RoBoSS: A Robust, Bounded, Sparse, and Smooth Loss Function for Supervised Learning

In the domain of machine learning algorithms, the significance of the loss function is paramount, especially in supervised learning tasks. It serves as a fundamental pillar that profoundly influences the behavior and efficacy of supervised learning algorithms. Traditional loss functions, while widely used, often struggle to handle noisy and high-dimensional data, impede model interpretability, and lead to slow convergence during training. In this paper, we address the aforementioned constraints by proposing a novel robust, bounded, sparse, and smooth (RoBoSS) loss function for supervised learning. Further, we incorporate the RoBoSS loss function within the framework of support vector machine (SVM) and introduce a new robust algorithm named $\mathcal{L}_{rbss}$-SVM. For the theoretical analysis, the classification-calibrated property and generalization ability are also presented. These investigations are crucial for gaining deeper insights into the performance of the RoBoSS loss function in the classification tasks and its potential to generalize well to unseen data. To empirically demonstrate the effectiveness of the proposed $\mathcal{L}_{rbss}$-SVM, we evaluate it on $88$ real-world UCI and KEEL datasets from diverse domains. Additionally, to exemplify the effectiveness of the proposed $\mathcal{L}_{rbss}$-SVM within the biomedical realm, we evaluated it on two medical datasets: the electroencephalogram (EEG) signal dataset and the breast cancer (BreaKHis) dataset. The numerical results substantiate the superiority of the proposed $\mathcal{L}_{rbss}$-SVM model, both in terms of its remarkable generalization performance and its efficiency in training time

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