We propose a novel boosting approach to multi-class classification problems, in which multiple classes are distinguished by a set of random projection matrices in essence. The approach uses random projections to alleviate the proliferation of binary classifiers typically required to perform multi-class classification. The result is a multi-class classifier with a single vector-valued parameter, irrespective of the number of classes involved. Two variants of this approach are proposed. The first method randomly projects the original data into new spaces, while the second method randomly projects the outputs of learned weak classifiers. These methods are not only conceptually simple but also effective and easy to implement. A series of experiments on synthetic, machine learning and visual recognition data sets demonstrate that our proposed methods compare favorably to existing multi-class boosting algorithms in terms of both the convergence rate and classification accuracy.
Learning a matrix of coefficients in a single optimization problem One learns a linear ensemble for each class. Given a test example, the label is predicted by @math @math Each row of the matrix @math corresponds to one of the classes. The sample is assigned to the class whose row has the largest value of the weighted combination. To learn the matrix @math , one can formulate the problem in the framework of multi-class maximum-margin learning. Shen and Hao show that the large-margin multi-class boosting can be implemented using column generation @cite_11 .
@cite_11
2011143997
Boosting-based object detection has received significant attention recently. In this paper, we propose totally corrective asymmetric boosting algorithms for real-time object detection. Our algorithms differ from Viola and Jones' detection framework in two ways. Firstly, our boosting algorithms explicitly optimize asymmetric loss of objectives, while AdaBoost used by Viola and Jones optimizes a symmetric loss. Secondly, by carefully deriving the Lagrange duals of the optimization problems, we design more efficient boosting in that the coefficients of the selected weak classifiers are updated in a totally corrective fashion, in contrast to the stagewise optimization commonly used by most boosting algorithms. Column generation is employed to solve the proposed optimization problems. Unlike conventional boosting, the proposed boosting algorithms are able to de-select those irrelevant weak classifiers in the ensemble while training a classification cascade. This results in improved detection performance as well as fewer weak classifiers in the learned strong classifier. Compared with AsymBoost of Viola and Jones, our proposed asymmetric boosting is nonheuristic and the training procedure is much simpler. Experiments on face and pedestrian detection demonstrate that our methods have superior detection performance than some of the state-of-the-art object detectors.