Constrained global optimization: algorithms and applications
Constrained global optimization: algorithms and applications
The nature of statistical learning theory
The nature of statistical learning theory
Classification on pairwise proximity data
Proceedings of the 1998 conference on Advances in neural information processing systems II
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Training Invariant Support Vector Machines
Machine Learning
Duality and Geometry in SVM Classifiers
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
On-Line Handwriting Recognition with Support Vector Machines " A Kernel Approach
IWFHR '02 Proceedings of the Eighth International Workshop on Frontiers in Handwriting Recognition (IWFHR'02)
Text classification using string kernels
The Journal of Machine Learning Research
A generalized kernel approach to dissimilarity-based classification
The Journal of Machine Learning Research
Training ν-Support Vector Classifiers: Theory and Algorithms
Neural Computation
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 02
Learning with non-metric proximity matrices
Proceedings of the 13th annual ACM international conference on Multimedia
Evolutionary learning with kernels: a generic solution for large margin problems
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Automatic learning of textual entailments with cross-pair similarities
ACL-44 Proceedings of the 21st International Conference on Computational Linguistics and the 44th annual meeting of the Association for Computational Linguistics
Edit distance-based kernel functions for structural pattern classification
Pattern Recognition
Invariant kernel functions for pattern analysis and machine learning
Machine Learning
Fast and effective kernels for relational learning from texts
Proceedings of the 24th international conference on Machine learning
Controlling overfitting with multi-objective support vector machines
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Training SVM with indefinite kernels
Proceedings of the 25th international conference on Machine learning
Grassmann discriminant analysis: a unifying view on subspace-based learning
Proceedings of the 25th international conference on Machine learning
Linear-Time Computation of Similarity Measures for Sequential Data
The Journal of Machine Learning Research
Hierarchical Bag of Paths for Kernel Based Shape Classification
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
On Euclidean Corrections for Non-Euclidean Dissimilarities
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Learning kernels from indefinite similarities
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
A Concept Lattice-Based Kernel for SVM Text Classification
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Improving Graph Classification by Isomap
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Encoding tree pair-based graphs in learning algorithms: the textual entailment recognition case
TextGraphs-3 Proceedings of the 3rd Textgraphs Workshop on Graph-Based Algorithms for Natural Language Processing
A machine learning approach to textual entailment recognition
Natural Language Engineering
Novel multiclass classifiers based on the minimization of the within-class variance
IEEE Transactions on Neural Networks
A Reformulation of Support Vector Machines for General Confidence Functions
ACML '09 Proceedings of the 1st Asian Conference on Machine Learning: Advances in Machine Learning
Graph classification by means of Lipschitz embedding
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A kernel-based approach to document retrieval
DAS '10 Proceedings of the 9th IAPR International Workshop on Document Analysis Systems
Nonlinear non-negative component analysis algorithms
IEEE Transactions on Image Processing
An empirical comparison of Kernel-based and dissimilarity-based feature spaces
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Improving vector space embedding of graphs through feature selection algorithms
Pattern Recognition
On the usefulness of similarity based projection spaces for transfer learning
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
Inexact graph matching based on kernels for object retrieval in image databases
Image and Vision Computing
Non-Euclidean or non-metric measures can be informative
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Probability model of covering algorithm (PMCA)
ICIC'06 Proceedings of the 2006 international conference on Intelligent Computing - Volume Part I
Geometrical interpretation and applications of membership functions with fuzzy rough sets
Fuzzy Sets and Systems
Towards the unification of structural and statistical pattern recognition
Pattern Recognition Letters
The dissimilarity space: Bridging structural and statistical pattern recognition
Pattern Recognition Letters
The dissimilarity representation for structural pattern recognition
CIARP'11 Proceedings of the 16th Iberoamerican Congress conference on Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Review: Supervised classification and mathematical optimization
Computers and Operations Research
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
Full length article: Regularization networks with indefinite kernels
Journal of Approximation Theory
Information Technology and Management
Structure of feature spaces related to fuzzy similarity relations as kernels
Fuzzy Sets and Systems
Approximation and Estimation Bounds for Subsets of Reproducing Kernel Kreĭn Spaces
Neural Processing Letters
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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, non-cpd kernels arise and demand application in SVMs. The procedure of "plugging驴 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 pseudo-Euclidean 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.