A Multiscale Scheme for Approximating the Quantron's Discriminating Function

• Published in: IEEE transaction on neural networks and learning systems 2009-08, Vol.20 (8), p.1254-1266
• Main Authors: Connolly, J.-F., Labib, R.
• Format: Article
• Language: English
• Subjects: Action Potentials; Algorithms; Applied sciences; Approximation; Artificial Intelligence; Artificial neural networks; Biological neural networks; Classification; Computer science; control theory; systems; Convergence; Exact sciences and technology; Global optimization; Humans; Industrial engineering; inverted parabola; Machine learning; Mathematical analysis; Membrane Potentials; Multiresolution analysis; multiresolution analysis (MRA); multiscale approximation; Neural networks; Neural Networks (Computer); Neurons - physiology; Pattern Recognition, Automated - methods; Periodicity; Quantron; Signal analysis; Stems; Support vector machine classification; Support vector machines; Synapses - physiology; Synaptic Transmission - physiology; Time Factors; Wave functions; Wavelet analysis
• ISSN: 1045-9227; 2162-237X; 1941-0093; 2162-2388
• DOI: 10.1109/TNN.2009.2022979

Finding an accurate approximation of a discriminating function in order to evaluate its extrema is a common problem in the field of machine learning. A new type of neural network, the Quantron, generates a complicated wave function whose global maximum value is crucial for classifying patterns. To obtain an analytical approximation of this maximum, we present a multiscale scheme based on compactly supported inverted parabolas. Motivated by the Quantron's architecture as well as Laplace's method, this scheme stems from the multiresolution analysis (MRA) developed in the theory of wavelets. This approximation method will be performed, first, one scale at a time and, second, as a global approach. Convergence will be proved and results analyzed.