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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… (More)

Principal curves have been deened as \self consistent" smooth curves which pass through the \middle" of a d-dimensional probability distribution or data cloud. They give a summary of the data and also serve as an eecient feature extraction tool. We take a new approach by deening principal curves as continuous curves of a given length which minimize the… (More)

We propose an algorithm to find piecewise linear skeletons of handwritten characters by using principal curves. The development of the method was inspired by the apparent similarity between the definition of principal curves (smooth curves which pass through the " middle " of a cloud of points) and the medial axis (smooth curves that go equidistantly from… (More)

—We consider the extension of the Whittaker–Shannon (WS) reconstruction formula to the case of signals sampled in the presence of noise and which are not necessarily band limited. Observing that in this situation the classical sampling expansion yields inconsistent reconstruction, we introduce a class of signal recovery methods with a smooth correction of… (More)

- Luc Devroye, Laszlo Gyorfi, Adam Krzyzak, Gabor Lugosi
- 1994

Two results are presented concerning the consistency of the k-nearest neighbor regression estimate. We show that all modes of convergence in L 1 (in probability, almost sure, complete) are equivalent if the regression variable is bounded. Under the additional condition k/logn-> oo we also obtain the strong universal consistency of the estimate .