Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
The nature of statistical learning theory
The nature of statistical learning theory
Machine Learning
An efficient cost scaling algorithm for the assignment problem
Mathematical Programming: Series A and B
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Transformation Invariance in Pattern Recognition-Tangent Distance and Tangent Propagation
Neural Networks: Tricks of the Trade, this book is an outgrowth of a 1996 NIPS workshop
Text classification using string kernels
The Journal of Machine Learning Research
The Journal of Machine Learning Research
Extensions of marginalized graph kernels
ICML '04 Proceedings of the twenty-first international conference on Machine learning
The Amsterdam Library of Object Images
International Journal of Computer Vision
Nuisance free recognition of hand postures over a tabletop display
VisHCI '06 Proceedings of the HCSNet workshop on Use of vision in human-computer interaction - Volume 56
Support Vector Machine incorporated with feature discrimination
Expert Systems with Applications: An International Journal
Efficient methods for point matching with known camera orientation
ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
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We extend Support Vector Machines to input spaces that are sets by ensuring that the classifier is invariant to permutations of sub-elements within each input. Such permutations include reordering of scalars in an input vector, re-orderings of tuples in an input matrix or re-orderings of general objects (in Hilbert spaces) within a set as well. This approach induces permutational invariance in the classifier which can then be directly applied to unusual set-based representations of data. The permutation invariant Support Vector Machine alternates the Hungarian method for maximum weight matching within the maximum margin learning procedure. We effectively estimate and apply permutations to the input data points to maximize classification margin while minimizing data radius. This procedure has a strong theoretical justification via well established error probability bounds. Experiments are shown on character recognition, 3D object recognition and various UCI datasets.