Self-Organizing MultiLayer Perceptron

In this paper, we propose an extension of a self-organizing map called self-organizing multilayer perceptron (SOMLP) whose purpose is to achieve quantization of spaces of functions. Based on the use of multilayer perceptron networks, SOMLP comprises the unsupervised as well as supervised learning algorithms. We demonstrate that it is possible to use the commonly used vector quantization algorithms (LVQ algorithms) to build new algorithms called functional quantization algorithms (LFQ algorithms). The SOMLP can be used to model nonlinear and/or nonstationary complex dynamic processes, such as speech signals. While most of the functional data analysis (FDA) research is based on B-spline or similar univariate functions, the SOMLP algorithm allows quantization of function with high dimensional input space. As a consequence, classical FDA methods can be outperformed by increasing the dimensionality of the input space of the functions under analysis. Experiments on artificial and real world examples are presented which illustrate the potential of this approach.