Modeling geometric structure in noisy data

Abstract

We present an approach for modeling noisy data via dimension reduction methods. Geometric structures, hidden in the ambient space defined by the dimension of the observations, are uncovered by the application of efficient clustering algorithms, based on the exploitation of nearest neighbor interactions. A new bi-directional Hebb rule in combination with the LBG algorithm was used to define a connectivity structure among disjoint regions in high-dimensional space. For a lossless representation of noisy data the Whitney Reduction Network was combined with the maximum noise fraction filter to create a more accurate model of the underlying data generator while utilizing the set of unit secants in a sequential algorithm to construct a good quality parameterization of the data. The nonlinear reconstruction of the data was addressed by the feedback of a model validation test on the residuals to form a radial basis function resource allocation architecture.