Multi-Scale Subspace Grids Based Approach for Recognising Patterns in Applications Involving Multidimensional Data

The work presented in this paper employs multiscale subspace grids for pattern recognition applications. The proposed approach addresses the curse of dimensionality problem often associated with this task. The paper uses a multi-scale approach where coarse scale, being stable and generic in nature, suits well for small sample sizes, and fine scales, being more specialized in nature, enhance classification accuracy. The paper first describes projection of multidimensional data to a number of lower dimensional subspaces. Principal component analysis (PCA) and multiple discriminant analysis (MDA) algorithms are used to define lower dimensional subspaces. The range of value associated with each vector of a subspace is divided into a number of equal parts to define coarse subspace grids. Coarse subspace grids are further divided equally into fine subspace grids. The approach is tested on two applications. In first application, a recursive procedure is employed to obtain rules from multiscale subspace grids to recognize patterns. In second application, a neural network algorithm is used to recognize patterns using multi-scale subspace grids. The results show that the use of subspaces grids produces good results to recognize patterns in multidimensional data. Keywords—subspace grids; machine learning; pattern recognition; principle component analysis; multiple discriminant analysis; multi-scale approach.