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

Robust Discrete Matrix Completion

Most existing matrix completion methods seek the matrix global structure in the real number domain and produce predictions that are inappropriate for applications retaining discrete structure, where an additional step is required to post-process prediction results with either heuristic threshold parameters or complicated mappings. Such an ad-hoc process is inefficient and impractical. In this paper, we propose a novel robust discrete matrix completion algorithm that produces the prediction from the collection of user specified discrete values by introducing a new discrete constraint to the matrix completion model. Our method achieves a high prediction accuracy, very close to the most optimal value of competitive methods with threshold values tuning. We solve the difficult integer programming problem via incorporating augmented Lagrangian method in an elegant way, which greatly accelerates the converge process of our method and provides the asymptotic convergence in theory. The proposed discrete matrix completion model is applied to solve three real-world applications, and all empirical results demonstrate the effectiveness of our method