document: Trading representability for scalability : adaptive multi-hyperplane machine for nonlinear classification Support Vector Machines ( SVMs ) are among the most popular and successful classification algorithms . Kernel SVMs often reach state-of-the-art accuracies , but suffer from the curse of kernelization due to linear model growth with data size on noisy data . Linear SVMs have the ability to efficiently learn from truly large data , but they are applicable to a limited number of domains due to low representational power . To fill the representability and scalability gap between linear and nonlinear SVMs , we propose the Adaptive Multi-hyperplane Machine ( AMM ) algorithm that accomplishes fast training and prediction and has capability to solve nonlinear classification problems . AMM model consists of a set of hyperplanes ( weights ) , each assigned to one of the multiple classes , and predicts based on the associated class of the weight that provides the largest prediction . The number of weights is automatically determined through an iterative algorithm based on the stochastic gradient descent algorithm which is guaranteed to converge to a local optimum . Since the generalization bound decreases with the number of weights , a weight pruning mechanism is proposed and analyzed . The experiments on several large data sets show that AMM is nearly as fast during training and prediction as the state-of-the-art linear SVM solver and that it can be orders of magnitude faster than kernel SVM . In accuracy , AMM is somewhere between linear and kernel SVMs . For example , on an OCR task with 8 million highly dimensional training examples , AMM trained in 300 seconds on a single-core processor had 0.54 % error rate , which was significantly lower than 2.03 % error rate of a linear SVM trained in the same time and comparable to 0.43 % error rate of a kernel SVM trained in 2 days on 512 processors . The results indicate that AMM could be an attractive option when solving large-scale classification problems . The software is available at www.dabi.temple.edu\/~vucetic\/AMM.html .
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