The Exact VC Dimension of the WiSARD n-Tuple Classifier

Autor:	Priscila M. V. Lima, Felipe M. G. França, Hugo C. C. Carneiro, Carlos E. Pedreira
Rok vydání:	2019
Předmět:	Artificial neural network business.industry Computer science Cognitive Neuroscience Single step Pattern recognition 02 engineering and technology 03 medical and health sciences VC dimension 0302 clinical medicine Arts and Humanities (miscellaneous) 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Artificial intelligence Tuple business Classifier (UML) 030217 neurology & neurosurgery
Zdroj:	Neural Computation. 31:176-207
ISSN:	1530-888X 0899-7667
DOI:	10.1162/neco_a_01149
Popis:	The Wilkie, Stonham, and Aleksander recognition device (WiSARD) [Formula: see text]-tuple classifier is a multiclass weightless neural network capable of learning a given pattern in a single step. Its architecture is determined by the number of classes it should discriminate. A target class is represented by a structure called a discriminator, which is composed of [Formula: see text] RAM nodes, each of them addressed by an [Formula: see text]-tuple. Previous studies were carried out in order to mitigate an important problem of the WiSARD [Formula: see text]-tuple classifier: having its RAM nodes saturated when trained by a large data set. Finding the VC dimension of the WiSARD [Formula: see text]-tuple classifier was one of those studies. Although no exact value was found, tight bounds were discovered. Later, the bleaching technique was proposed as a means to avoid saturation. Recent empirical results with the bleaching extension showed that the WiSARD [Formula: see text]-tuple classifier can achieve high accuracies with low variance in a great range of tasks. Theoretical studies had not been conducted with that extension previously. This work presents the exact VC dimension of the basic two-class WiSARD [Formula: see text]-tuple classifier, which is linearly proportional to the number of RAM nodes belonging to a discriminator, and exponentially to their addressing tuple length, precisely [Formula: see text]. The exact VC dimension of the bleaching extension to the WiSARD [Formula: see text]-tuple classifier, whose value is the same as that of the basic model, is also produced. Such a result confirms that the bleaching technique is indeed an enhancement to the basic WiSARD [Formula: see text]-tuple classifier as it does no harm to the generalization capability of the original paradigm.
Databáze:	OpenAIRE
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