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.
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. We present a novel approach to efficiently learn a label tree for large scale classification with many classes. The key contribution of the approach is a technique to simultaneously determine the structure of the tree and learn the classifiers for each node in the tree. This approach also allows fine grained control over the efficiency vs accuracy trade-off in designing a label tree, leading to more balanced trees. Experiments are performed on large scale image classification with 10184 classes and 9 million images. We demonstrate significant improvements in test accuracy and efficiency with less training time and more balanced trees compared to the previous state of the art by 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. Multi-class classification becomes challenging at test time when the number of classes is very large and testing against every possible class can become computationally infeasible. This problem can be alleviated by imposing (or learning) a structure over the set of classes. We propose an algorithm for learning a tree-structure of classifiers which, by optimizing the overall tree loss, provides superior accuracy to existing tree labeling methods. We also propose a method that learns to embed labels in a low dimensional space that is faster than non-embedding approaches and has superior accuracy to existing embedding approaches. Finally we combine the two ideas resulting in the label embedding tree that outperforms alternative methods including One-vs-Rest while being orders of magnitude faster. 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. In the real visual world, the number of categories a classifier needs to discriminate is on the order of hundreds or thousands. For example, the SUN dataset [24] contains 899 scene categories and ImageNet [6] has 15,589 synsets. Designing a multiclass classifier that is both accurate and fast at test time is an extremely important problem in both machine learning and computer vision communities. To achieve a good trade-off between accuracy and speed, we adopt the relaxed hierarchy structure from [15], where a set of binary classifiers are organized in a tree or DAG (directed acyclic graph) structure. At each node, classes are colored into positive and negative groups which are separated by a binary classifier while a subset of confusing classes is ignored. We color the classes and learn the induced binary classifier simultaneously using a unified and principled max-margin optimization. We provide an analysis on generalization error to justify our design. Our method has been tested on both Caltech-256 (object recognition) [9] and the SUN dataset (scene classification) [24], and shows significant improvement over existing methods. 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. LSHTC is a series of challenges which aims to assess the performance of classification systems in large-scale classification in a a large number of classes (up to hundreds of thousands). This paper describes the dataset that have been released along the LSHTC series. The paper details the construction of the datsets and the design of the tracks as well as the evaluation measures that we implemented and a quick overview of the results. All of these datasets are available online and runs may still be submitted on the online server of the challenges.  We provide a novel interpretation of the dual of support vector machines (SVMs) in terms of scatter with respect to class prototypes and their mean. As a key contribution, we extend this framework to multiple classes, providing a new joint Scatter SVM algorithm, at the level of its binary counterpart in the number of optimization variables. This enables us to implement computationally efficient solvers based on sequential minimal and chunking optimization. As a further contribution, the primal problem formulation is developed in terms of regularized risk minimization and the hinge loss, revealing the score function to be used in the actual classification of test patterns. We investigate Scatter SVM properties related to generalization ability, computational efficiency, sparsity and sensitivity maps, and report promising results. We study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time complexity logarithmic in the number of classes. We develop top-down tree construction approaches for constructing logarithmic depth trees. On the theoretical front, we formulate a new objective function, which is optimized at each node of the tree and creates dynamic partitions of the data which are both pure (in terms of class labels) and balanced. We demonstrate that under favorable conditions, we can construct logarithmic depth trees that have leaves with low label entropy. However, the objective function at the nodes is challenging to optimize computationally. We address the empirical problem with a new online decision tree construction procedure. Experiments demonstrate that this online algorithm quickly achieves improvement in test error compared to more common logarithmic training time approaches, which makes it a plausible method in computationally constrained large-k applications.