Enhancing Gaussian Mixture Model Efficiency Through Covariance Matrix Optimization, Singular Value Decomposition, and Block Toeplitz Matrices
Kanchana R, F. Mary Harin Fernandez · 2024
Gaussian Mixture Models (GMMs) are widely used for clustering, density estimation, and pattern recognition. Despite their versatility, GMMs often face computational challenges, particularly when dealing with large datasets or high-dimensional spaces. To address these issues, an approach is proposed to enhance the efficiency of GMMs by integrating covariance matrix optimization, Singular Value Decomposition (SVD), and Block Toeplitz matrices. The method involves refining the covariance matrix to better capture the underlying data structure, thereby reducing computational complexity. The application of SVD allows for dimensionality reduction and improved numerical stability. Additionally, the use of Block Toeplitz matrices facilitates efficient handling of structured covariance matrices, further accelerating computations. Experimental results demonstrate significant improvements in prediction accuracy and computational speed, providing a more scalable and efficient solution for GMM applications across various domains.