text: This paper concerns the distributed training of nonlinear kernel machines on Map-Reduce. We show that a re-formulation of Nystr "om approximation based solution which is solved using gradient based techniques is well suited for this, especially when it is necessary to work with a large number of basis points. The main advantages of this approach are: avoidance of computing the pseudo-inverse of the kernel sub-matrix corresponding to the basis points; simplicity and efficiency of the distributed part of the computations; and, friendliness to stage-wise addition of basis points. We implement the method using an AllReduce tree on Hadoop and demonstrate its value on a few large benchmark datasets.
  @cite_30: 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.
  @cite_18: Support vector machines (SVMs) have been extensively used. However, it is known that SVMs face difficulty in solving large complex problems due to the intensive computation involved in their training algorithms, which are at least quadratic with respect to the number of training examples. This paper proposes a new, simple, and efficient network architecture which consists of several SVMs each trained on a small subregion of the whole data sampling space and the same number of simple neural quantizer modules which inhibit the outputs of all the remote SVMs and only allow a single local SVM to fire (produce actual output) at any time. In principle, this region-computing based modular network method can significantly reduce the learning time of SVM algorithms without sacrificing much generalization performance. The experiments on a few real large complex benchmark problems demonstrate that our method can be significantly faster than single SVMs without losing much generalization performance.
  @cite_8: 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.
  @cite_29: In this paper, we propose a distributed parallel support vector machine (DPSVM) training mechanism in a configurable network environment for distributed data mining. The basic idea is to exchange support vectors among a strongly connected network (SCN) so that multiple servers may work concurrently on distributed data set with limited communication cost and fast training speed. The percentage of servers that can work in parallel and the communication overhead may be adjusted through network configuration. The proposed algorithm further speeds up through online implementation and synchronization. We prove that the global optimal classifier can be achieved iteratively over an SCN. Experiments on a real-world data set show that the computing time scales well with the size of the training data for most networks. Numerical results show that a randomly generated SCN may achieve better performance than the state of the art method, cascade SVM, in terms of total training time.
  @cite_3: Support Vector Machines (SVMs) are currently the state-of-the-art models for many classification problems but they suffer from the complexity of their training algorithm which is at least quadratic with respect to the number of examples, Hence, it is hopeless to try to solve real-life problems having more than a few hundreds of thousands examples with SVMs. The present paper proposes a new mixture of SVMs that can be easily implemented in parallel and where each SVM is trained on a small subset of the whole dataset. Experiments on a large benchmark dataset (Forest) as well as a difficult speech database, yielded significant time improvement (time complexity appears empirically to locally grow linearly with the number of examples). In addition, and that is a surprise, a significant improvement in generalization was observed on Forest.
  @cite_0: Sequential minimal optimization (SMO) is one popular algorithm for training support vector machine (SVM), but it still requires a large amount of computation time for solving large size problems. This paper proposes one parallel implementation of SMO for training SVM. The parallel SMO is developed using message passing interface (MPI). Specifically, the parallel SMO first partitions the entire training data set into smaller subsets and then simultaneously runs multiple CPU processors to deal with each of the partitioned data sets. Experiments show that there is great speedup on the adult data set and the Mixing National Institute of Standard and Technology (MNIST) data set when many processors are used. There are also satisfactory results on the Web data set.
  @cite_16: Parallel software for solving the quadratic program arising in training support vector machines for classification problems is introduced. The software implements an iterative decomposition technique and exploits both the storage and the computing resources available on multiprocessor systems, by distributing the heaviest computational tasks of each decomposition iteration. Based on a wide range of recent theoretical advances, relevant decomposition issues, such as the quadratic subproblem solution, the gradient updating, the working set selection, are systematically described and their careful combination to get an effective parallel tool is discussed. A comparison with state-of-the-art packages on benchmark problems demonstrates the good accuracy and the remarkable time saving achieved by the proposed software. Furthermore, challenging experiments on real-world data sets with millions training samples highlight how the software makes large scale standard nonlinear support vector machines effectively tractable on common multiprocessor systems. This feature is not shown by any of the available codes.
  @cite_13: 
  @cite_11: Machine learning techniques have facilitated image retrieval by automatically classifying and annotating images with keywords. Among them Support Vector Machines (SVMs) have been used extensively due to their generalization properties. However, SVM training is notably a computationally intensive process especially when the training dataset is large. This paper presents MRSMO, a MapReduce based distributed SVM algorithm for automatic image annotation. The performance of the MRSMO algorithm is evaluated in an experimental environment. By partitioning the training dataset into smaller subsets and optimizing the partitioned subsets across a cluster of computers, the MRSMO algorithm reduces the training time significantly while maintaining a high level of accuracy in both binary and multiclass classifications.
summary: There are methods @cite_11 @cite_18 that partition the full data into several nodes, obtain a solution on each partition and combine them centrally. This ensemble solution is usually very sub-optimal. Some methods @cite_3 @cite_30 @cite_8 @cite_29 @cite_13 do further processing of those solutions to come closer to full optimality, but this requires heavy communication of data, e.g., passing support vector data between nodes. There are methods that directly parallelize well-known sequential methods such as SMO and SVMlight @cite_0 @cite_16 , but these involve communication costs over a large number of iterations.