MATLAB Implementation of Dimensionality Reduction Using PCA and LDA

PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis) are two commonly used dimensionality reduction techniques that transform high-dimensional data into lower-dimensional representations while preserving maximum useful information. KNN (K-Nearest Neighbors) is a simple yet efficient classification algorithm frequently combined with dimensionality reduction methods.

The core concept of PCA dimensionality reduction involves projecting original data onto directions with maximum variance, known as principal components. By retaining the first few principal components, PCA reduces data dimensionality while maintaining data structure as much as possible. In MATLAB implementation, this is typically achieved using the pca() function which computes principal components and their corresponding eigenvalues. PCA is suitable for unsupervised learning scenarios since it doesn't consider class labels.

LDA, in contrast, is a supervised dimensionality reduction method that aims to find projection directions maximizing between-class differences while minimizing within-class differences. MATLAB's fitcdiscr() function can implement LDA by calculating optimal projection vectors that enhance class separability. This makes LDA particularly suitable for classification tasks as it incorporates sample class information to create dimensions more favorable for classification.

In practical face recognition applications, the typical workflow involves preprocessing image data (such as normalization), applying PCA or LDA for dimensionality reduction, and finally using KNN for classification. The KNN algorithm operates by finding K nearest neighbors in the training set for a given test sample, then determining the final classification through majority voting among their labels. In MATLAB, this can be implemented using the fitcknn() function with customizable distance metrics and K values.

The key to this entire process lies in selecting appropriate dimensionality reduction parameters and optimal K values for KNN, typically optimized through cross-validation techniques like cvpartition(). Furthermore, PCA and LDA can be used individually or combined (e.g., initial PCA reduction followed by LDA optimization) to enhance classification performance. Code implementation would involve sequential function calls and parameter tuning based on validation results.