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65
Marginalized kernels between labeled graphs
 Proceedings of the Twentieth International Conference on Machine Learning
, 2003
"... A new kernel function between two labeled graphs is presented. Feature vectors are defined as the counts of label paths produced by random walks on graphs. The kernel computation finally boils down to obtaining the stationary state of a discretetime linear system, thus is efficiently performed by s ..."
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Cited by 144 (14 self)
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A new kernel function between two labeled graphs is presented. Feature vectors are defined as the counts of label paths produced by random walks on graphs. The kernel computation finally boils down to obtaining the stationary state of a discretetime linear system, thus is efficiently performed by solving simultaneous linear equations. Our kernel is based on an infinite dimensional feature space, so it is fundamentally different from other string or tree kernels based on dynamic programming. We will present promising empirical results in classification of chemical compounds. 1 1.
Feature space interpretation of svms with indefinite kernels
 IEEE Trans Pattern Anal Mach Intell
, 2005
"... Abstract—Kernel methods are becoming increasingly popular for various kinds of machine learning tasks, the most famous being the support vector machine (SVM) for classification. The SVM is well understood when using conditionally positive definite (cpd) kernel functions. However, in practice, noncp ..."
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Cited by 57 (2 self)
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Abstract—Kernel methods are becoming increasingly popular for various kinds of machine learning tasks, the most famous being the support vector machine (SVM) for classification. The SVM is well understood when using conditionally positive definite (cpd) kernel functions. However, in practice, noncpd kernels arise and demand application in SVMs. The procedure of “plugging ” these indefinite kernels in SVMs often yields good empirical classification results. However, they are hard to interpret due to missing geometrical and theoretical understanding. In this paper, we provide a step toward the comprehension of SVM classifiers in these situations. We give a geometric interpretation of SVMs with indefinite kernel functions. We show that such SVMs are optimal hyperplane classifiers not by margin maximization, but by minimization of distances between convex hulls in pseudoEuclidean spaces. By this, we obtain a sound framework and motivation for indefinite SVMs. This interpretation is the basis for further theoretical analysis, e.g., investigating uniqueness, and for the derivation of practical guidelines like characterizing the suitability of indefinite SVMs. Index Terms—Support vector machine, indefinite kernel, pseudoEuclidean space, separation of convex hulls, pattern recognition. æ 1
Tangent Distance Kernels for Support Vector Machines
 IN PROCEEDINGS OF THE 16TH ICPR
, 2002
"... When dealing with pattern recognition problems one encounters different types of apriori knowledge. It is important to incorporate such knowledge into the classification method at hand. A very common type of apriori knowledge is transformation invariance of the input data, e.g. geometric transform ..."
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Cited by 33 (9 self)
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When dealing with pattern recognition problems one encounters different types of apriori knowledge. It is important to incorporate such knowledge into the classification method at hand. A very common type of apriori knowledge is transformation invariance of the input data, e.g. geometric transformations of imagedata like shifts, scaling etc. Distance based classification methods can make use of this by a modified distance measure called tangent distance [13, 14]. We introduce a new class of kernels for support vector machines which incorporate tangent distance and therefore are applicable in cases where such transformation invariances are known. We report experimental results which show that the performance of our method is comparable to other stateoftheart methods, while problems of existing ones are avoided.
2004), Learning with distance substitution kernels
 in Pattern Rcognition  Proc. of the 26th DAGM Symposium
"... Abstract. During recent years much effort has been spent in incorporating problem specific apriori knowledge into kernel methods for machine learning. A common example is apriori knowledge given by a distance measure between objects. A simple but effective approach for kernel construction consists ..."
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Cited by 26 (2 self)
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Abstract. During recent years much effort has been spent in incorporating problem specific apriori knowledge into kernel methods for machine learning. A common example is apriori knowledge given by a distance measure between objects. A simple but effective approach for kernel construction consists of substituting the Euclidean distance in ordinary kernel functions by the problem specific distance measure. We formalize this distance substitution procedure and investigate theoretical and empirical effects. In particular we state criteria for definiteness of the resulting kernels. We demonstrate the wide applicability by solving several classification tasks with SVMs. Regularization of the kernel matrices can additionally increase the recognition accuracy. 1
The Genetic Kernel Support Vector Machine: Description and Evaluation
 Artificial Intelligence Review
, 2005
"... Abstract. The Support Vector Machine (SVM) has emerged in recent years as a popular approach to the classification of data. One problem that faces the user of an SVM is how to choose a kernel and the specific parameters for that kernel. Applications of an SVM therefore require a search for the optim ..."
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Cited by 23 (0 self)
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Abstract. The Support Vector Machine (SVM) has emerged in recent years as a popular approach to the classification of data. One problem that faces the user of an SVM is how to choose a kernel and the specific parameters for that kernel. Applications of an SVM therefore require a search for the optimum settings for a particular problem. This paper proposes a classification technique, which we call the Genetic Kernel SVM (GK SVM), that uses Genetic Programming to evolve a kernel for a SVM classifier. Results of initial experiments with the proposed technique are presented. These results are compared with those of a standard SVM classifier using the Polynomial, RBF and Sigmoid kernel with various parameter settings.
A Novel Connectionist System for Unconstrained Handwriting Recognition
, 2008
"... Recognising lines of unconstrained handwritten text is a challenging task. The difficulty of segmenting cursive or overlapping characters, combined with the need to exploit surrounding context, has led to low recognition rates for even the best current recognisers. Most recent progress in the field ..."
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Cited by 23 (3 self)
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Recognising lines of unconstrained handwritten text is a challenging task. The difficulty of segmenting cursive or overlapping characters, combined with the need to exploit surrounding context, has led to low recognition rates for even the best current recognisers. Most recent progress in the field has been made either through improved preprocessing, or through advances in language modelling. Relatively little work has been done on the basic recognition algorithms. Indeed, most systems rely on the same hidden Markov models that have been used for decades in speech and handwriting recognition, despite their wellknown shortcomings. This paper proposes an alternative approach based on a novel type of recurrent neural network, specifically designed for sequence labelling tasks where the data is hard to segment and contains long range, bidirectional interdependencies. In experiments on two large unconstrained handwriting databases, our approach achieves word recognition accuracies of 79.7 % on online data and 74.1 % on offline data, significantly outperforming a stateoftheart HMMbased system. In addition, we demonstrate the network’s robustness to lexicon size, measure the individual influence of its hidden layers, and analyse its use of context. Lastly we provide an in depth discussion of the differences between the network and HMMs, suggesting reasons for the network’s superior performance.
Nonmercer kernel for SVM object recognition
 In British Machine Vision Conference (BMVC
, 2004
"... On the one hand, Support Vector Machines have met with significant success in solving difficult pattern recognition problems with global features representation. On the other hand, local features in images have shown to be suitable representations for efficient object recognition. Therefore, it is n ..."
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Cited by 21 (1 self)
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On the one hand, Support Vector Machines have met with significant success in solving difficult pattern recognition problems with global features representation. On the other hand, local features in images have shown to be suitable representations for efficient object recognition. Therefore, it is natural to try to combine SVM approach with local features representation to gain advantages on both sides. We study in this paper the Mercer property of matching kernels which mimic classical matching algorithms used in techniques based on points of interest. We introduce a new statistical approach of kernel positiveness. We show that despite the absence of an analytical proof of the Mercer property, we can provide bounds on the probability that the Gram matrix is actually positive definite for kernels in large class of functions, under reasonable assumptions. A few experiments validate those on object recognition tasks. 1
A Kernel for Time Series Based on Global Alignments
 In Proceedings of ICASSP’07, Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on, pages II–413 – II–416
, 2007
"... We propose in this paper a new family of kernels to handle times series, notably speech data, within the framework of kernel methods which includes popular algorithms such as the Support Vector Machine. These kernels elaborate on the well known Dynamic Time Warping (DTW) family of distances by consi ..."
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Cited by 18 (2 self)
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We propose in this paper a new family of kernels to handle times series, notably speech data, within the framework of kernel methods which includes popular algorithms such as the Support Vector Machine. These kernels elaborate on the well known Dynamic Time Warping (DTW) family of distances by considering the same set of elementary operations, namely substitutions and repetitions of tokens, to map a sequence onto another. Associating to each of these operations a given score, DTW algorithms use dynamic programming techniques to compute an optimal sequence of operations with high overall score. In this paper we consider instead the score spanned by all possible alignments, take a smoothed version of their maximum and derive a kernel out of this formulation. We prove that this kernel is positive de�nite under favorable conditions and show how it can be tuned effectively for practical applications as we report encouraging results on a speech recognition task. Index Terms — kernel methods, dynamic time warping, speech recognition, support vector machines. 1.
Directional features in online handwriting recognition
, 2006
"... The selection of valuable features is crucial in pattern recognition. In this paper we deal with the issue that part of features originate from directional instead of common linear data. Both for directional and linear data a theory for a statistical modeling exists. However, none of these theories ..."
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Cited by 14 (1 self)
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The selection of valuable features is crucial in pattern recognition. In this paper we deal with the issue that part of features originate from directional instead of common linear data. Both for directional and linear data a theory for a statistical modeling exists. However, none of these theories gives an integrated solution to problems, where linear and directional variables are to be combined in a single, multivariate probability density function. We describe a general approach for a unified statistical modeling, given the constraint that variances of the circular variables are small. The method is practically evaluated in the context of our online handwriting recognition system frog on hand and the socalled tangent slope angle feature. Recognition results are compared with two alternative modeling approaches. The proposed solution gives significant improvements in recognition accuracy, computational speed and memory requirements.
Mathematical Sketching: A New Approach to Creating and Exploring Dynamic Illustrations
, 2005
"... Diagrams and illustrations are frequently used to help explain mathematical concepts. Students often create them with pencil and paper as an intuitive aid in visualizing relationships among variables, constants, and functions, and use them as a guide in writing the appropriate mathematics to solve ..."
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Cited by 13 (3 self)
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Diagrams and illustrations are frequently used to help explain mathematical concepts. Students often create them with pencil and paper as an intuitive aid in visualizing relationships among variables, constants, and functions, and use them as a guide in writing the appropriate mathematics to solve the problem. However, such static diagrams generally assist only in the initial formulation of the required mathematics, not in “debugging ” or problem analysis. This can be a severe limitation, even for simple problems with a natural mapping to the temporal dimension or problems with complex spatial relationships. To overcome these limitations we present mathematical sketching, a novel, penbased, gestural interaction paradigm for mathematics problem solving. Mathematical sketching derives from the familiar pencilandpaper process of drawing supporting diagrams to facilitate the formulation of mathematical expressions; however, with mathematical sketching, users can also leverage their physical intuition by watching their handdrawn diagrams animate in response to continuous or discrete parameter changes in their written formulas. Diagram animation is driven by implicit associations that are inferred, either automatically or with gestural guidance, from mathematical expressions, diagram labels and drawing elements. We describe