PCA-Based Model Selection and Fitting for Linear Manifolds

Abstract

We construct an artificial neural network which achieves model selection and fitting concurrently if models are linear manifolds and data points distribute in the union of finite number of linear manifolds. For the achievement of this procedure, we are required to develop a method which determines the dimensions and parameters of each model and estimates the number of models in a data set. Therefore, we separate the method into two steps, in the first step, the dimension and the parameters of a model are determined applying the PCA for local data, and in the second step, the region is expanded using an equivalence relation based on the parameters. Our algorithm is also considered to be a generalization of the Hough transform which detects lines on a plane, since a line is a linear manifold on a plane.