MATLAB Function for Computing Linear Graph Embedding of High-Dimensional Data

This MATLAB function computes linear graph embedding for high-dimensional data, serving as a fundamental component for implementing various linear dimensionality reduction algorithms such as Locality Preserving Projection (LPP), Neighborhood Preserving Embedding (NPE), IsoProjection, and Locality Sensitive Discriminant Analysis (LSDA). The core functionality involves constructing an adjacency graph from high-dimensional data points and solving generalized eigenvalue problems to obtain optimal projection matrices. This transformation enables effective data visualization and analysis by mapping high-dimensional features to lower-dimensional spaces while preserving local data structures and neighborhood relationships. Typical applications include pattern recognition in complex datasets, outlier detection, clustering analysis, and data preprocessing for machine learning pipelines. The implementation typically handles graph weight matrix computation, eigenvalue decomposition, and projection vector selection through optimized linear algebra operations. Data scientists and machine learning engineers can leverage this function as a preprocessing step to enhance the performance of subsequent algorithms like classification or regression models. We are sharing this valuable resource to support your research and practical applications in data analysis and machine learning workflows. The function includes parameters for adjusting graph construction methods (k-nearest neighbors or epsilon-ball) and regularization options to handle singular matrices during eigenvalue computation.