Solving Multiclass Learning Problems via Error-Correcting Output Codes

Multiclass learning problems involve nding a de nition for an unknown function f(x) whose range is a discrete set containing k > 2 values (i.e., k \classes"). The de nition is acquired by studying collections of training examples of the form hxi; f(xi)i. Existing approaches to multiclass learning problems include direct application of multiclass algorithms such as the decision-tree algorithms C4.5 and CART, application of binary concept learning algorithms to learn individual binary functions for each of the k classes, and application of binary concept learning algorithms with distributed output representations. This paper compares these three approaches to a new technique in which error-correcting codes are employed as a distributed output representation. We show that these output representations improve the generalization performance of both C4.5 and backpropagation on a wide range of multiclass learning tasks. We also demonstrate that this approach is robust with respect to changes in the size of the training sample, the assignment of distributed representations to particular classes, and the application of over tting avoidance techniques such as decision-tree pruning. Finally, we show that|like the other methods|the error-correcting code technique can provide reliable class probability estimates. Taken together, these results demonstrate that error-correcting output codes provide a general-purpose method for improving the performance of inductive learning programs on multiclass problems.