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Updated: Jul 1, 2026
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Cross-Modal Multivariate Pattern Analysis
Published on: November 9, 2011
Generalization properties of finite-size polynomial support vector machines
1DRFMC/SPSMS CEA Grenoble, 17 avenue des Martyrs, 38054 Grenoble Cedex 09, France.
Summary
Finite-size polynomial support vector machines exhibit learning properties influenced by feature normalization. Generalization error shows a crossover behavior related to data distribution anisotropy and training set size.
Area of Science:
- Machine Learning
- Computational Statistics
- Pattern Recognition
Background:
- Support Vector Machines (SVMs) are powerful classification algorithms.
- Polynomial SVMs utilize high-order feature mappings.
- Understanding generalization error is crucial for model performance.
Purpose of the Study:
- To analyze the learning properties of finite-size polynomial SVMs.
- To investigate the impact of feature normalization on generalization error.
- To compare finite-size behavior with theoretical predictions.
Main Methods:
- Theoretical analysis of polynomial support vector machines.
- Feature space analysis incorporating normalization effects.
- Examination of generalization error as a function of training set size.
Main Results:
- Feature normalization introduces anisotropy in feature space.
- Generalization error exhibits a crossover between fast and slow decrease regimes.
- Behavior is dependent on data anisotropy and task complexity.
Conclusions:
- The study provides insights into the generalization error of finite-size polynomial SVMs.
- Theoretical findings align with numerical simulations.
- The crossover behavior offers a deeper understanding of SVM learning dynamics.
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