We propose a novel boosting approach to multi-class classification problems, in which multiple classes are distinguished by a set of random projection matrices in essence. The approach uses random projections to alleviate the proliferation of binary classifiers typically required to perform multi-class classification. The result is a multi-class classifier with a single vector-valued parameter, irrespective of the number of classes involved. Two variants of this approach are proposed. The first method randomly projects the original data into new spaces, while the second method randomly projects the outputs of learned weak classifiers. These methods are not only conceptually simple but also effective and easy to implement. A series of experiments on synthetic, machine learning and visual recognition data sets demonstrate that our proposed methods compare favorably to existing multi-class boosting algorithms in terms of both the convergence rate and classification accuracy.
Error correcting output coding (ECOC) The above two algorithms are special cases of ECOC. The idea of ECOC is to associate each class with a codeword which is a row of a coding matrix @math and @math . The algorithm trains @math binary classifiers to distinguish between @math different classes. During evaluation, the output of @math binary classifiers (a @math -bit string) is compared to each codeword and the sample is assigned to the class whose codeword has the minimal hamming distance. Diettrich and Bakiri report improved generalization ability of this method over the above two techniques @cite_44 . In boosting, the binary classifier is viewed as weak learner and each is learned one at a time in sequence. Some well-known ECOC based boostings are AdaBoost.MO, AdaBoost.OC and AdaBoost.ECC @cite_12 @cite_10 . Although this technique provides a simple solution to multi-class classification, it does not fully exploit the pairwise correlations between classes.
@cite_44 @cite_10 @cite_12
1578772208 2292376821 2101276256 2112076978
This paper describes a new technique for solv- ing multiclass learning problems by combining Freund and Schapire's boosting algorithm with the main ideas of Diet- terich and Bakiri's method of error-correcting output codes (ECOC). Boosting is a general method of improving the ac- curacy of a given base or "weak" learning algorithm. ECOC is a robust method of solving multiclass learning problems by reducing to a sequence of two-class problems. We show that our new hybrid method has advantages of both: Like ECOC, our method only requires that the base learning al- gorithm work on binary-labeled data. Like boosting, we prove that the method comes with strong theoretical guar- antees on the training and generalization error of the final combined hypothesis assuming only that the base learning algorithm perform slightly better than random guessing. Although previous methods were known for boosting multi- class problems, the new method may be significantly faster and require less programming effort in creating the base learning algorithm. We also compare the new algorithm experimentally to other voting methods. Traditional error-correcting output codes (ECOCs) decompose a multi-class classification problem into many binary problems. Although it seems natural to use ECOCs for multi-label problems as well, doing so naively creates issues related to: the validity of the encoding, the efficiency of the decoding, the predictability of the generated codeword, and the exploitation of the label dependency. Using canonical correlation analysis, we propose an error-correcting code for multi-label classification. Label dependency is characterized as the most predictable directions in the label space, which are extracted as canonical output variates and encoded into the codeword. Predictions for the codeword define a graphical model of labels with both Bernoulli potentials (from classifiers on the labels) and Gaussian potentials (from regression on the canonical output variates). Decoding is performed by mean-field approximation. We establish connections between the proposed code and research areas such as compressed sensing and ensemble learning. Some of these connections contribute to better understanding of the new code, and others lead to practical improvements in code design. In our empirical study, the proposed code leads to substantial improvements compared to various competitors in music emotion classification and outdoor scene recognition. We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a margin-based binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class is compared against all others, or in which all pairs of classes are compared to each other, or in which output codes with error-correcting properties are used. We propose a general method for combining the classifiers generated on the binary problems, and we prove a general empirical multiclass loss bound given the empirical loss of the individual binary learning algorithms. The scheme and the corresponding bounds apply to many popular classification learning algorithms including support-vector machines, AdaBoost, regression, logistic regression and decision-tree algorithms. We also give a multiclass generalization error analysis for general output codes with AdaBoost as the binary learner. Experimental results with SVM and AdaBoost show that our scheme provides a viable alternative to the most commonly used multiclass algorithms. In an earlier paper, we introduced a new "boosting" algorithm called AdaBoost which, theoretically, can be used to significantly reduce the error of any learning algorithm that con- sistently generates classifiers whose performance is a little better than random guessing. We also introduced the related notion of a "pseudo-loss" which is a method for forcing a learning algorithm of multi-label concepts to concentrate on the labels that are hardest to discriminate. In this paper, we describe experiments we carried out to assess how well AdaBoost with and without pseudo-loss, performs on real learning problems. We performed two sets of experiments. The first set compared boosting to Breiman's "bagging" method when used to aggregate various classifiers (including decision trees and single attribute- value tests). We compared the performance of the two methods on a collection of machine-learning benchmarks. In the second set of experiments, we studied in more detail the performance of boosting using a nearest-neighbor classifier on an OCR problem.