Data mining algorithms are originally designed by assuming the data is available at one centralized site. These algorithms also assume that the whole data is fit into main memory while running the algorithm. But in today's scenario the data has to be handled is distributed even geographically. Bringing the data into a centralized site is a bottleneck in terms of the bandwidth when compared with the size of the data. In this paper for multiclass SVM we propose an algorithm which builds a global SVM model by merging the local SVMs using a distributed approach(DSVM). And the global SVM will be communicated to each site and made it available for further classification. The experimental analysis has shown promising results with better accuracy when compared with both the centralized and ensemble method. The time complexity is also reduced drastically because of the parallel construction of local SVMs. The experiments are conducted by considering the data sets of size 100s to hundred of 100s which also addresses the issue of scalability.
Though a decent amount of work has been done in multiclass SVM and parallel distributed binary SVM individually, the research of distributed multiclass SVM needs more exploration by the research community. There is a continuous attention on SVM because it was proved as the best method in several applications even though it is computationally expensive @cite_1 .
@cite_1
1999428432 2007573800 1570978137 2117990954 2116444583 1537017777 2098368939 1496025956 1988935054 2043182541 2951858610 1975742283 2136251662 2212636544 2621615146 2136331731 2031823405 2162657744 2096613134 2154462399
We present an algorithm and implementation for distributed parallel training of single-machine multiclass SVMs. While there is ongoing and healthy debate about the best strategy for multiclass classification, there are some features of the single-machine approach that are not available when training alternatives such as one-vs-all, and that are quite complex for tree based methods. One obstacle to exploring single-machine approaches on large datasets is that they are usually limited to running on a single machine! We build on a framework borrowed from parallel convex optimization — the alternating direction method of multipliers (ADMM) — to develop a new consensus based algorithm for distributed training of single-machine approaches. This is demonstrated with an implementation of our novel sequential dual algorithm (DCMSVM) which allows distributed parallel training with small communication requirements. Benchmark results show significant reduction in wall clock time compared to current state of the art multiclass SVM implementation (Liblinear) on a single node. Experiments are performed on large scale image classification including results with modern high-dimensional features. With data sizes constantly expanding, and with classical machine learning algorithms that analyze such data requiring larger and larger amounts of computation time and storage space, the need to distribute computation and memory requirements among several computers has become apparent. Although substantial work has been done in developing distributed binary SVM algorithms and multi-class SVM algorithms individually, the field of multi-class distributed SVMs remains largely unexplored. This research proposes a novel algorithm that implements the Support Vector Machine over a multi-class dataset and is efficient in a distributed environment (here, Hadoop). The idea is to divide the dataset into half recursively and thus compute the optimal Support Vector Machine for this half during the training phase, much like a divide and conquer approach. While testing, this structure has been effectively exploited to significantly reduce the prediction time. Our algorithm has shown better computation time during the prediction phase than the traditional sequential SVM methods (One vs. One, One vs. Rest) and out-performs them as the size of the dataset grows. This approach also classifies the data with higher accuracy than the traditional multi-class algorithms. We compare Naive Bayes and Support Vector Machines on the task of multiclass text classification. Using a variety of approaches to combine the underlying binary classifiers, we find that SVMs substantially outperform Naive Bayes. We present full multiclass results on two well-known text data sets, including the lowest error to date on both data sets. We develop a new indicator of binary performance to show that the SVM’s lower multiclass error is a result of its improved binary performance. Furthermore, we demonstrate and explore the surprising result that one-vs-all classification performs favorably compared to other approaches even though it has no error-correcting properties. 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 (2-class problems), converging in a day or two, while a regular SVM never converged in over a week. Two-category support vector machines (SVM) have been very popular in the machine learning community for classification problems. Solving multicategory problems by a series of binary classifiers is quite common in the SVM paradigm; however, this approach may fail under various circumstances. We propose the multicategory support vector machine (MSVM), which extends the binary SVM to the multicategory case and has good theoretical properties. The proposed method provides a unifying framework when there are either equal or unequal misclassification costs. As a tuning criterion for the MSVM, an approximate leave-one-out cross-validation function, called Generalized Approximate Cross Validation, is derived, analogous to the binary case. The effectiveness of the MSVM is demonstrated through the applications to cancer classification using microarray data and cloud classification with satellite radiance profiles. Support vector machines (SVM) is originally designed for binary classification. To extend it to multi-class scenario, a typical conventional way is to decompose an M-class problem into a series of two-class problems, for which one-against-all is the earliest and one of the most widely used implementations. However, certain theoretical analysis reveals a drawback, i.e., the competence of each classifier is totally neglected when the results of classification from the multiple classifiers are combined for the final decision. To overcome this limitation, this paper introduces reliability measures into the multi-class framework. Two measures are designed: static reliability measure (SRM) and dynamic reliability measure (DRM). SRM works on a collective basis and yields a constant value regardless of the location of the test sample. DRM, on the other hand, accounts for the spatial variation of the classifier's performance. Based on these two reliability measures, a new decision strategy for the one-against-all method is proposed, which is tested on benchmark data sets and demonstrates its effectiveness. Multiclass SVMs are usually implemented by combining several two-class SVMs. The one-versus-all method using winner-takes-all strategy and the one-versus-one method implemented by max-wins voting are popularly used for this purpose. In this paper we give empirical evidence to show that these methods are inferior to another one-versus-one method: one that uses Platt's posterior probabilities together with the pairwise coupling idea of Hastie and Tibshirani. The evidence is particularly strong when the training dataset is sparse. Transductive SVM (TSVM) is a well known semi-supervised large margin learning method for binary text classification. In this paper we extend this method to multi-class and hierarchical classification problems. We point out that the determination of labels of unlabeled examples with fixed classifier weights is a linear programming problem. We devise an efficient technique for solving it. The method is applicable to general loss functions. We demonstrate the value of the new method using large margin loss on a number of multiclass and hierarchical classification datasets. For maxent loss we show empirically that our method is better than expectation regularization constraint and posterior regularization methods, and competitive with the version of entropy regularization method which uses label constraints. In the customer-centered marketplace, the understanding of customer behavior is a critical success factor. The big databases in an organization usually involve multiplex data such as static, time series, symbolic sequential and textual data which are separately stored in different databases of different sections. It poses a challenge to traditional centralized customer behavior prediction. In this study, a novel approach called collaborative multiple kernel support vector machine (C-MK-SVM) is developed for distributed customer behavior prediction using multiplex data. The alternating direction method of multipliers (ADMM) is used for the global optimization of the distributed sub-models in C-MK-SVM. Computational experiments on a practical retail dataset are reported. Computational results show that C-MK-SVM exhibits better customer behavior prediction performance and higher computational speed than support vector machine and multiple kernel support vector machine. The support vector machine (SVM) is known for its good performance in two-class classification, but its extension to multiclass classification is still an ongoing research issue. In this article, we propose a new approach for classification, called the import vector machine (IVM), which is built on kernel logistic regression (KLR). We show that the IVM not only performs as well as the SVM in two-class classification, but also can naturally be generalized to the multiclass case. Furthermore, the IVM provides an estimate of the underlying probability. Similar to the support points of the SVM, the IVM model uses only a fraction of the training data to index kernel basis functions, typically a much smaller fraction than the SVM. This gives the IVM a potential computational advantage over the SVM. The kernel support vector machine (SVM) is one of the most widely used classification methods; however, the amount of computation required becomes the bottleneck when facing millions of samples. In this paper, we propose and analyze a novel divide-and-conquer solver for kernel SVMs (DC-SVM). In the division step, we partition the kernel SVM problem into smaller subproblems by clustering the data, so that each subproblem can be solved independently and efficiently. We show theoretically that the support vectors identified by the subproblem solution are likely to be support vectors of the entire kernel SVM problem, provided that the problem is partitioned appropriately by kernel clustering. In the conquer step, the local solutions from the subproblems are used to initialize a global coordinate descent solver, which converges quickly as suggested by our analysis. By extending this idea, we develop a multilevel Divide-and-Conquer SVM algorithm with adaptive clustering and early prediction strategy, which outperforms state-of-the-art methods in terms of training speed, testing accuracy, and memory usage. As an example, on the covtype dataset with half-a-million samples, DC-SVM is 7 times faster than LIBSVM in obtaining the exact SVM solution (to within @math relative error) which achieves 96.15 prediction accuracy. Moreover, with our proposed early prediction strategy, DC-SVM achieves about 96 accuracy in only 12 minutes, which is more than 100 times faster than LIBSVM. The new parallel multiclass stochastic gradient descent algorithms aim at classifying million images with very-high-dimensional signatures into thousands of classes. We extend the stochastic gradient descent (SGD) for support vector machines (SVM-SGD) in several ways to develop the new multiclass SVM-SGD for efficiently classifying large image datasets into many classes. We propose (1) a balanced training algorithm for learning binary SVM-SGD classifiers, and (2) a parallel training process of classifiers with several multi-core computers grid. The evaluation on 1000 classes of ImageNet, ILSVRC 2010 shows that our algorithm is 270 times faster than the state-of-the-art linear classifier LIBLINEAR. This paper addresses the problem of the classification of hyperspectral remote sensing images by support vector machines (SVMs). First, we propose a theoretical discussion and experimental analysis aimed at understanding and assessing the potentialities of SVM classifiers in hyperdimensional feature spaces. Then, we assess the effectiveness of SVMs with respect to conventional feature-reduction-based approaches and their performances in hypersubspaces of various dimensionalities. To sustain such an analysis, the performances of SVMs are compared with those of two other nonparametric classifiers (i.e., radial basis function neural networks and the K-nearest neighbor classifier). Finally, we study the potentially critical issue of applying binary SVMs to multiclass problems in hyperspectral data. In particular, four different multiclass strategies are analyzed and compared: the one-against-all, the one-against-one, and two hierarchical tree-based strategies. Different performance indicators have been used to support our experimental studies in a detailed and accurate way, i.e., the classification accuracy, the computational time, the stability to parameter setting, and the complexity of the multiclass architecture. The results obtained on a real Airborne Visible Infrared Imaging Spectroradiometer hyperspectral dataset allow to conclude that, whatever the multiclass strategy adopted, SVMs are a valid and effective alternative to conventional pattern recognition approaches (feature-reduction procedures combined with a classification method) for the classification of hyperspectral remote sensing data. With different principles, support vector machines (SVMs) and multiple classifier systems (MCSs) have shown excellent performances for classifying hyperspectral remote sensing images. In order to further improve the performance, we propose a novel ensemble approach, namely, rotation-based SVM (RoSVM), which combines SVMs and MCSs together. The basic idea of RoSVM is to generate diverse SVM classification results using random feature selection and data transformation, which can enhance both individual accuracy and diversity within the ensemble simultaneously. Two simple data transformation methods, i.e., principal component analysis and random projection, are introduced into RoSVM. An empirical study on three hyperspectral data sets demonstrates that the proposed RoSVM ensemble method outperforms the single SVM and random subspace SVM. The impacts of the parameters on the overall accuracy of RoSVM (different training sets, ensemble sizes, and numbers of features in the subset) are also investigated in this paper. In many problems of machine learning, the data are distributed nonlinearly. One way to address this kind of data is training a nonlinear classifier such as kernel support vector machine (kernel SVM). However, the computational burden of kernel SVM limits its application to large scale datasets. In this paper, we propose a Clustered Support Vector Machine (CSVM), which tackles the data in a divide and conquer manner. More specifically, CSVM groups the data into several clusters, followed which it trains a linear support vector machine in each cluster to separate the data locally. Meanwhile, CSVM has an additional global regularization, which requires the weight vector of each local linear SVM aligning with a global weight vector. The global regularization leverages the information from one cluster to another, and avoids over-fitting in each cluster. We derive a data-dependent generalization error bound for CSVM, which explains the advantage of CSVM over linear SVM. Experiments on several benchmark datasets show that the proposed method outperforms linear SVM and some other related locally linear classifiers. It is also comparable to a fine-tuned kernel SVM in terms of prediction performance, while it is more efficient than kernel SVM. In some pattern analysis problems, there exists expert knowledge, in addition to the original data involved in the classification process. The vast majority of existing approaches simply ignore such auxiliary (privileged) knowledge. Recently a new paradigm-learning using privileged information-was introduced in the framework of SVM+. This approach is formulated for binary classification and, as typical for many kernel-based methods, can scale unfavorably with the number of training examples. While speeding up training methods and extensions of SVM+ to multiclass problems are possible, in this paper we present a more direct novel methodology for incorporating valuable privileged knowledge in the model construction phase, primarily formulated in the framework of generalized matrix learning vector quantization. This is done by changing the global metric in the input space, based on distance relations revealed by the privileged information. Hence, unlike in SVM+, any convenient classifier can be used after such metric modification, bringing more flexibility to the problem of incorporating privileged information during the training. Experiments demonstrate that the manipulation of an input space metric based on privileged data improves classification accuracy. Moreover, our methods can achieve competitive performance against the SVM+ formulations. While classical kernel-based classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimization of the coefficients of such a combination reduces to a convex optimization problem known as a quadratically-constrained quadratic program (QCQP). Unfortunately, current convex optimization toolboxes can solve this problem only for a small number of kernels and a small number of data points; moreover, the sequential minimal optimization (SMO) techniques that are essential in large-scale implementations of the SVM cannot be applied because the cost function is non-differentiable. We propose a novel dual formulation of the QCQP as a second-order cone programming problem, and show how to exploit the technique of Moreau-Yosida regularization to yield a formulation to which SMO techniques can be applied. We present experimental results that show that our SMO-based algorithm is significantly more efficient than the general-purpose interior point methods available in current optimization toolboxes. We consider multiclass classification problems where the set of labels are organized hierarchically as a category tree. We associate each node in the tree with a classifier and classify the examples recursively from the root to the leaves. We propose a hierarchical Support Vector Machine (SVM) that encourages the classifier at each node to be different from the classifiers at its ancestors. More specifically, we introduce regularizations that force the normal vector of the classifying hyperplane at each node to be orthogonal to those at its ancestors as much as possible. We establish conditions under which training such a hierarchical SVM is a convex optimization problem, and develop an efficient dual-averaging method for solving it. A computationally efficient approach to local learning with kernel methods is presented. The Fast Local Kernel Support Vector Machine (FaLK-SVM) trains a set of local SVMs on redundant neighbourhoods in the training set and an appropriate model for each query point is selected at testing time according to a proximity strategy. Supported by a recent result by Zakai and Ritov (2009) relating consistency and localizability, our approach achieves high classification accuracies by dividing the separation function in local optimisation problems that can be handled very efficiently from the computational viewpoint. The introduction of a fast local model selection further speeds-up the learning process. Learning and complexity bounds are derived for FaLK-SVM, and the empirical evaluation of the approach (with data sets up to 3 million points) showed that it is much faster and more accurate and scalable than state-of-the-art accurate and approximated SVM solvers at least for non high-dimensional data sets. More generally, we show that locality can be an important factor to sensibly speed-up learning approaches and kernel methods, differently from other recent techniques that tend to dismiss local information in order to improve scalability. While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constrained quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classification. Experimental results show that the proposed algorithm works for hundred thousands of examples or hundreds of kernels to be combined, and helps for automatic model selection, improving the interpretability of the learning result. In a second part we discuss general speed up mechanism for SVMs, especially when used with sparse feature maps as appear for string kernels, allowing us to train a string kernel SVM on a 10 million real-world splice data set from computational biology. We integrated multiple kernel learning in our machine learning toolbox SHOGUN for which the source code is publicly available at http: www.fml.tuebingen.mpg.de raetsch projects shogun .