Extreme semi-supervised learning for multiclass classification

Abstract

Semi-Supervised Support Vector Machines (S3VMs) provide a powerful framework for Semi-Supervised Learning (SSL) tasks which leverage widely available unlabeled data to improve performance. However, there exist three issues in S3VMs: (i) S3VMs require concurrently training c one-against-all (OAA) classifiers (c is the number of classes) for multiclass classification, which is prohibitive for large c; (ii) S3VMs require huge computational time and large storage (because of the large kernel matrix) in large-scale training and testing; (iii) S3VMs require the balance constraint in the unlabeled data, which not only needs prior knowledge from the unlabeled data (the prior knowledge is unavailable in some applications), but also makes their nonconvex optimization problem more intractable. To address these issues, a novel method called Extreme Semi-Supervised Learning (ESSL) is proposed in this paper. First, the framework of Extreme Learning Machine (ELM) is adopted to handle both binary and multiclass classification problems in a unified model. Second, the hidden layer is encoded by an extremely small approximate empirical kernel map (AEKM) to greatly reduce the computational cost and the memory usage for training and testing. Third, the balance constraint (prior knowledge) in the unlabeled data is removed through the elaborative design of weighting function (which emphasizes the importance of labeled data and the minority pattern in the labeled data).By these three ways, ESSL can be solved effectively and efficiently based on alternating optimization (AO). More specifically, ESSL can be analytically and simply solved by generalized pseudoinverse and oneHotMap function (without any optimization solver and the OAA strategy) in the AO procedure, and consequently, better performance and much faster training speed are always achieved in ESSL. Our empirical study shows that ESSL significantly outperforms existing efficient SSL methods (e.g., meanS3VM and SS-ELM) in terms of accuracy, efficiency and memory, especially for large-scale multiclass problems. As an example, on the 20Newsgroups dataset, ESSL respectively runs 45 and 120 times faster than meanS3VM for training and testing with the improvement in accuracy of 3%, while the memory usage is reduced to 1/14. It is noteworthy that even though all the model parameters are with default values, ESSL already produces very excellent performance without fine-tuning parameters.