The nature of statistical learning theory
The nature of statistical learning theory
Pattern classification: a unified view of statistical and neural approaches
Pattern classification: a unified view of statistical and neural approaches
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
On the influence of the kernel on the consistency of support vector machines
The Journal of Machine Learning Research
Maximal margin classification for metric spaces
Journal of Computer and System Sciences - Special issue: Learning theory 2003
The infinite polynomial kernel for support vector machine
ADMA'05 Proceedings of the First international conference on Advanced Data Mining and Applications
FRSVMs: Fuzzy rough set based support vector machines
Fuzzy Sets and Systems
A novel discourse parser based on support vector machine classification
ACL '09 Proceedings of the Joint Conference of the 47th Annual Meeting of the ACL and the 4th International Joint Conference on Natural Language Processing of the AFNLP: Volume 2 - Volume 2
Inconsistency-based active learning for support vector machines
Pattern Recognition
A vector-valued support vector machine model for multiclass problem
Information Sciences: an International Journal
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In this paper we focus our topic on linear separability of two data sets in feature space, including finite and infinite data sets. We first develop a method to construct a mapping that maps original data set into a high dimensional feature space, on which inner product is defined by a dot product kernel. Our method can also be applied to the Gaussian kernels. Via this mapping, structure of features in the feature space is easily observed, and the linear separability of data sets in feature space could be studied. We obtain that any two finite sets of data with empty overlap in original input space will become linearly separable in an infinite dimensional feature space. For two infinite data sets, we present several sufficient and necessary conditions for their linear separability in feature space. We also obtain a meaningful formula to judge linear separability of two infinite data sets in feature space by information in original input space.