Responsible Gaussian Model: Matrix-Based Approximation of Gaussian Mixture Model

The rapid development of machine learning, particularly by deep learning, has made previously complex computational tasks more accessible. However, its mechanisms are often viewed as a black box and are difficult to interpret or control precisely using mathematical or engineering principles. In contrast, statistics shares similar theoretical foundations and application areas with machine learning but offers more interpretable models and mathematically rigorous frameworks. However, statistical methods face limitations when dealing with analytically intractable problems. The Gaussian mixture model (GMM) is a distribution obtained by adding normal distributions. In addition, it is a flexible probability distribution. It is highly practical but difficult to solve analytically; however, iterative methods, such as EM algorithm, can be applied to solve it. In this study, we propose the model with a new model, we propose The Responsible Gaussian Model a novel alternative to the Gaussian Mixture Model to avoid iterative solutions and obtain analytical approximation. To evaluate its performance, we applied the model to clustering on Iris plants dataset, Wine recognition dataset, Optical recognition of Handwritten digits dataset, and CIFAR-10.