Method of combining the classification powers of several classifiers is regarded as a general problem in various application areas of pattern recognition, and a systematic investigation has been made. Possible solutions to the problem can be divided into three categories according to the levels of information available from the various classifiers. Four approaches are proposed based on different methodologies for solving this problem. One is suitable for combining individual classifiers such as Bayesian, k-NN and various distance classifiers. The other three could be used for combining any kind of individual classifiers. On applying these methods to combine several classifiers for recognizing totally unconstrained handwritten numerals, the experimental results show that the performance of individual classifiers could be improved significantly. For example, on the U.S. zipcode database, the result of 98.9% recognition with 0.90% substitution and 0.2% rejection can be obtained, as well as a high reliability with 95% recognition, 0% substitution and 5% rejection. These results compared favorably to other research p u p s in Europe, Asia, and North America.

AbstractÐPrincipal curves have been defined as ªself-consistentº smooth curves which pass through the ªmiddleº of a d-dimensional probability distribution or data cloud. They give a summary of the data and also serve as an efficient feature extraction tool. We take a new approach by defining principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution. The new definition makes it possible to theoretically analyze principal curve learning from training data and it also leads to a new practical construction. Our theoretical learning scheme chooses a curve from a class of polygonal lines with k segments and with a given total length to minimize the average squared distance over n training points drawn independently. Convergence properties of this learning scheme are analyzed and a practical version of this theoretical algorithm is implemented. In each iteration of the algorithm, a new vertex is added to the polygonal line and the positions of the vertices are updated so that they minimize a penalized squared distance criterion. Simulation results demonstrate that the new algorithm compares favorably with previous methods, both in terms of performance and computational complexity, and is more robust to varying data models.

It is shown that frequency sensitive competitive learning (FSCL), one version of the recently improved competitive learning (CL) algorithms, significantly deteriorates in performance when the number of units is inappropriately selected. An algorithm called rival penalized competitive learning (RPCL) is proposed. In this algorithm, not only is the winner unit modified to adapt to the input for each input, but its rival (the 2nd winner) is delearned by a smaller learning rate. RPCL can be regarded as an unsupervised extension of Kohonen's supervised LVQ2. RPCL has the ability to automatically allocate an appropriate number of units for an input data set. The experimental results show that RPCL outperforms FSCL when used for unsupervised classification, for training a radial basis function (RBF) network, and for curve detection in digital images.

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