04 Svm

Last updated on 2025-07-10 | Edit this page

Support Vector Machine (SVM) with Breast Cancer Dataset

This notebook demonstrates the use of Support Vector Machines (SVM) for classifying tumors in the Breast Cancer dataset.

What is an SVM?

Support Vector Machines are powerful supervised learning models for classification. An SVM finds the hyperplane that best separates data points from two classes.

It maximizes the margin, which is the distance between the hyperplane and the nearest points from each class (support vectors).

Step 1: Load the Breast Cancer Dataset

PYTHON 

from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
import pandas as pd

# Load dataset
data = load_breast_cancer()
X = data.data
y = data.target

# Split dataset
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.3, random_state=31
)

# Normalize (Standardize) features
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

Step 3: Train an SVM Model

We use the SVC class from sklearn.svm with default kernel (RBF).

PYTHON 

from sklearn.svm import SVC

model = SVC(probability=True)
model.fit(X_train, y_train)

#sk-container-id-1 { /* Definition of color scheme common for light and dark mode / –sklearn-color-text: #000; –sklearn-color-text-muted: #666; –sklearn-color-line: gray; / Definition of color scheme for unfitted estimators / –sklearn-color-unfitted-level-0: #fff5e6; –sklearn-color-unfitted-level-1: #f6e4d2; –sklearn-color-unfitted-level-2: #ffe0b3; –sklearn-color-unfitted-level-3: chocolate; / Definition of color scheme for fitted estimators */ –sklearn-color-fitted-level-0: #f0f8ff; –sklearn-color-fitted-level-1: #d4ebff; –sklearn-color-fitted-level-2: #b3dbfd; –sklearn-color-fitted-level-3: cornflowerblue;

/* Specific color for light theme */ –sklearn-color-text-on-default-background: var(–sg-text-color, var(–theme-code-foreground, var(–jp-content-font-color1, black))); –sklearn-color-background: var(–sg-background-color, var(–theme-background, var(–jp-layout-color0, white))); –sklearn-color-border-box: var(–sg-text-color, var(–theme-code-foreground, var(–jp-content-font-color1, black))); –sklearn-color-icon: #696969;

@media (prefers-color-scheme: dark) { /* Redefinition of color scheme for dark theme */ –sklearn-color-text-on-default-background: var(–sg-text-color, var(–theme-code-foreground, var(–jp-content-font-color1, white))); –sklearn-color-background: var(–sg-background-color, var(–theme-background, var(–jp-layout-color0, #111))); –sklearn-color-border-box: var(–sg-text-color, var(–theme-code-foreground, var(–jp-content-font-color1, white))); –sklearn-color-icon: #878787; } }

#sk-container-id-1 { color: var(–sklearn-color-text); }

#sk-container-id-1 pre { padding: 0; }

#sk-container-id-1 input.sk-hidden–visually { border: 0; clip: rect(1px 1px 1px 1px); clip: rect(1px, 1px, 1px, 1px); height: 1px; margin: -1px; overflow: hidden; padding: 0; position: absolute; width: 1px; }

#sk-container-id-1 div.sk-dashed-wrapped { border: 1px dashed var(–sklearn-color-line); margin: 0 0.4em 0.5em 0.4em; box-sizing: border-box; padding-bottom: 0.4em; background-color: var(–sklearn-color-background); }

#sk-container-id-1 div.sk-container { /* jupyter’s normalize.less sets [hidden] { display: none; } but bootstrap.min.css set [hidden] { display: none !important; } so we also need the !important here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */ display: inline-block !important; position: relative; }

#sk-container-id-1 div.sk-text-repr-fallback { display: none; }

div.sk-parallel-item, div.sk-serial, div.sk-item { /* draw centered vertical line to link estimators */ background-image: linear-gradient(var(–sklearn-color-text-on-default-background), var(–sklearn-color-text-on-default-background)); background-size: 2px 100%; background-repeat: no-repeat; background-position: center center; }

/* Parallel-specific style estimator block */

#sk-container-id-1 div.sk-parallel-item::after { content: ““; width: 100%; border-bottom: 2px solid var(–sklearn-color-text-on-default-background); flex-grow: 1; }

#sk-container-id-1 div.sk-parallel { display: flex; align-items: stretch; justify-content: center; background-color: var(–sklearn-color-background); position: relative; }

#sk-container-id-1 div.sk-parallel-item { display: flex; flex-direction: column; }

#sk-container-id-1 div.sk-parallel-item:first-child::after { align-self: flex-end; width: 50%; }

#sk-container-id-1 div.sk-parallel-item:last-child::after { align-self: flex-start; width: 50%; }

#sk-container-id-1 div.sk-parallel-item:only-child::after { width: 0; }

/* Serial-specific style estimator block */

#sk-container-id-1 div.sk-serial { display: flex; flex-direction: column; align-items: center; background-color: var(–sklearn-color-background); padding-right: 1em; padding-left: 1em; }

/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is clickable and can be expanded/collapsed. - Pipeline and ColumnTransformer use this feature and define the default style - Estimators will overwrite some part of the style using the sk-estimator class */

/* Pipeline and ColumnTransformer style (default) */

#sk-container-id-1 div.sk-toggleable { /* Default theme specific background. It is overwritten whether we have a specific estimator or a Pipeline/ColumnTransformer */ background-color: var(–sklearn-color-background); }

/* Toggleable label */ #sk-container-id-1 label.sk-toggleable__label { cursor: pointer; display: flex; width: 100%; margin-bottom: 0; padding: 0.5em; box-sizing: border-box; text-align: center; align-items: start; justify-content: space-between; gap: 0.5em; }

#sk-container-id-1 label.sk-toggleable__label .caption { font-size: 0.6rem; font-weight: lighter; color: var(–sklearn-color-text-muted); }

#sk-container-id-1 label.sk-toggleable__label-arrow:before { /* Arrow on the left of the label */ content: “▸”; float: left; margin-right: 0.25em; color: var(–sklearn-color-icon); }

#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before { color: var(–sklearn-color-text); }

/* Toggleable content - dropdown */

#sk-container-id-1 div.sk-toggleable__content { display: none; text-align: left; /* unfitted */ background-color: var(–sklearn-color-unfitted-level-0); }

#sk-container-id-1 div.sk-toggleable__content.fitted { /* fitted */ background-color: var(–sklearn-color-fitted-level-0); }

#sk-container-id-1 div.sk-toggleable__content pre { margin: 0.2em; border-radius: 0.25em; color: var(–sklearn-color-text); /* unfitted */ background-color: var(–sklearn-color-unfitted-level-0); }

#sk-container-id-1 div.sk-toggleable__content.fitted pre { /* unfitted */ background-color: var(–sklearn-color-fitted-level-0); }

#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content { /* Expand drop-down */ display: block; width: 100%; overflow: visible; }

#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before { content: “▾”; }

/* Pipeline/ColumnTransformer-specific style */

#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label { color: var(–sklearn-color-text); background-color: var(–sklearn-color-unfitted-level-2); }

#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label { background-color: var(–sklearn-color-fitted-level-2); }

/* Estimator-specific style */

/* Colorize estimator box */ #sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label { /* unfitted */ background-color: var(–sklearn-color-unfitted-level-2); }

#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label { /* fitted */ background-color: var(–sklearn-color-fitted-level-2); }

#sk-container-id-1 div.sk-label label.sk-toggleable__label, #sk-container-id-1 div.sk-label label { /* The background is the default theme color */ color: var(–sklearn-color-text-on-default-background); }

/* On hover, darken the color of the background */ #sk-container-id-1 div.sk-label:hover label.sk-toggleable__label { color: var(–sklearn-color-text); background-color: var(–sklearn-color-unfitted-level-2); }

/* Label box, darken color on hover, fitted */ #sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted { color: var(–sklearn-color-text); background-color: var(–sklearn-color-fitted-level-2); }

/* Estimator label */

#sk-container-id-1 div.sk-label label { font-family: monospace; font-weight: bold; display: inline-block; line-height: 1.2em; }

#sk-container-id-1 div.sk-label-container { text-align: center; }

/* Estimator-specific / #sk-container-id-1 div.sk-estimator { font-family: monospace; border: 1px dotted var(–sklearn-color-border-box); border-radius: 0.25em; box-sizing: border-box; margin-bottom: 0.5em; / unfitted */ background-color: var(–sklearn-color-unfitted-level-0); }

#sk-container-id-1 div.sk-estimator.fitted { /* fitted */ background-color: var(–sklearn-color-fitted-level-0); }

/* on hover / #sk-container-id-1 div.sk-estimator:hover { / unfitted */ background-color: var(–sklearn-color-unfitted-level-2); }

#sk-container-id-1 div.sk-estimator.fitted:hover { /* fitted */ background-color: var(–sklearn-color-fitted-level-2); }

/* Specification for estimator info (e.g. “i” and “?”) */

/* Common style for “i” and “?” */

.sk-estimator-doc-link, a:link.sk-estimator-doc-link, a:visited.sk-estimator-doc-link { float: right; font-size: smaller; line-height: 1em; font-family: monospace; background-color: var(–sklearn-color-background); border-radius: 1em; height: 1em; width: 1em; text-decoration: none !important; margin-left: 0.5em; text-align: center; /* unfitted */ border: var(–sklearn-color-unfitted-level-1) 1pt solid; color: var(–sklearn-color-unfitted-level-1); }

.sk-estimator-doc-link.fitted, a:link.sk-estimator-doc-link.fitted, a:visited.sk-estimator-doc-link.fitted { /* fitted */ border: var(–sklearn-color-fitted-level-1) 1pt solid; color: var(–sklearn-color-fitted-level-1); }

/* On hover / div.sk-estimator:hover .sk-estimator-doc-link:hover, .sk-estimator-doc-link:hover, div.sk-label-container:hover .sk-estimator-doc-link:hover, .sk-estimator-doc-link:hover { / unfitted */ background-color: var(–sklearn-color-unfitted-level-3); color: var(–sklearn-color-background); text-decoration: none; }

div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover, .sk-estimator-doc-link.fitted:hover, div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover, .sk-estimator-doc-link.fitted:hover { /* fitted */ background-color: var(–sklearn-color-fitted-level-3); color: var(–sklearn-color-background); text-decoration: none; }

/* Span, style for the box shown on hovering the info icon / .sk-estimator-doc-link span { display: none; z-index: 9999; position: relative; font-weight: normal; right: .2ex; padding: .5ex; margin: .5ex; width: min-content; min-width: 20ex; max-width: 50ex; color: var(–sklearn-color-text); box-shadow: 2pt 2pt 4pt #999; / unfitted */ background: var(–sklearn-color-unfitted-level-0); border: .5pt solid var(–sklearn-color-unfitted-level-3); }

.sk-estimator-doc-link.fitted span { /* fitted */ background: var(–sklearn-color-fitted-level-0); border: var(–sklearn-color-fitted-level-3); }

.sk-estimator-doc-link:hover span { display: block; }

/* “?”-specific style due to the `` HTML tag */

#sk-container-id-1 a.estimator_doc_link { float: right; font-size: 1rem; line-height: 1em; font-family: monospace; background-color: var(–sklearn-color-background); border-radius: 1rem; height: 1rem; width: 1rem; text-decoration: none; /* unfitted */ color: var(–sklearn-color-unfitted-level-1); border: var(–sklearn-color-unfitted-level-1) 1pt solid; }

#sk-container-id-1 a.estimator_doc_link.fitted { /* fitted */ border: var(–sklearn-color-fitted-level-1) 1pt solid; color: var(–sklearn-color-fitted-level-1); }

/* On hover / #sk-container-id-1 a.estimator_doc_link:hover { / unfitted */ background-color: var(–sklearn-color-unfitted-level-3); color: var(–sklearn-color-background); text-decoration: none; }

#sk-container-id-1 a.estimator_doc_link.fitted:hover { /* fitted */ background-color: var(–sklearn-color-fitted-level-3); }

.estimator-table summary { padding: .5rem; font-family: monospace; cursor: pointer; }

.estimator-table details[open] { padding-left: 0.1rem; padding-right: 0.1rem; padding-bottom: 0.3rem; }

.estimator-table .parameters-table { margin-left: auto !important; margin-right: auto !important; }

.estimator-table .parameters-table tr:nth-child(odd) { background-color: #fff; }

.estimator-table .parameters-table tr:nth-child(even) { background-color: #f6f6f6; }

.estimator-table .parameters-table tr:hover { background-color: #e0e0e0; }

.estimator-table table td { border: 1px solid rgba(106, 105, 104, 0.232); }

.user-set td { color:rgb(255, 94, 0); text-align: left; }

.user-set td.value pre { color:rgb(255, 94, 0) !important; background-color: transparent !important; }

.default td { color: black; text-align: left; }

.user-set td i, .default td i { color: black; }

.copy-paste-icon { background-image: url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9IjAgMCA0NDggNTEyIj48IS0tIUZvbnQgQXdlc29tZSBGcmVlIDYuNy4yIGJ5IEBmb250YXdlc29tZSAtIGh0dHBzOi8vZm9udGF3ZXNvbWUuY29tIExpY2Vuc2UgLSBodHRwczovL2ZvbnRhd2Vzb21lLmNvbS9saWNlbnNlL2ZyZWUgQ29weXJpZ2h0IDIwMjUgRm9udGljb25zLCBJbmMuLS0+PHBhdGggZD0iTTIwOCAwTDMzMi4xIDBjMTIuNyAwIDI0LjkgNS4xIDMzLjkgMTQuMWw2Ny45IDY3LjljOSA5IDE0LjEgMjEuMiAxNC4xIDMzLjlMNDQ4IDMzNmMwIDI2LjUtMjEuNSA0OC00OCA0OGwtMTkyIDBjLTI2LjUgMC00OC0yMS41LTQ4LTQ4bDAtMjg4YzAtMjYuNSAyMS41LTQ4IDQ4LTQ4ek00OCAxMjhsODAgMCAwIDY0LTY0IDAgMCAyNTYgMTkyIDAgMC0zMiA2NCAwIDAgNDhjMCAyNi41LTIxLjUgNDgtNDggNDhMNDggNTEyYy0yNi41IDAtNDgtMjEuNS00OC00OEwwIDE3NmMwLTI2LjUgMjEuNS00OCA0OC00OHoiLz48L3N2Zz4=); background-repeat: no-repeat; background-size: 14px 14px; background-position: 0; display: inline-block; width: 14px; height: 14px; cursor: pointer; } SVC(probability=True)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.SVC?Documentation for SVCiFitted

Parameters

C 1.0
kernel ‘rbf’
degree 3
gamma ‘scale’
coef0 0.0
shrinking True
probability True
tol 0.001
cache_size 200
class_weight None
verbose False
max_iter -1
decision_function_shape ‘ovr’
break_ties False
random_state None

function copyToClipboard(text, element) { // Get the parameter prefix from the closest toggleable content const toggleableContent = element.closest(’.sk-toggleable__content’); const paramPrefix = toggleableContent ? toggleableContent.dataset.paramPrefix : ’’; const fullParamName = paramPrefix ? ${paramPrefix}${text} : text;

SH 

const originalStyle = element.style;
const computedStyle = window.getComputedStyle(element);
const originalWidth = computedStyle.width;
const originalHTML = element.innerHTML.replace('Copied!', '');

navigator.clipboard.writeText(fullParamName)
    .then(() => {
        element.style.width = originalWidth;
        element.style.color = 'green';
        element.innerHTML = "Copied!";

        setTimeout(() => {
            element.innerHTML = originalHTML;
            element.style = originalStyle;
        }, 2000);
    })
    .catch(err => {
        console.error('Failed to copy:', err);
        element.style.color = 'red';
        element.innerHTML = "Failed!";
        setTimeout(() => {
            element.innerHTML = originalHTML;
            element.style = originalStyle;
        }, 2000);
    });
return false;

}

document.querySelectorAll(‘.fa-regular.fa-copy’).forEach(function(element) { const toggleableContent = element.closest(’.sk-toggleable__content’); const paramPrefix = toggleableContent ? toggleableContent.dataset.paramPrefix : ’’; const paramName = element.parentElement.nextElementSibling.textContent.trim(); const fullParamName = paramPrefix ? ${paramPrefix}${paramName} : paramName;

SH 

element.setAttribute('title', fullParamName);

});

Step 4: Evaluate the Model

PYTHON 

from sklearn.metrics import (
    accuracy_score, precision_score, recall_score, f1_score,
    ConfusionMatrixDisplay, classification_report, roc_curve, auc
)

y_pred = model.predict(X_test)
print("Accuracy:", accuracy_score(y_test, y_pred))
print("Precision:", precision_score(y_test, y_pred))
print("Recall:", recall_score(y_test, y_pred))
print("F1 Score:", f1_score(y_test, y_pred))
print("\nClassification Report:\n", classification_report(y_test, y_pred))

SH 

Accuracy: 0.9766081871345029
Precision: 0.972972972972973
Recall: 0.9908256880733946
F1 Score: 0.9818181818181818

Classification Report:
               precision    recall  f1-score   support

           0       0.98      0.95      0.97        62
           1       0.97      0.99      0.98       109

    accuracy                           0.98       171
   macro avg       0.98      0.97      0.97       171
weighted avg       0.98      0.98      0.98       171

What is a Confusion Matrix?

A confusion matrix is a summary of prediction results:

Predicted Positive Predicted Negative
Actual Positive True Positive (TP) False Negative (FN)
Actual Negative False Positive (FP) True Negative (TN)
  • Accuracy, Precision, Recall, F1 Score are all derived from this table.

PYTHON 

import matplotlib.pyplot as plt
import seaborn as sns

ConfusionMatrixDisplay.from_estimator(model, X_test, y_test)
plt.title('SVM Confusion Matrix')
plt.show()
png
png

What is an ROC Curve?

The ROC Curve shows the trade-off between True Positive Rate (Recall) and False Positive Rate. The AUC (Area Under Curve) summarizes the performance into a single number.

PYTHON 

y_proba = model.predict_proba(X_test)[:, 1]
fpr, tpr, _ = roc_curve(y_test, y_proba)
roc_auc = auc(fpr, tpr)

plt.plot(fpr, tpr, label='AUC = ' + str(round(roc_auc, 2)))
plt.plot([0, 1], [0, 1], 'k--')
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('SVM ROC Curve')
plt.legend()
plt.show()
png
png