Comparative Analysis of Sparse Multinomial Logistic Regression and Convolutional Neural Networks for Multi-Class Image Classification

The classification problem represents a funda-mental challenge in machine learning, with logistic regression serving as a traditional yet widely utilized method across various scientific disciplines. The current popular method for solving multi classification problems is deep neural networks, especially convolutional neural networks. However, as the number of neural network layers increases, the hardware requirements for model solving will be very high. Therefore, it is meaningful to study methods for multi classification problems with limited computing resources. In this study, we proposed using semidefinite proximal alternating direction method of multipliers(spADMM) to solve the multinomial logistic regression model and compared it with convolutional neural network models. Our results demonstrate that the spADMM not only achieves comparable accuracy to several prevalent convolutional neural network models but also ex- hibits significant improvements in time efficiency with limited computing resources.