By I.M. Gel'Fand, G.E. Shilov
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Extra resources for Generalized Functions
One of them was used for choosing the initial prototypes and training the classiﬁers, and the other one was used in their validation (or testing). Later, the role of these sets were interchanged. Experimental Parameters: As in all algorithms, choosing the parameters12 of the PRS and the conventional prototype selection schemes play an important role in determining the quality of the solution. 2 respectively) and the PRS-based schemes such as the CNN, PNN, and HYB, are summarized as: 1. Parameters for the RAND, RAND C, and KCentres : In RAND, a total of 10 % of the samples were randomly selected from the original training data set.
Fig. 9. A comparison of the decision regions used for node generation in an SOTM versus an SOHVM. The latter attempts to new insert nodes (open circles) at the extremities of the data described by a winning node (closed circle) – wk* is the winning center, and its eigenvalue/vector pair (k*,qk*) describe local variance properties. X’s are invalid sites for node insertion. Each neuron in the network consists of a dual memory element to track information regarding a discovered prototype. In addition to center position (as in most other self-organizing structures), Hebbian-based Maximum Eigenfilters (HME)  simultaneously estimate the maximal variance of local data, presenting an 12 L.
Campilho and M. ): ICIAR 2006, LNCS 4141, pp. 15–28, 2006. -W. J. Oommen 1 Introduction The ﬁeld of statistical Pattern Recognition,  has matured since its infancy in the 1950’s, and the aspiration to enlarge the horizons has led to numerous philosophically-new avenues of research. The fundamental questions tackled involve (among others) increasing the accuracy of the classiﬁer system, minimizing the time required for training and testing, reducing the eﬀects of the curse of dimensionality, and reducing the eﬀects of peculiar data distributions.