Abstract
This paper presents the multiclass classifier based on analytical center of feasible space (MACM). This multiclass classifier is formulated as quadratic constrained linear optimization and does not need repeatedly constructing classifiers to separate a single class from all the others. Its generalization error upper bound is proved theoretically. The experiments on benchmark datasets validate the generalization performance of MACM.
Highlights
Multiclass classification is an important and on-going research subject in machine learning
Reference [12] proposes multiclass support vector machine (MSVM), which corresponds to simple quadratic optimization and need not repeat constructing binary classifier
In order to further simplify the formulation of multiclass analytical center classifier, we introduce some notations as follows: M = k ∗ (k − 1) ∗ ∑ki=1 mi, B = {Vec(Ãil, i, j) | i, j = 1, . . . , k, i ≠ j, l = 1, . . . , mi} ∈ RM×k∗(d+1); let Bi represent the ith row vector of B
Summary
Multiclass classification is an important and on-going research subject in machine learning. The first multiclass classification approach is extending binary classifier to handle the multiclass case directly This included neural networks, decision trees, support vector machines, naive Bayes, and K-nearest neighbors. For the all-versus-all method, a binary classifier is built to discriminate between each pair of classes, while discarding the rest of the classes. This requires building K(K−1)/2 binary classifiers for K classes problem. For error-correcting output coding, it works by training N binary classifiers to distinguish between the K different classes. Reference [12] proposes multiclass support vector machine (MSVM), which corresponds to simple quadratic optimization and need not repeat constructing binary classifier. The experiments on benchmark dataset validate the generalization performance of MACM
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