Introducing Subspace Grids to Recognise Patterns in Multidimensinal Data

The work presented in this paper proposes a new approach of using subspace grids for recognizing patterns in multidimensional data. The proposed approach addresses the two problems often associated with this task: i) curse of dimensionality ii) cases with small sample sizes. To handle the curse of dimensionality problem, this paper introduces subspace grids and shows how it can be employed for pattern recognition tasks efficiently. To address the cases with small sample sizes, this paper proposes 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. A recursive procedure is then employed to obtain rules where coarse and fine subspace grids form premises of rules. The system is tested on the bench mark IRIS data set having 150 examples. (50 examples belonging to each class type). The results show that the use of subspaces grids produces good results to recognize patterns in multidimensional data.