Keywords: Feature Selection, Canonical Elements, Object Recognition, and Reconstruction Abstract: The problem of representing a large dataset consisiting of complex patterns with a smaller more compact form has been tackled through synthesis of new data points to represent clusters of the original data points (feature transformation). In contrast, the focus of this research is on the development of a generic methods for selecting canonical subsets of data-sets that are highly representative of the original complex patterns. The development of the canonical subset method was motivated by the fact that in many cases feature transformation may not be practical, relevant, or even possible. Our objective is to expose the underlying structure of the data and have the global topology drive the subset-selection process. The contributions of the work are formulation of the subset selection problem as an optimization problem, an analysis of the complexity of the problem, the development of approximation algorithms to compute canonical subsets, and a demonstration of the utility of the algorithms in several problem domains.