MATLAB Code Implementation of Feature Dimensionality Reduction Methods

Feature dimensionality reduction serves as a critical preprocessing step in machine learning and data analysis, effectively reducing data dimensions, improving model performance, and lowering computational complexity. In MATLAB, developers can conveniently implement various classical feature dimensionality reduction methods, primarily categorized into the following four techniques:

Principal Component Analysis (PCA) PCA is an unsupervised linear dimensionality reduction method that maps original features to a set of uncorrelated principal components through orthogonal transformation. MATLAB's built-in `pca` function directly computes projection matrices for eigenvectors, allowing users to specify either the preserved variance ratio or the number of principal components for dimensionality reduction. Its core algorithm maximizes variance retention in data directions, making it suitable for high-dimensional data visualization or noise reduction scenarios. Implementation involves calling `[coeff,score,latent] = pca(X)` where `coeff` contains principal components and `latent` stores explained variances.

Sequential Forward Floating Search (SFFS) SFFS belongs to wrapper-based feature selection methods, combining greedy strategies with backtracking mechanisms. Starting from an empty feature set, it incrementally adds features that most improve model performance while permitting temporary removal of selected features to avoid local optima. In MATLAB, this can be implemented through custom loops and cross-validation with classifiers like `fitcsvm`, requiring careful setting of floating step size to balance efficiency and effectiveness. The algorithm typically uses criterion functions like classification accuracy with forward/backward tracking.

Sequential Backward Selection (SBS) SBS operates oppositely to SFFS, starting with all features and iteratively removing those contributing least to model performance. Its advantage lies in rapid dimension reduction, though the greedy nature may overlook feature interactions. MATLAB implementation requires monitoring model accuracy after each removal, often using the `sequentialfs` function with backward elimination strategy. This method suits initial stages with large feature sets, where `sequentialfs` can be configured with `'direction','backward'` parameter.

Sequential Forward Selection (SFS) SFS is a simplified version of SFFS featuring unidirectional feature addition without backtracking. While computationally efficient, it may converge to suboptimal solutions. In MATLAB, implementation can be achieved through stepwise regression (`stepwisefit`) or manually written feature evaluation loops, making it suitable as a baseline method for comparison with other strategies. The algorithm evaluates feature subsets using metrics like AIC or BIC during sequential incorporation.

Extended Considerations: Practical applications require method selection based on data characteristics—PCA suits scenarios with strong feature correlations, while feature selection methods (SFFS/SBS/SFS) prioritize feature interpretability. MATLAB's Statistics and Machine Learning Toolbox provides underlying support for these methods, and combining them with cross-validation further optimizes dimensionality reduction effects. Key functions include `crossval` for performance validation and `pcares` for PCA residual analysis.