1,539 research outputs found
Convex Optimization for Binary Classifier Aggregation in Multiclass Problems
Multiclass problems are often decomposed into multiple binary problems that
are solved by individual binary classifiers whose results are integrated into a
final answer. Various methods, including all-pairs (APs), one-versus-all (OVA),
and error correcting output code (ECOC), have been studied, to decompose
multiclass problems into binary problems. However, little study has been made
to optimally aggregate binary problems to determine a final answer to the
multiclass problem. In this paper we present a convex optimization method for
an optimal aggregation of binary classifiers to estimate class membership
probabilities in multiclass problems. We model the class membership probability
as a softmax function which takes a conic combination of discrepancies induced
by individual binary classifiers, as an input. With this model, we formulate
the regularized maximum likelihood estimation as a convex optimization problem,
which is solved by the primal-dual interior point method. Connections of our
method to large margin classifiers are presented, showing that the large margin
formulation can be considered as a limiting case of our convex formulation.
Numerical experiments on synthetic and real-world data sets demonstrate that
our method outperforms existing aggregation methods as well as direct methods,
in terms of the classification accuracy and the quality of class membership
probability estimates.Comment: Appeared in Proceedings of the 2014 SIAM International Conference on
Data Mining (SDM 2014
Sub-Classifier Construction for Error Correcting Output Code Using Minimum Weight Perfect Matching
Multi-class classification is mandatory for real world problems and one of
promising techniques for multi-class classification is Error Correcting Output
Code. We propose a method for constructing the Error Correcting Output Code to
obtain the suitable combination of positive and negative classes encoded to
represent binary classifiers. The minimum weight perfect matching algorithm is
applied to find the optimal pairs of subset of classes by using the
generalization performance as a weighting criterion. Based on our method, each
subset of classes with positive and negative labels is appropriately combined
for learning the binary classifiers. Experimental results show that our
technique gives significantly higher performance compared to traditional
methods including the dense random code and the sparse random code both in
terms of accuracy and classification times. Moreover, our method requires
significantly smaller number of binary classifiers while maintaining accuracy
compared to the One-Versus-One.Comment: 7 pages, 3 figure
On the design of an ECOC-compliant genetic algorithm
Genetic Algorithms (GA) have been previously applied to Error-Correcting Output Codes (ECOC) in state-of-the-art works in order to find a suitable coding matrix. Nevertheless, none of the presented techniques directly take into account the properties of the ECOC matrix. As a result the considered search space is unnecessarily large. In this paper, a novel Genetic strategy to optimize the ECOC coding step is presented. This novel strategy redefines the usual crossover and mutation operators in order to take into account the theoretical properties of the ECOC framework. Thus, it reduces the search space and lets the algorithm to converge faster. In addition, a novel operator that is able to enlarge the code in a smart way is introduced. The novel methodology is tested on several UCI datasets and four challenging computer vision problems. Furthermore, the analysis of the results done in terms of performance, code length and number of Support Vectors shows that the optimization process is able to find very efficient codes, in terms of the trade-off between classification performance and the number of classifiers. Finally, classification performance per dichotomizer results shows that the novel proposal is able to obtain similar or even better results while defining a more compact number of dichotomies and SVs compared to state-of-the-art approaches
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