On the optimality of sequential forward feature selection using class separability measure
This paper studies sequential forward feature selection that uses the scatter-matrix-based class separability measure. We find that by adding a scale factor to each iteration of the conventional sequential selection, a sequential selection that guarantees the global optimum can be attained. We give a thorough theoretical proof of its optimality via a novel geometric interpretation, and this leads to a unified framework including the optimal sequential selection, the conventional sequential selection and the best-individual-N selection. In addition, we show that with our formulation, feature selection can be treated as a linear fractional maximization problem, and it can be efficiently solved by algorithms well developed in the literature. This gives a non-sequential globally optimal feature selection algorithm. Both theoretical and experimental study demonstrate their efficiency.
Wang, L., Shen, C. & Hartley, R. (2011). On the optimality of sequential forward feature selection using class separability measure. Proceedings of 2011 International Conference on Digital Image Computing: Techniques and Applications (DICTA) (pp. 203-208). USA: IEEE.