A Framework for Kernel-Based Multi-Category Classification
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Abstract
A geometric framework for understanding multi-category classification is introduced, through which many existing 'all-together' algorithms can be understood. The structure enables parsimonious optimisation, through a direct extension of the binary methodology. The focus is on Support Vector Classification, with parallels drawn to related methods.
The ability of the framework to compare algorithms is illustrated by a brief discussion of Fisher consistency. Its utility in improving understanding of multi-category analysis is demonstrated through a derivation of improved generalisation bounds.
It is also described how this architecture provides insights regarding how to further improve on the speed of existing multi-category classification algorithms. An initial example of how this might be achieved is developed in the formulation of a straightforward multi-category Sequential Minimal Optimisation algorithm. Proof-of-concept experimental results have shown that this, combined with the mapping of pairwise results, is comparable with benchmark optimisation speeds.
The ability of the framework to compare algorithms is illustrated by a brief discussion of Fisher consistency. Its utility in improving understanding of multi-category analysis is demonstrated through a derivation of improved generalisation bounds.
It is also described how this architecture provides insights regarding how to further improve on the speed of existing multi-category classification algorithms. An initial example of how this might be achieved is developed in the formulation of a straightforward multi-category Sequential Minimal Optimisation algorithm. Proof-of-concept experimental results have shown that this, combined with the mapping of pairwise results, is comparable with benchmark optimisation speeds.
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