The error correcting output codes (ECOC) is a general framework to extend any binary classifier to the multiclass case. Finding the optimal ECOC is known as a NP hard problem. In this paper, we present a spectral analysis approach for the design of ECOC. We construct a similarity graph of the classes and generate ECOC with a subset of thresholded eigenvectors of the graph Laplacian. Using the spectral analysis, the coding efficiency, classifier's diversity, Hamming distance among codewords, and binary classifiers' accuracy can be simultaneously considered. The resulting ECOC is efficient, thus only a small set of binary classifiers are to be evaluated when making a decision. In experiments with large multiclass problems, our method is between 3 and 12 times faster comparing to one-against-all, with comparable classification accuracy. Our method also shows a better performance than the most of leading methods, e.g., ClassMap, random dense ECOC, random sparse ECOC, and discriminant ECOC.
['Xiao Zhang', 'Lin Liang', 'Heung-Yeung Shum']
Spectral error correcting output codes for efficient multiclass recognition