• Corpus ID: 7725461

Learning SVM Classifiers with Indefinite Kernels

@inproceedings{Gu2012LearningSC,
  title={Learning SVM Classifiers with Indefinite Kernels},
  author={Suicheng Gu and Yuhong Guo},
  booktitle={AAAI},
  year={2012}
}
Recently, training support vector machines with indefinite kernels has attracted great attention in the machine learning community. In this paper, we tackle this problem by formulating a joint optimization model over SVM classifications and kernel principal component analysis. We first reformulate the kernel principal component analysis as a general kernel transformation framework, and then incorporate it into the SVM classification to formulate a joint optimization model. The proposed model… 

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References

SHOWING 1-10 OF 20 REFERENCES
Support vector machine classification with indefinite kernels
TLDR
This work proposes a method for support vector machine classification using indefinite kernels that simultaneously computes support vectors and a proxy kernel matrix used in forming the loss.
Training SVM with indefinite kernels
TLDR
This paper considers a regularized SVM formulation, in which the indefinite kernel matrix is treated as a noisy observation of some unknown positive semidefinite one (proxy kernel) and the support vectors and the proxy kernel can be computed simultaneously.
Learning kernels from indefinite similarities
TLDR
A method is introduced that aims to simultaneously find a reproducing kernel Hilbert space based on the given similarities and train a classifier with good generalization in that space and whose associated convex conic program can be solved efficiently.
Analysis of SVM with Indefinite Kernels
TLDR
It is shown that the objective function is continuously differentiable and its gradient can be explicitly computed, and that its gradient is Lipschitz continuous, which greatly facilitates the application of gradient-based algorithms.
Kernel Discriminant Analysis for Positive Definite and Indefinite Kernels
  • E. Pekalska, B. Haasdonk
  • Computer Science, Mathematics
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 2009
TLDR
This paper derives an additional kernel tool that is still missing, namely kernel quadratic discriminant (KQD), and provides classifiers that are applicable to kernels defined by any symmetric similarity measure.
A Reformulation of Support Vector Machines for General Confidence Functions
TLDR
A generalized view of support vector machines is presented that does not rely on a Euclidean geometric interpretation nor even positive semidefinite kernels, but is able to derive a principled relaxation of the SVM criterion that yields a convex upper bound.
A comparison of methods for multiclass support vector machines
TLDR
Decomposition implementations for two "all-together" multiclass SVM methods are given and it is shown that for large problems methods by considering all data at once in general need fewer support vectors.
Learning with non-positive kernels
TLDR
A general representer theorem for constrained stabilization is shown and generalization bounds are proved by computing the Rademacher averages of the kernel class.
A Study on Sigmoid Kernels for SVM and the Training of non-PSD Kernels by SMO-type Methods
TLDR
This paper discusses non-PSD kernels through the viewpoint of separability, and shows that the sigmoid kernel matrix is conditionally positive definite (CPD) in certain parameters and thus are valid kernels there.
A Generalized Kernel Approach to Dissimilarity-based Classification
TLDR
It is shown that other, more global classification techniques are preferable to the nearest neighbor rule, in such cases when dissimilarities used in practice are far from ideal and the performance of the nearest neighbors rule suffers from its sensitivity to noisy examples.
...
1
2
...