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.
All-versus-all In all-versus-all classifiers, the algorithm compares each class to all other classes. A binary classifier is built to discriminate between each pair of classes while discarding the rest of the classes. The algorithm thus builds @math binary classifiers. During evaluation the class with the maximum number of votes wins. Allwein al conclude that all-versus-all often has better generalization performance than one-versus-all algorithm @cite_7 . The drawback of this algorithm is that the complexity grows quadratically with the number of classes. Thus it is not scalable in the number of classes.
@cite_7
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The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly imbalanced classification problems. The classifiers constructed by both methods are created as unions of parallel axis rectangles around the positive examples, and thus have the benefit of being interpretable. The first algorithm uses mixed integer programming to optimize a weighted balance between positive and negative class accuracies. Regularization is introduced to improve generalization performance. The second method uses an approximation in order to assist with scalability. Specifically, it follows a approach, where the positive class is characterized first by boxes, and then each box boundary becomes a separate discriminative classifier. This method has the computational advantages that it can be easily parallelized, and considers only the relevant regions of feature space. Abstract This paper introduces a two-stage strategy for multi-class classification problems. The proposed technique is an advancement of tradition binary decomposition method. In the first stage, the classifiers are trained for each class versus the remaining classes. A modified fitness value is used to select good discriminators for the imbalanced data. In the second stage, the classifiers are integrated and treated as a single chromosome that can classify any of the classes from the dataset. A population of such classifier-chromosomes is created from good classifiers (for individual classes) of the first phase. This population is evolved further, with a fitness that combines accuracy and conflicts. The proposed method encourages the classifier combination with good discrimination among all classes and less conflicts. The two-stage learning has been tested on several benchmark datasets and results are found encouraging. 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 the real visual world, the number of categories a classifier needs to discriminate is on the order of hundreds or thousands. For example, the SUN dataset [24] contains 899 scene categories and ImageNet [6] has 15,589 synsets. Designing a multiclass classifier that is both accurate and fast at test time is an extremely important problem in both machine learning and computer vision communities. To achieve a good trade-off between accuracy and speed, we adopt the relaxed hierarchy structure from [15], where a set of binary classifiers are organized in a tree or DAG (directed acyclic graph) structure. At each node, classes are colored into positive and negative groups which are separated by a binary classifier while a subset of confusing classes is ignored. We color the classes and learn the induced binary classifier simultaneously using a unified and principled max-margin optimization. We provide an analysis on generalization error to justify our design. Our method has been tested on both Caltech-256 (object recognition) [9] and the SUN dataset (scene classification) [24], and shows significant improvement over existing methods.