Training of one-vs.-rest SVMs can be parallelized over the number of classes in a straight forward way. Given enough computational resources, one-vs.-rest SVMs can thus be trained on data involving a large number of classes. The same cannot be stated, however, for the so-called all-in-one SVMs, which require solving a quadratic program of size quadratically in the number of classes. We develop distributed algorithms for two all-in-one SVM formulations ( and Weston and Watkins) that parallelize the computation evenly over the number of classes. This allows us to compare these models to one-vs.-rest SVMs on unprecedented scale. The results indicate superior accuracy on text classification data.
Most approaches to parallelization of MCSVM training are based on OVO or OVR @cite_25 , including a number of approaches that attempt to learn a hierarchy of labels @cite_22 @cite_14 @cite_23 @cite_17 @cite_19 @cite_10 or train ensembles of SVMs on individual subsets of the data @cite_26 @cite_15 @cite_13 @cite_20 .
@cite_13 @cite_14 @cite_26 @cite_22 @cite_19 @cite_23 @cite_15 @cite_10 @cite_25 @cite_20 @cite_17
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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. 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. A fast SVM training algorithm for multi-classes consisting of parallel and sequential optimizations is presented. The main advantage of the parallel optimization step is to remove most non-support vectors quickly, which dramatically reduces the training time at the stage of sequential optimization. In addition, some strategies such as kernel caching, shrinking and calling BLAS functions are effectively integrated into the algorithm to speed up the training. Experiments on MNIST handwritten digit database have shown that, without sacrificing the generalization performance, the proposed algorithm has achieved a speed-up factor of 110, when compared with 's modified SMO. Moreover, for the first time ever we investigated the training performance of SVM on handwritten Chinese database ETL9B with more than 3000 categories and about 500,000 training samples. The total training time is just 5.1 hours. The raw error rate of 1.1 on ETL9B has been achieved. 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.