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561
On the algorithmic implementation of multiclass kernelbased vector machines
 Journal of Machine Learning Research
"... In this paper we describe the algorithmic implementation of multiclass kernelbased vector machines. Our starting point is a generalized notion of the margin to multiclass problems. Using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic ob ..."
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Cited by 559 (13 self)
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In this paper we describe the algorithmic implementation of multiclass kernelbased vector machines. Our starting point is a generalized notion of the margin to multiclass problems. Using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic objective function. Unlike most of previous approaches which typically decompose a multiclass problem into multiple independent binary classification tasks, our notion of margin yields a direct method for training multiclass predictors. By using the dual of the optimization problem we are able to incorporate kernels with a compact set of constraints and decompose the dual problem into multiple optimization problems of reduced size. We describe an efficient fixedpoint algorithm for solving the reduced optimization problems and prove its convergence. We then discuss technical details that yield significant running time improvements for large datasets. Finally, we describe various experiments with our approach comparing it to previously studied kernelbased methods. Our experiments indicate that for multiclass problems we attain stateoftheart accuracy.
The Boosting Approach to Machine Learning: An Overview
, 2002
"... Boosting is a general method for improving the accuracy of any given learning algorithm. Focusing primarily on the AdaBoost algorithm, this chapter overviews some of the recent work on boosting including analyses of AdaBoost's training error and generalization error; boosting's connecti ..."
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Cited by 440 (16 self)
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Boosting is a general method for improving the accuracy of any given learning algorithm. Focusing primarily on the AdaBoost algorithm, this chapter overviews some of the recent work on boosting including analyses of AdaBoost's training error and generalization error; boosting's connection to game theory and linear programming; the relationship between boosting and logistic regression; extensions of AdaBoost for multiclass classification problems; methods of incorporating human knowledge into boosting; and experimental and applied work using boosting.
Online passiveaggressive algorithms
 JMLR
, 2006
"... We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the nonrealizable case. The end result is new alg ..."
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Cited by 435 (24 self)
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We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the nonrealizable case. The end result is new algorithms and accompanying loss bounds for hingeloss regression and uniclass. We also get refined loss bounds for previously studied classification algorithms.
Ultraconservative Online Algorithms for Multiclass Problems
 Journal of Machine Learning Research
, 2001
"... In this paper we study online classification algorithms for multiclass problems in the mistake bound model. The hypotheses we use maintain one prototype vector per class. Given an input instance, a multiclass hypothesis computes a similarityscore between each prototype and the input instance and th ..."
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Cited by 320 (21 self)
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In this paper we study online classification algorithms for multiclass problems in the mistake bound model. The hypotheses we use maintain one prototype vector per class. Given an input instance, a multiclass hypothesis computes a similarityscore between each prototype and the input instance and then sets the predicted label to be the index of the prototype achieving the highest similarity. To design and analyze the learning algorithms in this paper we introduce the notion of ultraconservativeness. Ultraconservative algorithms are algorithms that update only the prototypes attaining similarityscores which are higher than the score of the correct label's prototype. We start by describing a family of additive ultraconservative algorithms where each algorithm in the family updates its prototypes by finding a feasible solution for a set of linear constraints that depend on the instantaneous similarityscores. We then discuss a specific online algorithm that seeks a set of prototypes which have a small norm. The resulting algorithm, which we term MIRA (for Margin Infused Relaxed Algorithm) is ultraconservative as well. We derive mistake bounds for all the algorithms and provide further analysis of MIRA using a generalized notion of the margin for multiclass problems.
In defense of onevsall classification
 Journal of Machine Learning Research
, 2004
"... Editor: John ShaweTaylor We consider the problem of multiclass classification. Our main thesis is that a simple “onevsall ” scheme is as accurate as any other approach, assuming that the underlying binary classifiers are welltuned regularized classifiers such as support vector machines. This the ..."
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Cited by 318 (0 self)
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Editor: John ShaweTaylor We consider the problem of multiclass classification. Our main thesis is that a simple “onevsall ” scheme is as accurate as any other approach, assuming that the underlying binary classifiers are welltuned regularized classifiers such as support vector machines. This thesis is interesting in that it disagrees with a large body of recent published work on multiclass classification. We support our position by means of a critical review of the existing literature, a substantial collection of carefully controlled experimental work, and theoretical arguments.
Sharing Features: Efficient Boosting Procedures for Multiclass Object Detection
 IN CVPR
, 2004
"... We consider the problem of detecting a large number of different object classes in cluttered scenes. Traditional approaches require applying a battery of different classifiers to the image, which can be slow and require much training data. We present a multiclass boosting procedure (joint boosting) ..."
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Cited by 309 (16 self)
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We consider the problem of detecting a large number of different object classes in cluttered scenes. Traditional approaches require applying a battery of different classifiers to the image, which can be slow and require much training data. We present a multiclass boosting procedure (joint boosting) that reduces both the computational and sample complexity, by finding common features that can be shared across the classes. The detectors for each class are trained jointly, rather than independently. For a given performance level, the total number of features required is observed to scale approximately logarithmically with the number of classes. In addition, we find that the features selected by independently trained classifiers are often specific to the class, whereas the features selected by the jointly trained classifiers are more generic features, such as lines and edges.
Probability Estimates for Multiclass Classification by Pairwise Coupling
 Journal of Machine Learning Research
, 2003
"... Pairwise coupling is a popular multiclass classification method that combines together all pairwise 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. ..."
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Cited by 303 (2 self)
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Pairwise coupling is a popular multiclass classification method that combines together all pairwise 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.
Sharing Visual Features for Multiclass And Multiview Object Detection
, 2004
"... We consider the problem of detecting a large number of different classes of objects in cluttered scenes. Traditional approaches require applying a battery of different classifiers to the image, at multiple locations and scales. This can be slow and can require a lot of training data, since each clas ..."
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Cited by 279 (6 self)
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We consider the problem of detecting a large number of different classes of objects in cluttered scenes. Traditional approaches require applying a battery of different classifiers to the image, at multiple locations and scales. This can be slow and can require a lot of training data, since each classifier requires the computation of many different image features. In particular, for independently trained detectors, the (runtime) computational complexity, and the (trainingtime) sample complexity, scales linearly with the number of classes to be detected. It seems unlikely that such an approach will scale up to allow recognition of hundreds or thousands of objects.
On the Learnability and Design of Output Codes for Multiclass Problems
 In Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
, 2000
"... . Output coding is a general framework for solving multiclass categorization problems. Previous research on output codes has focused on building multiclass machines given predefined output codes. In this paper we discuss for the first time the problem of designing output codes for multiclass problem ..."
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Cited by 228 (6 self)
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. Output coding is a general framework for solving multiclass categorization problems. Previous research on output codes has focused on building multiclass machines given predefined output codes. In this paper we discuss for the first time the problem of designing output codes for multiclass problems. For the design problem of discrete codes, which have been used extensively in previous works, we present mostly negative results. We then introduce the notion of continuous codes and cast the design problem of continuous codes as a constrained optimization problem. We describe three optimization problems corresponding to three different norms of the code matrix. Interestingly, for the l 2 norm our formalism results in a quadratic program whose dual does not depend on the length of the code. A special case of our formalism provides a multiclass scheme for building support vector machines which can be solved efficiently. We give a time and space efficient algorithm for solving the quadratic program. We describe preliminary experiments with synthetic data show that our algorithm is often two orders of magnitude faster than standard quadratic programming packages. We conclude with the generalization properties of the algorithm. Keywords: Multiclass categorization,output coding, SVM 1.
Chunking with Support Vector Machines
, 2001
"... We apply Support Vector Machines (SVMs) to identify English base phrases (chunks). SVMs are known to achieve high generalization performance even with input data of high dimensional feature spaces. Furthermore, by the Kernel principle, SVMs can carry out training with smaller computational overhead ..."
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Cited by 219 (11 self)
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We apply Support Vector Machines (SVMs) to identify English base phrases (chunks). SVMs are known to achieve high generalization performance even with input data of high dimensional feature spaces. Furthermore, by the Kernel principle, SVMs can carry out training with smaller computational overhead independent of their dimensionality. We apply weighted voting of 8 SVMsbased systems trained with distinct chunk representations. Experimental results show that our approach achieves higher accuracy than previous approaches.