A Simple Example of Principal Component Analysis (PCA)

This documentation provides a beginner-friendly MATLAB example of Principal Component Analysis (PCA) - a fundamental dimensionality reduction and data visualization technique. The implementation demonstrates how to apply PCA to multivariate datasets and interpret the analytical outcomes using MATLAB's built-in functions. First, we import the dataset and perform essential preprocessing steps. For this example, we utilize a housing dataset containing variables such as price, area, number of bedrooms, and number of bathrooms. Data standardization is implemented using MATLAB's zscore function to ensure equal weighting of all variables, calculated as (data - mean(data)) / std(data). This critical preprocessing step prevents variables with larger scales from disproportionately influencing the PCA results. Next, we perform PCA using MATLAB's pca function, which computes the covariance matrix and identifies linear combinations of variables that capture maximum variance. The algorithm sequentially determines principal components through eigenvalue decomposition of the covariance matrix, where each component represents an orthogonal direction of maximum variance. The pca function returns three key outputs: component coefficients (loadings), transformed data (scores), and variance explained by each component. Finally, we interpret the principal components by analyzing the loading vectors to understand variable contributions, and visualize results using MATLAB's plotting functions like scatter3 and biplot. The first component typically represents the most significant data pattern, while subsequent components capture residual variance. Visualization techniques help reveal relationships between variables and identify potential clusters or outliers in the data. This example provides a practical foundation for understanding PCA implementation in MATLAB, demonstrating complete workflow from data preparation to result interpretation. The code structure follows best practices for reproducible research and can be adapted for various multidimensional datasets.