Conference Paper

Discriminant Parallel Perceptrons.

Universidad Autónoma de Madrid, Madrid, Madrid, Spain
DOI: 10.1007/11550907_3 Conference: Artificial Neural Networks: Formal Models and Their Applications - ICANN 2005, 15th International Conference, Warsaw, Poland, September 11-15, 2005, Proceedings, Part II
Source: DBLP


Parallel perceptrons (PPs), a novel approach to committee machine training requiring minimal communication between outputs
and hidden units, allows the construction of efficient and stable nonlinear classifiers. In this work we shall explore how
to improve their performance allowing their output weights to have real values, computed by applying Fisher’s linear discriminant
analysis to the committee machine’s perceptron outputs. We shall see that the final performance of the resulting classifiers
is comparable to that of the more complex and costlier to train multilayer perceptrons.

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Available from: José R. Dorronsoro
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    • "Because of this, we have studied their applicability to imbalanced classification problems, where we try to remove possibly label–noisy patterns, either directly [15] or through a boosting procedure [13] [16]. Moreover, while the output weights of standard PPs are fixed to 1 (i.e., they simply add the outputs of their individual pcps), in [18] it is shown how to improve their performance allowing their output weights to have real values that are computed by applying Fisher's linear discriminant analysis to them. This improves the final performance of the resulting classifiers over that of standard PPs, making it comparable to that of the more complex and costlier to train multilayer perceptrons. "
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    ABSTRACT: The Parallel Perceptron (PP) is a simple neural network which has been shown to be a universal approximator, and it can be trained using the Parallel Delta (P-Delta) rule. This rule tries to maximize the distance between the perceptron activations and their decision hyperplanes in order to increase its generalization ability, following the principles of the Statistical Learning Theory. In this paper we propose a closed-form analytical expression to calculate, without iterations, the PP weights for classification tasks. The calculated weights globally optimize a cost function which takes simultaneously into account the training error and the perceptron margin, similarly to the P-Delta rule. Our approach, called Direct Parallel Perceptron (DPP) has a linear computational complexity in the number of inputs, being very interesting for high-dimensional problems. DPP is competitive with SVM and other approaches (included P-Delta) for two-class classification problems but, as opposed to most of them, the tunable parameters of DPP do not influence the results very much. Besides, the absence of an iterative training stage gives to DPP the ability of on-line learning.
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