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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TL;DR: The two main results are that cue combination can be performed adequately with a simple linear model and that a proper, explicit treatment of texture is required to detect boundaries in natural images.
Abstract: The goal of this work is to accurately detect and localize boundaries in natural scenes using local image measurements. We formulate features that respond to characteristic changes in brightness, color, and texture associated with natural boundaries. In order to combine the information from these features in an optimal way, we train a classifier using human labeled images as ground truth. The output of this classifier provides the posterior probability of a boundary at each image location and orientation. We present precision-recall curves showing that the resulting detector significantly outperforms existing approaches. Our two main results are 1) that cue combination can be performed adequately with a simple linear model and 2) that a proper, explicit treatment of texture is required to detect boundaries in natural images.
2,229 citations
20 Aug 2006
TL;DR: A Cutting Plane Algorithm for training linear SVMs that provably has training time 0(s,n) for classification problems and o(sn log (n)) for ordinal regression problems and several orders of magnitude faster than decomposition methods like svm light for large datasets.
Abstract: Linear Support Vector Machines (SVMs) have become one of the most prominent machine learning techniques for high-dimensional sparse data commonly encountered in applications like text classification, word-sense disambiguation, and drug design. These applications involve a large number of examples n as well as a large number of features N, while each example has only s
2,173 citations
TL;DR: This paper proposes a 3-D CNN-based FE model with combined regularization to extract effective spectral-spatial features of hyperspectral imagery and reveals that the proposed models with sparse constraints provide competitive results to state-of-the-art methods.
Abstract: Due to the advantages of deep learning, in this paper, a regularized deep feature extraction (FE) method is presented for hyperspectral image (HSI) classification using a convolutional neural network (CNN). The proposed approach employs several convolutional and pooling layers to extract deep features from HSIs, which are nonlinear, discriminant, and invariant. These features are useful for image classification and target detection. Furthermore, in order to address the common issue of imbalance between high dimensionality and limited availability of training samples for the classification of HSI, a few strategies such as L2 regularization and dropout are investigated to avoid overfitting in class data modeling. More importantly, we propose a 3-D CNN-based FE model with combined regularization to extract effective spectral-spatial features of hyperspectral imagery. Finally, in order to further improve the performance, a virtual sample enhanced method is proposed. The proposed approaches are carried out on three widely used hyperspectral data sets: Indian Pines, University of Pavia, and Kennedy Space Center. The obtained results reveal that the proposed models with sparse constraints provide competitive results to state-of-the-art methods. In addition, the proposed deep FE opens a new window for further research.
2,059 citations
Cites methods from "LIBSVM: A library for support vecto..."
..., C and γ [48]; thus, we applied 2-D grid search from a wide range (i....
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02 Nov 2010
TL;DR: This work considers a standard non-spatial representation in which the frequencies but not the locations of quantized image features are used to discriminate between classes analogous to how words are used for text document classification without regard to their order of occurrence, and considers two spatial extensions.
Abstract: We investigate bag-of-visual-words (BOVW) approaches to land-use classification in high-resolution overhead imagery. We consider a standard non-spatial representation in which the frequencies but not the locations of quantized image features are used to discriminate between classes analogous to how words are used for text document classification without regard to their order of occurrence. We also consider two spatial extensions, the established spatial pyramid match kernel which considers the absolute spatial arrangement of the image features, as well as a novel method which we term the spatial co-occurrence kernel that considers the relative arrangement. These extensions are motivated by the importance of spatial structure in geographic data.The methods are evaluated using a large ground truth image dataset of 21 land-use classes. In addition to comparisons with standard approaches, we perform extensive evaluation of different configurations such as the size of the visual dictionaries used to derive the BOVW representations and the scale at which the spatial relationships are considered.We show that even though BOVW approaches do not necessarily perform better than the best standard approaches overall, they represent a robust alternative that is more effective for certain land-use classes. We also show that extending the BOVW approach with our proposed spatial co-occurrence kernel consistently improves performance.
1,896 citations
TL;DR: In this paper, the authors present two approaches for obtaining class probabilities, which can be reduced to linear systems and are easy to implement, and show conceptually and experimentally that the proposed approaches are more stable than the two existing popular methods: voting and the method by Hastie and Tibshirani (1998).
Abstract: Pairwise coupling is a popular multi-class classification method that combines all comparisons for each pair of classes. This paper presents two approaches for obtaining class probabilities. Both methods can be reduced to linear systems and are easy to implement. We show conceptually and experimentally that the proposed approaches are more stable than the two existing popular methods: voting and the method by Hastie and Tibshirani (1998)
1,888 citations
References
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TL;DR: High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated and the performance of the support- vector network is compared to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.
Abstract: The support-vector network is a new learning machine for two-group classification problems. The machine conceptually implements the following idea: input vectors are non-linearly mapped to a very high-dimension feature space. In this feature space a linear decision surface is constructed. Special properties of the decision surface ensures high generalization ability of the learning machine. The idea behind the support-vector network was previously implemented for the restricted case where the training data can be separated without errors. We here extend this result to non-separable training data.
High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated. We also compare the performance of the support-vector network to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.
37,861 citations
"LIBSVM: A library for support vecto..." refers background in this paper
...{1,-1}, C-SVC [Boser et al. 1992; Cortes and Vapnik 1995] solves 4LIBSVM Tools: http://www.csie.ntu.edu.tw/~cjlin/libsvmtools. the following primal optimization problem: l t min 1 w T w +C .i (1) w,b,. 2 i=1 subject to yi(w T f(xi) +b) =1 -.i, .i =0,i =1,...,l, where f(xi)maps xi into a…...
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01 Jan 1998
TL;DR: Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.
Abstract: A comprehensive look at learning and generalization theory. The statistical theory of learning and generalization concerns the problem of choosing desired functions on the basis of empirical data. Highly applicable to a variety of computer science and robotics fields, this book offers lucid coverage of the theory as a whole. Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.
26,531 citations
"LIBSVM: A library for support vecto..." refers background in this paper
...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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...It can be clearly seen that C-SVC and one-class SVM are already in the form of problem (11)....
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..., l, in two classes, and a vector y ∈ Rl such that yi ∈ {1,−1}, C-SVC (Cortes and Vapnik, 1995; Vapnik, 1998) solves the following primal problem:...
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...Then, according to the SVM formulation, svm train one calls a corresponding subroutine such as solve c svc for C-SVC and solve nu svc for ....
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...Note that b of C-SVC and E-SVR plays the same role as -. in one-class SVM, so we de.ne ....
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01 Jul 1992
TL;DR: A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented, applicable to a wide variety of the classification functions, including Perceptrons, polynomials, and Radial Basis Functions.
Abstract: A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of the classification functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters is adjusted automatically to match the complexity of the problem. The solution is expressed as a linear combination of supporting patterns. These are the subset of training patterns that are closest to the decision boundary. Bounds on the generalization performance based on the leave-one-out method and the VC-dimension are given. Experimental results on optical character recognition problems demonstrate the good generalization obtained when compared with other learning algorithms.
11,211 citations
"LIBSVM: A library for support vecto..." refers background in this paper
...It can be clearly seen that C-SVC and one-class SVM are already in the form of problem (11)....
[...]
...Then, according to the SVM formulation, svm train one calls a corresponding subroutine such as solve c svc for C-SVC and solve nu svc for ....
[...]
...Note that b of C-SVC and E-SVR plays the same role as -. in one-class SVM, so we de.ne ....
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...In Section 2, we describe SVM formulations supported in LIBSVM: C-Support Vector Classi.cation (C-SVC), ....
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...{1,-1}, C-SVC [Boser et al. 1992; Cortes and Vapnik 1995] solves 4LIBSVM Tools: http://www.csie.ntu.edu.tw/~cjlin/libsvmtools. the following primal optimization problem: l t min 1 w T w +C .i (1) w,b,. 2 i=1 subject to yi(w T f(xi) +b) =1 -.i, .i =0,i =1,...,l, where f(xi)maps xi into a higher-dimensional space and C > 0 is the regularization parameter....
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01 Jan 2008
TL;DR: A simple procedure is proposed, which usually gives reasonable results and is suitable for beginners who are not familiar with SVM.
Abstract: Support vector machine (SVM) is a popular technique for classication. However, beginners who are not familiar with SVM often get unsatisfactory results since they miss some easy but signicant steps. In this guide, we propose a simple procedure, which usually gives reasonable results.
7,069 citations
"LIBSVM: A library for support vecto..." refers methods in this paper
...A Simple Example of Running LIBSVM While detailed instructions of using LIBSVM are available in the README file of the package and the practical guide by Hsu et al. [2003], here we give a simple example....
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...For instructions of using LIBSVM, see the README file included in the package, the LIBSVM FAQ,3 and the practical guide by Hsu et al. [2003]. LIBSVM supports the following learning tasks....
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TL;DR: Decomposition implementations for two "all-together" multiclass SVM methods are given and it is shown that for large problems methods by considering all data at once in general need fewer support vectors.
Abstract: Support vector machines (SVMs) were originally designed for binary classification. How to effectively extend it for multiclass classification is still an ongoing research issue. Several methods have been proposed where typically we construct a multiclass classifier by combining several binary classifiers. Some authors also proposed methods that consider all classes at once. As it is computationally more expensive to solve multiclass problems, comparisons of these methods using large-scale problems have not been seriously conducted. Especially for methods solving multiclass SVM in one step, a much larger optimization problem is required so up to now experiments are limited to small data sets. In this paper we give decomposition implementations for two such "all-together" methods. We then compare their performance with three methods based on binary classifications: "one-against-all," "one-against-one," and directed acyclic graph SVM (DAGSVM). Our experiments indicate that the "one-against-one" and DAG methods are more suitable for practical use than the other methods. Results also show that for large problems methods by considering all data at once in general need fewer support vectors.
6,562 citations