Unified Locally Linear Classifiers With Diversity-Promoting Anchor Points

Abstract

Locally Linear Support Vector Machine (LLSVM) has been actively used in classification tasks due to its capability of classifying nonlinear patterns. However, existing LLSVM suffers from two drawbacks: (1) a particular and appropriate regularization for LLSVM has not yet been addressed; (2) it usually adopts a three-stage learning scheme composed of learning anchor points by clustering, learning local coding coordinates by a predefined coding scheme, and finally learning for training classifiers. We argue that this decoupled approaches oversimplifies the original optimization problem, resulting in a large deviation due to the disparate purpose of each step. To address the first issue, we propose a novel diversified regularization which could capture infrequent patterns and reduce the model size without sacrificing the representation power. Based on this regularization, we develop a joint optimization algorithm among anchor points, local coding coordinates and classifiers to simultaneously minimize the overall classification risk, which is termed as Diversified and Unified Locally Linear Support Vector Machine (DU-LLSVM for short). To the best of our knowledge, DU-LLSVM is the first principled method that directly learns sparse local coding and can be easily generalized to other supervised learning models. Extensive experiments showed that DU-LLSVM consistently surpassed several state-of-the-art methods with a predefined local coding scheme (e.g. LLSVM) or a supervised anchor point learning (e.g. SAPL-LLSVM).