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107
Training a support vector machine in the primal
 Neural Computation
, 2007
"... Most literature on Support Vector Machines (SVMs) concentrate on the dual optimization problem. In this paper, we would like to point out that the primal problem can also be solved efficiently, both for linear and nonlinear SVMs, and that there is no reason for ignoring this possibilty. On the cont ..."
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Cited by 154 (5 self)
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Most literature on Support Vector Machines (SVMs) concentrate on the dual optimization problem. In this paper, we would like to point out that the primal problem can also be solved efficiently, both for linear and nonlinear SVMs, and that there is no reason for ignoring this possibilty. On the contrary, from the primal point of view new families of algorithms for large scale SVM training can be investigated.
Fast Kernel Classifiers With Online And Active Learning
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Very high dimensional learning systems become theoretically possible when training examples are abundant. The computing cost then becomes the limiting factor. Any efficient learning algorithm should at least take a brief look at each example. But should all examples be given equal attention? This ..."
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Cited by 153 (18 self)
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Very high dimensional learning systems become theoretically possible when training examples are abundant. The computing cost then becomes the limiting factor. Any efficient learning algorithm should at least take a brief look at each example. But should all examples be given equal attention? This contribution proposes an empirical answer. We first present an online SVM algorithm based on this premise. LASVM yields competitive misclassification rates after a single pass over the training examples, outspeeding stateoftheart SVM solvers. Then we show how active example selection can yield faster training, higher accuracies, and simpler models, using only a fraction of the training example labels.
Core vector machines: Fast SVM training on very large data sets
 Journal of Machine Learning Research
, 2005
"... Standard SVM training has O(m 3) time and O(m 2) space complexities, where m is the training set size. It is thus computationally infeasible on very large data sets. By observing that practical SVM implementations only approximate the optimal solution by an iterative strategy, we scale up kernel met ..."
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Cited by 133 (15 self)
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Standard SVM training has O(m 3) time and O(m 2) space complexities, where m is the training set size. It is thus computationally infeasible on very large data sets. By observing that practical SVM implementations only approximate the optimal solution by an iterative strategy, we scale up kernel methods by exploiting such “approximateness ” in this paper. We first show that many kernel methods can be equivalently formulated as minimum enclosing ball (MEB) problems in computational geometry. Then, by adopting an efficient approximate MEB algorithm, we obtain provably approximately optimal solutions with the idea of core sets. Our proposed Core Vector Machine (CVM) algorithm can be used with nonlinear kernels and has a time complexity that is linear in m and a space complexity that is independent of m. Experiments on large toy and realworld data sets demonstrate that the CVM is as accurate as existing SVM implementations, but is much faster and can handle much larger data sets than existing scaleup methods. For example, CVM with the Gaussian kernel produces superior results on the KDDCUP99 intrusion detection data, which has about five million training patterns, in only 1.4 seconds on a 3.2GHz Pentium–4 PC.
Combining svms with various feature selection strategies
 Taiwan University
, 2005
"... Feature selection is an important issue in many research areas. There are some reasons for selecting important features such as reducing the learning time, improving the accuracy, etc. This thesis investigates the performance of combining support vector machines (SVM) and various feature selection s ..."
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Cited by 126 (0 self)
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Feature selection is an important issue in many research areas. There are some reasons for selecting important features such as reducing the learning time, improving the accuracy, etc. This thesis investigates the performance of combining support vector machines (SVM) and various feature selection strategies. The first part of the thesis mainly describes the existing feature selection methods and our experience on using those methods to attend a competition. The second part studies more feature selection strategies using the SVM. ii �ì��¬¡÷ � ��å�ç¢�ß��� � selection)��¥ì����£��È�� ����È������Ú���£����æÁ ç��£�����û�� ì�Öù�¡�È��(feature é£�æÁ©Â����℄���� � �Ü � ����Æ���È��℄�¡��û���℄�ø�¢�§���� �(Support Vector Machine) iii
Extreme learning machine: Theory and applications
, 2006
"... It is clear that the learning speed of feedforward neural networks is in general far slower than required and it has been a major bottleneck in their applications for past decades. Two key reasons behind may be: (1) the slow gradientbased learning algorithms are extensively used to train neural net ..."
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Cited by 114 (9 self)
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It is clear that the learning speed of feedforward neural networks is in general far slower than required and it has been a major bottleneck in their applications for past decades. Two key reasons behind may be: (1) the slow gradientbased learning algorithms are extensively used to train neural networks, and (2) all the parameters of the networks are tuned iteratively by using such learning algorithms. Unlike these conventional implementations, this paper proposes a new learning algorithm called extreme learning machine (ELM) for singlehidden layer feedforward neural networks (SLFNs) which randomly chooses hidden nodes and analytically determines the output weights of SLFNs. In theory, this algorithm tends to provide good generalization performance at extremely fast learning speed. The experimental results based on a few artificial and real benchmark function approximation and classification problems including very large complex applications show that the new algorithm can produce good generalization performance in most cases and can learn thousands of times faster than conventional popular learning algorithms for feedforward neural networks.
Extreme learning machine: A new learning scheme of feedforward neural networks
 IN PROC. INT. JOINT CONF. NEURAL NETW
, 2006
"... It is clear that the learning speed of feedforward neural networks is in general far slower than required and it has been a major bottleneck in their applications for past decades. Two key reasons behind may be: 1) the slow gradientbased learning algorithms are extensively used to train neural netwo ..."
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Cited by 112 (17 self)
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It is clear that the learning speed of feedforward neural networks is in general far slower than required and it has been a major bottleneck in their applications for past decades. Two key reasons behind may be: 1) the slow gradientbased learning algorithms are extensively used to train neural networks, and 2) all the parameters of the networks are tuned iteratively by using such learning algorithms. Unlike these traditional implementations, this paper proposes a new learning algorithm called extreme learning machine (ELM) for singlehidden layer feedforward neural networks (SLFNs) which randomly chooses the input weights and analytically determines the output weights of SLFNs. In theory, this algorithm tends to provide the best generalization performance at extremely fast learning speed. The experimental results based on realworld benchmarking function approximation and classification problems including large complex applications show that the new algorithm can produce best generalization performance in some cases and can learn much faster than traditional popular learning algorithms for feedforward neural networks.
Fast Support Vector Machine Training and Classification
 on Graphics Processors, Proc. 25th Int. Conf. Machine Learning
, 2008
"... Recent developments in programmable, highly parallel Graphics Processing Units (GPUs) have enabled high performance implementations of machine learning algorithms. We describe a solver for Support Vector Machine training running on a GPU, using the Sequential Minimal Optimization algorithm and an ad ..."
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Cited by 77 (2 self)
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Recent developments in programmable, highly parallel Graphics Processing Units (GPUs) have enabled high performance implementations of machine learning algorithms. We describe a solver for Support Vector Machine training running on a GPU, using the Sequential Minimal Optimization algorithm and an adaptive first and second order working set selection heuristic, which achieves speedups of 935 × over LIBSVM running on a traditional processor. We also present a GPUbased system for SVM classification which achieves speedups of 81138 × over LIBSVM (524 × over our own CPU based SVM classifier). 1.
Parallel support vector machines: The cascade svm
 In Advances in Neural Information Processing Systems
, 2005
"... We describe an algorithm for support vector machines (SVM) that can be parallelized efficiently and scales to very large problems with hundreds of thousands of training vectors. Instead of analyzing the whole training set in one optimization step, the data are split into subsets and optimized separa ..."
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Cited by 73 (2 self)
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We describe an algorithm for support vector machines (SVM) that can be parallelized efficiently and scales to very large problems with hundreds of thousands of training vectors. Instead of analyzing the whole training set in one optimization step, the data are split into subsets and optimized separately with multiple SVMs. The partial results are combined and filtered again in a ‘Cascade ’ of SVMs, until the global optimum is reached. The Cascade SVM can be spread over multiple processors with minimal communication overhead and requires far less memory, since the kernel matrices are much smaller than for a regular SVM. Convergence to the global optimum is guaranteed with multiple passes through the Cascade, but already a single pass provides good generalization. A single pass is 5x – 10x faster than a regular SVM for problems of 100,000 vectors when implemented on a single processor. Parallel implementations on a cluster of 16 processors were tested with over 1 million vectors (2class problems), converging in a day or two, while a regular SVM never converged in over a week. 1
Extreme Learning Machine for Regression and Multiclass Classification
"... Abstract—Due to the simplicity of their implementations, least square support vector machine (LSSVM) and proximal support vector machine (PSVM) have been widely used in binary classification applications. The conventional LSSVM and PSVM cannot be used in regression and multiclass classification ap ..."
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Cited by 61 (5 self)
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Abstract—Due to the simplicity of their implementations, least square support vector machine (LSSVM) and proximal support vector machine (PSVM) have been widely used in binary classification applications. The conventional LSSVM and PSVM cannot be used in regression and multiclass classification applications directly, although variants of LSSVM and PSVM have been proposed to handle such cases. This paper shows that both LSSVM and PSVM can be simplified further and a unified learning framework of LSSVM, PSVM, and other regularization algorithms referred to extreme learning machine (ELM) can be built. ELM works for the “generalized ” singlehiddenlayer feedforward networks (SLFNs), but the hidden layer (or called feature mapping) in ELM need not be tuned. Such SLFNs include but are not limited to SVM, polynomial network, and the conventional feedforward neural networks. This paper shows the following: 1) ELM provides a unified learning platform with a widespread type of feature mappings and can be applied in regression and multiclass classification applications directly; 2) from the optimization method point of view, ELM has milder optimization constraints compared to LSSVM and PSVM; 3) in theory, compared to ELM, LSSVM and PSVM achieve suboptimal solutions and require higher computational complexity; and 4) in theory, ELM can approximate any target continuous function and classify any disjoint regions. As verified by the simulation results, ELM tends to have better scalability and achieve similar (for regression and binary class cases) or much better (for multiclass cases) generalization performance at much faster learning speed (up to thousands times) than traditional SVM and LSSVM. Index Terms—Extreme learning machine (ELM), feature mapping, kernel, least square support vector machine (LSSVM), proximal support vector machine (PSVM), regularization network. I.
Fast SVM training algorithm with decomposition on very large data sets
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2005
"... Training a support vector machine on a data set of huge size with thousands of classes is a challenging problem. This paper proposes an efficient algorithm to solve this problem. The key idea is to introduce a parallel optimization step to quickly remove most of the nonsupport vectors, where block ..."
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Cited by 38 (2 self)
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Training a support vector machine on a data set of huge size with thousands of classes is a challenging problem. This paper proposes an efficient algorithm to solve this problem. The key idea is to introduce a parallel optimization step to quickly remove most of the nonsupport vectors, where block diagonal matrices are used to approximate the original kernel matrix so that the original problem can be split into hundreds of subproblems which can be solved more efficiently. In addition, some effective strategies such as kernel caching and efficient computation of kernel matrix are integrated to speed up the training process. Our analysis of the proposed algorithm shows that its time complexity grows linearly with the number of classes and size of the data set. In the experiments, many appealing properties of the proposed algorithm have been investigated and the results show that the proposed algorithm has a much better scaling capability than Libsvm, SVM light, and SVMTorch. Moreover, the good generalization performances on several large databases have also been achieved.