MATLAB Code Implementation for Calculating Mahalanobis Distance

Mahalanobis distance is a distance metric that accounts for data correlations, making it particularly suitable for multivariate statistical analysis. It standardizes feature scales by incorporating the inverse of the covariance matrix and eliminates the effects of inter-feature correlations. The core steps for calculating Mahalanobis distance in MATLAB can be divided into three main phases: Data Preparation First, construct the sample matrix (where each row represents an observation and each column represents a feature) and the target vector. When calculating distances between two sample sets, ensure their feature dimensions are aligned. In MATLAB code, this typically involves creating matrices X (reference data) and Y (query data) with consistent column dimensions. Covariance Matrix Inversion Use MATLAB's `cov` function to compute the sample covariance matrix, followed by the `inv` function for matrix inversion. For high-dimensional data, implement regularization techniques (such as adding a small diagonal matrix) to prevent singularity issues. The code implementation should include checks for matrix conditioning using `cond` or `rcond` functions. Distance Calculation Utilize the `pdist2` function (requires Statistics and Machine Learning Toolbox) with the 'mahalanobis' parameter, or manually implement the distance formula. For manual implementation, employ matrix operations to compute the quadratic form: `sqrt((x-y)*inv(C)*(x-y)')` where C represents the covariance matrix. Vectorized implementation using broadcasting can efficiently handle batch calculations. Key Implementation Details: - When dealing with dimensional redundancy, perform PCA dimensionality reduction using `pca` function before distance calculation - For single-sample distance testing, reuse the covariance matrix from the training set to maintain consistency - The Mahalanobis function demonstrates excellent performance in anomaly detection and classification problems Typical application scenarios include feature matching in image recognition and outlier detection in financial data. MATLAB's vectorized operations efficiently handle batch distance computation tasks through matrix-based implementations that leverage built-in linear algebra routines. The implementation can be optimized using Cholesky decomposition for covariance matrices to improve numerical stability.