Principal Component Analysis (PCA)👨🏼‍🏫

Principal Component Analysis is a dimensionality-reduction method that is often used to reduce the dimensionality of large dataset. The idea of PCA is simple — reduce the number of variables of a data set, while preserving as much information as possible. Following the application of this method, we have several benefits

• we can rank the observations based on several variables
• overcome multi-collinearity
• data visualization (biplot)

This method is based on the following steps:

1. Standardize the range of continuous initial variables
2. Compute the covariance matrix to identify correlations
3. Compute the eigenvectors and eigenvalues of the covariance matrix to identify the principal components
4. Create a feature vector to decide which principal components to keep
5. Recast the data along the principal components axes

We will apply Principal Component Analysis for breast cancer Wisconsin (original) dataset. The dataset contains 699 real observations considering 9 independent variables that allow us to classify the dependent variable as malignant or benign. A brief description of the medical terminology can be consulted in this notebook.

📚References.

• Steven M. Holland, Univ. of Georgia: Principal Components Analysis
• skymind.ai: Eigenvectors, Eigenvalues, PCA, Covariance and Entropy
• Lindsay I. Smith: A tutorial on Principal Component Analysis