Cave of Python

Let’s take a look at applying PCA to a dataset that has many more than just a few data series.

The Wisconsin breast cancer dataset from Scikit-learn contains thirty columns of data. The data apparently concerns the digitally-detected shape of the nuclei of cells in breast tumour biopsies. We are also told whether the diagnosis was “malignant” or “benign”.

Our goal is therefore to predict the diagnosis based on this mechanically-assembled information.

First let’s take a look at the data.

from sklearn.linear_model import LogisticRegression
from sklearn.datasets import load_breast_cancer
import numpy as np

cancer = load_breast_cancer(as_frame=True)

X = cancer['data']
y = np.choose(cancer['target'], cancer['target_names'])

print(X.columns)
print(cancer['target_names'])

Index(['mean radius', 'mean texture', 'mean perimeter', 'mean area',
       'mean smoothness', 'mean compactness', 'mean concavity',
       'mean concave points', 'mean symmetry', 'mean fractal dimension',
       'radius error', 'texture error', 'perimeter error', 'area error',
       'smoothness error', 'compactness error', 'concavity error',
       'concave points error', 'symmetry error', 'fractal dimension error',
       'worst radius', 'worst texture', 'worst perimeter', 'worst area',
       'worst smoothness', 'worst compactness', 'worst concavity',
       'worst concave points', 'worst symmetry', 'worst fractal dimension'],
      dtype='object')
['malignant' 'benign']

You can see the data looks a lot like the iris data in terms of how we load it. It just contains different data series and target names. Instead of four measurements on iris petals and sepals, we have thirty measurements on tumour cell nuclei. Instead of three iris species, we have two possible diagnoses.

To try to predict the diagnosis on the basis of the cell nucleus shape data, we’ll take the following steps.

Here’s the code.

from sklearn.linear_model import LogisticRegression

from sklearn.datasets import load_breast_cancer
from sklearn.metrics import normalized_mutual_info_score
from sklearn.model_selection import train_test_split
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt
import pandas as pd
from sklearn.metrics import confusion_matrix, ConfusionMatrixDisplay
from sklearn.preprocessing import StandardScaler

import numpy as np

cancer = load_breast_cancer(as_frame=True)

X = cancer['data']

y = np.choose(cancer['target'], cancer['target_names'])

X_train, X_test, y_train, y_test = train_test_split(X, y, shuffle=True, train_size=0.7)

scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

pca = PCA(0.95)

components = pca.fit_transform(X_train)
print("Number of components:", pca.n_components_)

model = LogisticRegression()
model.fit(components, y_train)

test_components = pca.transform(X_test)
y_predicted = model.predict(test_components)

labels = cancer['target_names']
cm = confusion_matrix(y_test, y_predicted, labels=labels)
cm_display = ConfusionMatrixDisplay(confusion_matrix=cm, display_labels=labels)
cm_display.plot()

plt.show()

You can see our predictions have been quite successful. We have five failed predictions (two benign cases that were predicted to be malignant and three malignant cases that were predicted to be beign) and 166 correct predictions.