Maximum Margin Multi-Dimensional Classification

Regression-Based Hyperparameter Learning for Support Vector Machines

Unification of classification and regression is a major challenge in machine learning and has attracted increasing attentions from researchers. In this article, we present a new idea for this challenge, where we convert the classification problem into a regression problem, and then use the methods in regression to solve the problem in classification. To this end, we leverage the widely used maximum margin classification algorithm and its typical representative, support vector machine (SVM). More specifically, we convert SVM into a piecewise linear regression task and propose a regression-based SVM (RBSVM) hyperparameter learning algorithm, where regression methods are used to solve several key problems in classification, such as learning of hyperparameters, calculation of prediction probabilities, and measurement of model uncertainty. To analyze the uncertainty of the model, we propose a new concept of model entropy, where the leave-one-out prediction probability of each sample is converted into entropy, and then used to quantify the uncertainty of the model. The model entropy is different from the classification margin, in the sense that it considers the distribution of all samples, not just the support vectors. Therefore, it can assess the uncertainty of the model more accurately than the classification margin. In the case of the same classification margin, the farther the sample distribution is from the classification hyperplane, the lower the model entropy. Experiments show that our algorithm (RBSVM) provides higher prediction accuracy and lower model uncertainty, when compared with state-of-the-art algorithms, such as Bayesian hyperparameter search and gradient-based hyperparameter learning algorithms.

Multi-dimensional Classification via Selective Feature Augmentation

In multi-dimensional classification (MDC), the semantics of objects are characterized by multiple class spaces from different dimensions. Most MDC approaches try to explicitly model the dependencies among class spaces in output space. In contrast, the recently proposed feature augmentation strategy, which aims at manipulating feature space, has also been shown to be an effective solution for MDC. However, existing feature augmentation approaches only focus on designing holistic augmented features to be appended with the original features, while better generalization performance could be achieved by exploiting multiple kinds of augmented features. In this paper, we propose the selective feature augmentation strategy that focuses on synergizing multiple kinds of augmented features. Specifically, by assuming that only part of the augmented features is pertinent and useful for each dimension’s model induction, we derive a classification model which can fully utilize the original features while conduct feature selection for the augmented features. To validate the effectiveness of the proposed strategy, we generate three kinds of simple augmented features based on standard kNN, weighted kNN, and maximum margin techniques, respectively. Comparative studies show that the proposed strategy achieves superior performance against both state-of-the-art MDC approaches and its degenerated versions with either kind of augmented features.