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Journal ArticleDOI

LIBSVM: A library for support vector machines

TL;DR: Issues such as solving SVM optimization problems theoretical convergence multiclass classification probability estimates and parameter selection are discussed in detail.
Abstract: LIBSVM is a library for Support Vector Machines (SVMs). We have been actively developing this package since the year 2000. The goal is to help users to easily apply SVM to their applications. LIBSVM has gained wide popularity in machine learning and many other areas. In this article, we present all implementation details of LIBSVM. Issues such as solving SVM optimization problems theoretical convergence multiclass classification probability estimates and parameter selection are discussed in detail.

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Citations
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Journal Article
TL;DR: Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems, focusing on bringing machine learning to non-specialists using a general-purpose high-level language.
Abstract: Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems. This package focuses on bringing machine learning to non-specialists using a general-purpose high-level language. Emphasis is put on ease of use, performance, documentation, and API consistency. It has minimal dependencies and is distributed under the simplified BSD license, encouraging its use in both academic and commercial settings. Source code, binaries, and documentation can be downloaded from http://scikit-learn.sourceforge.net.

47,974 citations


Cites methods from "LIBSVM: A library for support vecto..."

  • ...While the package is mostly written in Python, it incorporates the C++ libraries LibSVM (Chang and Lin, 2001) and LibLinear (Fan et al....

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Journal ArticleDOI
TL;DR: This paper provides an introduction to the WEKA workbench, reviews the history of the project, and, in light of the recent 3.6 stable release, briefly discusses what has been added since the last stable version (Weka 3.4) released in 2003.
Abstract: More than twelve years have elapsed since the first public release of WEKA. In that time, the software has been rewritten entirely from scratch, evolved substantially and now accompanies a text on data mining [35]. These days, WEKA enjoys widespread acceptance in both academia and business, has an active community, and has been downloaded more than 1.4 million times since being placed on Source-Forge in April 2000. This paper provides an introduction to the WEKA workbench, reviews the history of the project, and, in light of the recent 3.6 stable release, briefly discusses what has been added since the last stable version (Weka 3.4) released in 2003.

19,603 citations


Cites methods from "LIBSVM: A library for support vecto..."

  • ...• Wrapper classifiers: allow the well known algorithms provided by the LibSVM [5] and LibLINEAR [9] thirdparty libraries to be used in WEKA....

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  • ...Supported .le formats include WEKA s own ARFF format, CSV, LibSVM s format, and C4.5 s format....

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  • ...6 is the ability to read and write data in the format used by the well known LibSVM and SVM-Light support vector machine implementations [5]....

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  • ...This complements the new LibSVM and LibLIN-EAR wrapper classi.ers....

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  • ...Wrapper classi.ers: allow the well known algorithms provided by the LibSVM [5] and LibLINEAR [9] third­party libraries to be used in WEKA....

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Proceedings ArticleDOI
16 Jun 2012
TL;DR: The autonomous driving platform is used to develop novel challenging benchmarks for the tasks of stereo, optical flow, visual odometry/SLAM and 3D object detection, revealing that methods ranking high on established datasets such as Middlebury perform below average when being moved outside the laboratory to the real world.
Abstract: Today, visual recognition systems are still rarely employed in robotics applications. Perhaps one of the main reasons for this is the lack of demanding benchmarks that mimic such scenarios. In this paper, we take advantage of our autonomous driving platform to develop novel challenging benchmarks for the tasks of stereo, optical flow, visual odometry/SLAM and 3D object detection. Our recording platform is equipped with four high resolution video cameras, a Velodyne laser scanner and a state-of-the-art localization system. Our benchmarks comprise 389 stereo and optical flow image pairs, stereo visual odometry sequences of 39.2 km length, and more than 200k 3D object annotations captured in cluttered scenarios (up to 15 cars and 30 pedestrians are visible per image). Results from state-of-the-art algorithms reveal that methods ranking high on established datasets such as Middlebury perform below average when being moved outside the laboratory to the real world. Our goal is to reduce this bias by providing challenging benchmarks with novel difficulties to the computer vision community. Our benchmarks are available online at: www.cvlibs.net/datasets/kitti

11,283 citations


Cites methods from "LIBSVM: A library for support vecto..."

  • ...We found that for the classification task SVMs [11] clearly outperform nearest neighbor classification....

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  • ...All Classification Similarity SVM[11] 0....

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Journal ArticleDOI
TL;DR: This tutorial gives an overview of the basic ideas underlying Support Vector (SV) machines for function estimation, and includes a summary of currently used algorithms for training SV machines, covering both the quadratic programming part and advanced methods for dealing with large datasets.
Abstract: In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.

10,696 citations

Journal Article
TL;DR: LIBLINEAR is an open source library for large-scale linear classification that supports logistic regression and linear support vector machines and provides easy-to-use command-line tools and library calls for users and developers.
Abstract: LIBLINEAR is an open source library for large-scale linear classification. It supports logistic regression and linear support vector machines. We provide easy-to-use command-line tools and library calls for users and developers. Comprehensive documents are available for both beginners and advanced users. Experiments demonstrate that LIBLINEAR is very efficient on large sparse data sets.

7,848 citations

References
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Journal ArticleDOI
TL;DR: A result shows that, in final iterations of the decomposition method, only a particular set of variables are still being modified, which supports the use of the shrinking and caching techniques in some existing implementations.
Abstract: In a previous paper, the author (2001) proved the convergence of a commonly used decomposition method for support vector machines (SVMs). However, there is no theoretical justification about its stopping criterion, which is based on the gap of the violation of the optimality condition. It is essential to have the gap asymptotically approach zero, so we are sure that existing implementations stop in a finite number of iterations after reaching a specified tolerance. Here, we prove this result and illustrate it by two extensions: /spl nu/-SVM and a multiclass SVM by Crammer and Singer (2001). A further result shows that, in final iterations of the decomposition method, only a particular set of variables are still being modified. This supports the use of the shrinking and caching techniques in some existing implementations. Finally, we prove the asymptotic convergence of a decomposition method for this multiclass SVM. Discussions on the difference between this convergence proof and the one in another paper by Lin are also included.

92 citations


"LIBSVM: A library for support vecto..." refers background in this paper

  • ...proposed in Section 3.2 only variables corresponding to a small set are still allowed to move ( Lin, 2002b, Theorem II.3):...

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Journal Article
TL;DR: It is shown 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.
Abstract: 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.

91 citations


Additional excerpts

  • ...Under given parameters C > 0and E> 0, the standard form of support vector regression [Vapnik 1998] is ll tt 1 T min w w + C .i + C .i * w,b,.,. * 2 i=1 i=1 subject to w T f(xi) + b- zi = E + .i, zi - w T f(xi) - b = E + .i * , * .i,.i = 0,i = 1,...,l....

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Journal ArticleDOI
TL;DR: This paper provides a model algorithm for decomposition, and shows that when the slack multiplier C satisfies √1/2 ≤ C ≤ mL, then it takes no more than 4LC2m4/∈ iterations to drive the criterion to within ∈ of its optimum.
Abstract: This paper studies the convergence properties of a general class of decomposition algorithms for support vector machines (SVMs). We provide a model algorithm for decomposition, and prove necessary and sufficient conditions for stepwise improvement of this algorithm. We introduce a simple “rate certifying” condition and prove a polynomial-time bound on the rate of convergence of the model algorithm when it satisfies this condition. Although it is not clear that existing SVM algorithms satisfy this condition, we provide a version of the model algorithm that does. For this algorithm we show that when the slack multiplier C satisfies \sqrt{1/2} ≤ C ≤ mL, where m is the number of samples and L is a matrix norm, then it takes no more than 4LC2m4/e iterations to drive the criterion to within e of its optimum.

85 citations


Additional excerpts

  • ...iterations. An earlier work is in ( Hush and Scovel, 2003 )....

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Journal Article
TL;DR: The convergence to an optimal solution of a variant termed hybrid maximum-gain working set selection is proved, which is empirically compared to the prominent most violating pair selection and the latest algorithm using second order information.
Abstract: Support vector machines are trained by solving constrained quadratic optimization problems. This is usually done with an iterative decomposition algorithm operating on a small working set of variables in every iteration. The training time strongly depends on the selection of these variables. We propose the maximum-gain working set selection algorithm for large scale quadratic programming. It is based on the idea to greedily maximize the progress in each single iteration. The algorithm takes second order information from cached kernel matrix entries into account. We prove the convergence to an optimal solution of a variant termed hybrid maximum-gain working set selection. This method is empirically compared to the prominent most violating pair selection and the latest algorithm using second order information. For large training sets our new selection scheme is significantly faster.

82 citations

Journal ArticleDOI
TL;DR: This work considers the convex quadratic programming problem arising in support vector machine (SVM), which is a technique designed to solve a variety of learning and pattern recognition problems, and proposes a decomposition method on the basis of a proximal point modification of the subproblem and a working set selection rule.
Abstract: In this work, we consider the convex quadratic programming problem arising in support vector machine (SVM), which is a technique designed to solve a variety of learning and pattern recognition problems. Since the Hessian matrix is dense and real applications lead to large-scale problems, several decomposition methods have been proposed, which split the original problem into a sequence of smaller subproblems. SVM light algorithm is a commonly used decomposition method for SVM, and its convergence has been proved only recently under a suitable block-wise convexity assumption on the objective function. In SVM light algorithm, the size q of the working set, i.e. the dimension of the subproblem, can be any even number. In the present paper, we propose a decomposition method on the basis of a proximal point modification of the subproblem and the basis of a working set selection rule that includes, as a particular case, the one used by the SVM light algorithm. We establish the asymptotic convergence of the metho...

49 citations