Support matrix machine: A review

Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists in matrix format, which is given as input to SVM by reshaping the matrices into vectors. The process of reshaping disrupts the spatial correlations inherent in the matrix data. Also, converting matrices into vectors results in input data with a high dimensionality, which introduces significant computational complexity. To overcome these issues in classifying matrix input data, support matrix machine (SMM) is proposed. It represents one of the emerging methodologies tailored for handling matrix input data. The SMM method preserves the structural information of the matrix data by using the spectral elastic net property which is a combination of the nuclear norm and Frobenius norm. This article provides the first in-depth analysis of the development of the SMM model, which can be used as a thorough summary by both novices and experts. We discuss numerous SMM variants, such as robust, sparse, class imbalance, and multi-class classification models. We also analyze the applications of the SMM model and conclude the article by outlining potential future research avenues and possibilities that may motivate academics to advance the SMM algorithm

LSTSVR-PI: Least square twin support vector regression with privileged information

In an educational setting, a teacher plays a crucial role in various classroom teaching patterns. Similarly, mirroring this aspect of human learning, the learning using privileged information (LUPI) paradigm introduces additional information to instruct learning models during the training stage. A different approach to train the twin variant of the regression model is provided by the new least square twin support vector regression using privileged information (LSTSVR-PI), which integrates the LUPI paradigm to utilize additional sources of information into the least square twin support vector regression. The proposed LSTSVR-PI solves system of linear equations which adds up to the efficiency of the model. Further, we also establish a generalization error bound based on the Rademacher complexity of the proposed model and incorporate the structural risk minimization principle. The proposed LSTSVR-PI fills the gap between the contemporary paradigm of LUPI and classical LSTSVR. Further, to assess the performance of the proposed model, we conduct numerical experiments along with the baseline models across various artificially generated and real-world datasets. The various experiments and statistical analysis infer the superiority of the proposed model. Moreover, as an application, we conduct experiments on time series datasets, which results in the superiority of the proposed LSTSVR-PI