution of 10 Core Mean Features") +
  theme_minimal()

** What I Noticed:

This grid shows all 10 "_mean" features at once. A few observations:

area_mean has a much wider range (0-2500) compared to something like symmetry_mean (0.1-0.3)
Most features show right-skewed distributions
radius_mean, perimeter_mean, and area_mean look very similar - which makes sense since they’re all measuring size in different ways

All Standard Error Features Distribution

breast_cancer %>%
  select(ends_with("_se"), -diagnosis) %>%
  pivot_longer(everything(), names_to = "feature", values_to = "value") %>%
  ggplot(aes(x = value)) +
  geom_histogram(bins = 30, fill = "#009E73", color = "white") +
  facet_wrap(~ feature, scales = "free", ncol = 4) +
  labs(title = "Distribution of 10 Core Standard Error Features") +
  theme_minimal()

** What I Noticed:

The SE features show how much variation exists within each tumor. What stands out here is that almost all of them are heavily concentrated near zero with long right tails. Most tumors are pretty uniform (low variability), but a few show high heterogeneity.

All Worst Case Features Distribution

breast_cancer %>% 
  select(ends_with("_worst"), -diagnosis) %>%
  pivot_longer(everything(), names_to = "feature", values_to = "value") %>%
  ggplot(aes(x = value)) +
  geom_histogram(bins = 30, fill = "#D55E00", color = "white") +
  facet_wrap(~ feature, scales = "free", ncol = 4) +
  labs(title = "Distribtuion of 10 Core Worst Features") + 
  theme_minimal()

The “worst” features capture the most extreme measurements. Compared to the mean features, these distributions are:

Shifted further right (larger values) More spread out (wider ranges) Still right-skewed but with even longer tails

For example, radius_worst goes up to 35+ μm compared to radius_mean maxing around 28 μm.

Scatter Plot with Eclipse

ggplot(breast_cancer, aes(x = radius_mean, y = concave_points_mean, color = diagnosis)) +
  geom_point(alpha = 0.6, size = 2.5) +
  stat_ellipse(level = 0.95, linetype = "dashed", size = 1) +
  scale_color_manual(values = c("Benign" = "#0072B2", "Malignant" = "#D55E00")) +
  labs(title = "Size vs Concave Points", x = "Radius Mean", y = "Concave Points Mean") +
  theme_minimal()

**What I see:

There’s clear diagonal separation. You could almost draw a line from bottom-right to top-left and separate most of the cases correctly. The ellipses overlap a bit in the middle, but overall the groups are well-separated. This tells me that combining size and shape features gives us better separation than using either one alone.

Correlation Matrix

cor_matrix <- cor(breast_cancer %>% select(-diagnosis))
corrplot(cor_matrix, 
         method = "color", 
         type = "upper",
         order = "hclust",
         tl.col = "black", 
         tl.cex = 0.7)

** My Findings:

radius_mean, perimeter_mean, and area_mean are almost perfectly correlated (makes sense - they’re all measuring size). Same pattern for their "_worst" versions. This redundancy is exactly why we need feature selection - keeping all three doesn’t add new information.

feature Correlation With Diagnosis

correlation_data <- breast_cancer %>%
  mutate(diagnosis_num = ifelse(diagnosis == "Malignant", 1, 0)) %>%
  select_if(is.numeric) %>%
  cor()

diagnosis_cor <- as.data.frame(correlation_data) %>%
  select(diagnosis_num) %>%
  arrange(desc(diagnosis_num)) %>%
  mutate(feature = rownames(.)) %>%
  filter(feature != "diagnosis_num")

ggplot(diagnosis_cor, aes(x = reorder(feature, diagnosis_num), y = diagnosis_num, fill = diagnosis_num)) +
  geom_col() +
  coord_flip() +
  scale_fill_gradient(low = "#E8F4F8", high = "#0C4160") +
  geom_hline(yintercept = 0.7, linetype = "dashed", color = "red", size = 1) +
  labs(title = "Feature Correlation with Malignancy", x = "Feature", y = "Correlation") +
  theme_minimal()

** What I Noticed:

This horizontal bar chart ranks all 30 features by how well they predict cancer. The red dashed line at r = 0.7 marks “strong predictor” territory. Top 5 predictors:

concave_points_worst (~0.79) perimeter_worst (~0.78) concave_points_mean (~0.77) radius_worst (~0.76) area_worst (~0.73)

=====Feature Selection=====

Remove Highly Correlated Features

target <- breast_cancer$diagnosis
features <- breast_cancer %>% select(-diagnosis)

cor_matrix <- cor(features)
highly_correlated <- findCorrelation(cor_matrix, cutoff = 0.90)
features_filtered <- features[, -highly_correlated]

Lasso Feature Selection

x <- as.matrix(features_filtered)
y <- as.factor(target)

set.seed(42)
cv_lasso <- cv.glmnet(x, y, family = "binomial", alpha = 1, nfolds = 10)

plot(cv_lasso, main = "LASSO Cross-Validation")
abline(v = log(cv_lasso$lambda.min), col = "red", lty = 2)
abline(v = log(cv_lasso$lambda.1se), col = "blue", lty = 2)
legend("topright", 
       legend = c("Lambda Min", "Lambda 1SE"), 
       col = c("red", "blue"), 
       lty = 2)

** What I Noticed:

The lASSO CV curve shows model error (y-axis) across different penalty values (x-axis). The numbers across the top show how many features remain at each lambda value. Key observations:

Far left: Using ~20 features, error around 0.04 At lambda.1se (blue line): Using ~10-12 features, error around 0.06 Far right: Using 0 features, error shoots up

The error bars are pretty tight throughout, which means performance is consistent across different data splits. The blue line (lambda.1se) is what we used - it picks a simpler model (fewer features) that performs almost as well as the minimum error point.

Get Top 10 Features

coeffs <- coef(cv_lasso, s = cv_lasso$lambda.1se)
feature_importance <- data.frame(
  feature = rownames(coeffs)[-1],
  coefficient = as.numeric(coeffs[-1]),
  abs_coefficient = abs(as.numeric(coeffs[-1]))
) %>%
  arrange(desc(abs_coefficient)) %>%
  head(10)  # Always get 10 features regardless of zeros

top10_features <- feature_importance$feature

Visualize Selected Features

ggplot(feature_importance, aes(x = reorder(feature, abs_coefficient), y = coefficient, fill = coefficient > 0)) +
  geom_col() +
  coord_flip() +
  scale_fill_manual(values = c("TRUE" = "#00BA38", "FALSE" = "#F8766D")) +
  labs(title = "Top 10 Features Selected by LASSO", x = "Feature", y = "Coefficient") +
  theme_minimal()

** What I Noticed:

The negative coefficient is fascinating: More variation in fractal dimension actually suggests BENIGN. This makes sense biologically - benign cells naturally vary more, while cancer cells are uniformly abnormal. Feature composition:

Mostly “worst” features (as predicted!) Mix of size, shape, and texture One SE feature made the cut despite being generally weak

#====Model Training====

# Prepare data with selected features
model_data <- breast_cancer %>%
  select(diagnosis, all_of(top10_features))

# Train-Test Split
set.seed(123)
trainIndex <- createDataPartition(model_data$diagnosis, p = 0.8, list = FALSE)
train_data <- model_data[trainIndex, ]
test_data <- model_data[-trainIndex, ]


# Cross Validation Setup
ctrl <- trainControl(
  method = "cv",
  number = 10,
  classProbs = TRUE,
  summaryFunction = twoClassSummary,
  savePredictions = "final"
)

Logistic Regression Model

set.seed(42)
model_logistic <- train(
  diagnosis ~ .,
  data = train_data,
  method = "glm",
  family = "binomial",
  trControl = ctrl,
  metric = "ROC"
)

Random Forest Model

set.seed(42)
model_rf <- train(
  diagnosis ~ .,
  data = train_data,
  method = "rf",
  trControl = ctrl,
  metric = "ROC",
  tuneLength = 5,
  ntree = 500
)

Support Vector Machine Model

set.seed(42)
model_svm <- train(
  diagnosis ~ .,
  data = train_data,
  method = "svmRadial",
  trControl = ctrl,
  metric = "ROC",
  tuneLength = 5
)

The CV summary shows performance across 10 folds for all three models: ROC (AUC):

Logistic: Min 0.983, Mean ~0.988 Random Forest: Min 0.989, Mean ~0.994 SVM: Min 0.974, Mean ~0.998

Sensitivity:

All three models: Mean around 0.96-0.97

Specificity: All models above 0.96 First impression: Random Forest edges slightly ahead in ROC, but all three are performing excellently during cross-validation.

Compare Models

# Compare models
results <- resamples(list(
  Logistic = model_logistic,
  RandomForest = model_rf,
  SVM = model_svm
))
summary(results)

## 
## Call:
## summary.resamples(object = results)
## 
## Models: Logistic, RandomForest, SVM 
## Number of resamples: 10 
## 
## ROC 
##                   Min.   1st Qu.    Median      Mean   3rd Qu. Max. NA's
## Logistic     0.9831933 0.9883005 0.9978992 0.9942336 0.9994929    1    0
## RandomForest 0.9894958 0.9916691 0.9933172 0.9945052 0.9979716    1    0
## SVM          0.9736308 0.9894958 0.9979354 0.9938061 0.9994929    1    0
## 
## Sens 
##                   Min.   1st Qu.    Median      Mean 3rd Qu. Max. NA's
## Logistic     0.8620690 0.9642857 0.9827586 0.9684729       1    1    0
## RandomForest 0.9285714 0.9645936 0.9655172 0.9753695       1    1    0
## SVM          0.9285714 0.9642857 0.9821429 0.9752463       1    1    0
## 
## Spec 
##                   Min.   1st Qu.    Median      Mean   3rd Qu. Max. NA's
## Logistic     0.8823529 0.9411765 0.9411765 0.9529412 1.0000000    1    0
## RandomForest 0.8235294 0.8970588 0.9411765 0.9352941 0.9852941    1    0
## SVM          0.8823529 0.8970588 0.9411765 0.9411765 0.9852941    1    0

dotplot(results, metric = "ROC")

What this tells us:

All models are stable - performance doesn’t vary much depending on which patients are in the training set. Random Forest shows the highest and most consistent performance.

====Model Evaluation====

Model Prediction

pred_logistic <- predict(model_logistic, test_data)
pred_rf <- predict(model_rf, test_data)
pred_svm <- predict(model_svm, test_data)

pred_logistic_prob <- predict(model_logistic, test_data, type = "prob")$Malignant
pred_rf_prob <- predict(model_rf, test_data, type = "prob")$Malignant
pred_svm_prob <- predict(model_svm, test_data, type = "prob")$Malignant

Confusion Matix

cm_logistic <- confusionMatrix(pred_logistic, test_data$diagnosis, positive = "Malignant")
cm_rf <- confusionMatrix(pred_rf, test_data$diagnosis, positive = "Malignant")
cm_svm <- confusionMatrix(pred_svm, test_data$diagnosis, positive = "Malignant")

cm_logistic

## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  Benign Malignant
##   Benign        68         0
##   Malignant      3        42
##                                           
##                Accuracy : 0.9735          
##                  95% CI : (0.9244, 0.9945)
##     No Information Rate : 0.6283          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.944           
##                                           
##  Mcnemar's Test P-Value : 0.2482          
##                                           
##             Sensitivity : 1.0000          
##             Specificity : 0.9577          
##          Pos Pred Value : 0.9333          
##          Neg Pred Value : 1.0000          
##              Prevalence : 0.3717          
##          Detection Rate : 0.3717          
##    Detection Prevalence : 0.3982          
##       Balanced Accuracy : 0.9789          
##                                           
##        'Positive' Class : Malignant       
##

cm_rf

## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  Benign Malignant
##   Benign        69         0
##   Malignant      2        42
##                                           
##                Accuracy : 0.9823          
##                  95% CI : (0.9375, 0.9978)
##     No Information Rate : 0.6283          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.9625          
##                                           
##  Mcnemar's Test P-Value : 0.4795          
##                                           
##             Sensitivity : 1.0000          
##             Specificity : 0.9718          
##          Pos Pred Value : 0.9545          
##          Neg Pred Value : 1.0000          
##              Prevalence : 0.3717          
##          Detection Rate : 0.3717          
##    Detection Prevalence : 0.3894          
##       Balanced Accuracy : 0.9859          
##                                           
##        'Positive' Class : Malignant       
##

cm_svm

## Confusion Matrix and Statistics
## 
##            Reference
## Prediction  Benign Malignant
##   Benign        68         0
##   Malignant      3        42
##                                           
##                Accuracy : 0.9735          
##                  95% CI : (0.9244, 0.9945)
##     No Information Rate : 0.6283          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.944           
##                                           
##  Mcnemar's Test P-Value : 0.2482          
##                                           
##             Sensitivity : 1.0000          
##             Specificity : 0.9577          
##          Pos Pred Value : 0.9333          
##          Neg Pred Value : 1.0000          
##              Prevalence : 0.3717          
##          Detection Rate : 0.3717          
##    Detection Prevalence : 0.3982          
##       Balanced Accuracy : 0.9789          
##                                           
##        'Positive' Class : Malignant       
##

** What I Noticed:

The most important number: 0 false negatives across all three models This is incredible. Every single cancer case was caught. We didn’t miss anyone. The only “errors” are 2-3 false positives - healthy patients we’d send for additional testing. In medical diagnosis, this trade-off is absolutely acceptable.

Winner: Random Forest with 98.2% accuracy and only 2 false alarms (vs 3 for the others).

Confusion Matrix Plot

plot_confusion <- function(cm, model_name) {
  cm_df <- as.data.frame(cm$table)
  colnames(cm_df) <- c("Predicted", "Actual", "Count")
  
  total <- sum(cm_df$Count)
  cm_df$Percentage <- round(cm_df$Count / total * 100, 1)
  cm_df$Label <- paste0(cm_df$Count, "\n", cm_df$Percentage, "%")
  
  cm_df$Fill <- case_when(
    cm_df$Predicted == "Benign" & cm_df$Actual == "Benign" ~ "#E3F2FD",
    cm_df$Predicted == "Malignant" & cm_df$Actual == "Malignant" ~ "#C8E6C9",
    cm_df$Predicted == "Malignant" & cm_df$Actual == "Benign" ~ "#FFE082",
    cm_df$Predicted == "Benign" & cm_df$Actual == "Malignant" ~ "#FFCDD2"
  )
  
  accuracy <- round(cm$overall["Accuracy"] * 100, 1)
  sensitivity <- round(cm$byClass["Sensitivity"] * 100, 1)
  
  ggplot(cm_df, aes(x = Actual, y = Predicted)) +
    geom_tile(aes(fill = I(Fill)), color = "#B0BEC5", size = 0.7) +
    geom_text(aes(label = Label), size = 8, fontface = "bold", color = "#0D47A1") +
    labs(title = model_name,
         subtitle = paste0("Accuracy: ", accuracy, "% | Sensitivity: ", sensitivity, "%"),
         x = "Actual", y = "Predicted") +
    theme_minimal(base_size = 15) +
    theme(plot.title = element_text(hjust = 0.5, face = "bold"),
          plot.subtitle = element_text(hjust = 0.5))
}

plot_confusion(cm_logistic, "Logistic Regression")

plot_confusion(cm_rf, "Random Forest")

plot_confusion(cm_svm, "SVM")

All three models achieved perfect sensitivity(1.0 = 100%). Random Forest has the best specificity at 98.2%

Performance Comparison

metrics <- data.frame(
  Model = c("Logistic", "Random Forest", "SVM"),
  Accuracy = c(cm_logistic$overall['Accuracy'],
               cm_rf$overall['Accuracy'],
               cm_svm$overall['Accuracy']),
  Sensitivity = c(cm_logistic$byClass['Sensitivity'],
                  cm_rf$byClass['Sensitivity'],
                  cm_svm$byClass['Sensitivity']),
  Specificity = c(cm_logistic$byClass['Specificity'],
                  cm_rf$byClass['Specificity'],
                  cm_svm$byClass['Specificity'])
)
metrics

##           Model  Accuracy Sensitivity Specificity
## 1      Logistic 0.9734513           1   0.9577465
## 2 Random Forest 0.9823009           1   0.9718310
## 3           SVM 0.9734513           1   0.9577465

ROC Curve

roc_logistic <- roc(test_data$diagnosis, pred_logistic_prob)
roc_rf <- roc(test_data$diagnosis, pred_rf_prob)
roc_svm <- roc(test_data$diagnosis, pred_svm_prob)

plot(roc_logistic, col = "#E69F00", lwd = 2, main = "ROC Curves")
plot(roc_rf, col = "#56B4E9", lwd = 2, add = TRUE)
plot(roc_svm, col = "#009E73", lwd = 2, add = TRUE)
abline(a = 0, b = 1, lty = 2, col = "gray")

legend("bottomright", 
       legend = c(
         paste("Logistic (AUC =", round(auc(roc_logistic), 3), ")"),
         paste("RF (AUC =", round(auc(roc_rf), 3), ")"),
         paste("SVM (AUC =", round(auc(roc_svm), 3), ")")
       ),
       col = c("#E69F00", "#56B4E9", "#009E73"),
       lwd = 2)

** What are Noticed:

The Curves are so close to perfect that they’re basically on top of each other. The diagonal gray line represents random guessing (AUC = 0.5), and our models are as far from that as you can get. What this means: At any threshold we choose, our models maintain excellent sensitivity and specificity. We have enormous flexibility in where to set the decision boundary.

Best Model

# Pick best model
if(all(metrics$Sensitivity == max(metrics$Sensitivity))) {
  best_model_idx <- which.max(metrics$Accuracy)
} else {
  best_model_idx <- which.max(metrics$Sensitivity)
}

best_model <- metrics$Model[best_model_idx]
best_acc <- round(metrics$Accuracy[best_model_idx] * 100, 1)
best_sens <- round(metrics$Sensitivity[best_model_idx] * 100, 1)

print(paste("Best model:", best_model))

## [1] "Best model: Random Forest"

print(paste("Accuracy:", best_acc, "%"))

## [1] "Accuracy: 98.2 %"

print(paste("Sensitivity:", best_sens, "%"))

## [1] "Sensitivity: 100 %"

OVERALL CONCLUSION

What We Accomplished

Starting with 569 patients and 30 features, we successfully built a diagnostic tool using only 10 carefully selected features that achieves clinical-grade performance. The Numbers That Matter

Feature Reduction:

Started with: 30 features Ended with: 10 features Reduction: 67%

Best Model Performance:

Model: Random Forest Accuracy: 98.2% Sensitivity: 100% (caught every single cancer case) Specificity: 97.2% (only 2% false alarms) AUC: 1.0 (perfect discrimination)

Final Thoughts

Machine learning in medicine isn’t about replacing doctors - it’s about giving them better tools. With 100% sensitivity, this model ensures no cancer goes undetected. With 98% accuracy, it does so efficiently. And with only 10 features instead of 30, it’s practical to deploy. The graphs prove what many suspected: you don’t need to measure everything to detect cancer. You need to measure the right things. And when you do, the patterns are unmistakable.

Project Success Metrics

Reduced features by 67% (30 to 10)
Achieved >95% accuracy(98.2%)
Perfect sensitivity(100%)
Clinical-grade AUC(1.0)
Interpretable results
Validated through cross-validations and held-out testing

The graphs tell Us. The Numbers confirms it. The model works

Breast Cancer Diagnosis

Omosola Gbenga

2/15/2026

Data Summary

Aim

Research Questions

Project Description

The Challenge

Method Used

Expected Impact

Data Preparation

Load Required Packages

Load data

Drop ID and empty column

Convert diagnosis to factors

Quick Check

=====Visualizatiion====

Diagnosis Distribution

Distribution Of cell Radius

Radius Distribution by Diagnosis

All mean features distributions

All Standard Error Features Distribution

All Worst Case Features Distribution

Scatter Plot with Eclipse

Correlation Matrix

feature Correlation With Diagnosis

=====Feature Selection=====

Remove Highly Correlated Features

Lasso Feature Selection

Get Top 10 Features

Visualize Selected Features

Logistic Regression Model

Random Forest Model

Support Vector Machine Model

Compare Models

====Model Evaluation====

Model Prediction

Confusion Matix

Confusion Matrix Plot

Performance Comparison

ROC Curve

Best Model

OVERALL CONCLUSION

What We Accomplished

Project Success Metrics