ITR-Score algorithm: An efficient Trace ratio criterion based algorithm for supervised dimensionality reduction

Dimensionality reduction has been a fundamental tool when dealing with high-dimensional dataset. And trace ration optimization has been widely used in dimensionality reduction because Trace ratio can directly reflect the similarity (Euclidean distance) of data points. Conventionally, there is no close-form solution to the original trace ratio problem. Prior works have indicated that trace ratio problem can be solved by an iterative way. In this paper, we propose an efficient algorithm to find the optimal solutions. The proposed algorithm can be easily extended to its corresponding kernel version for handling the nonlinear problems. Finally, we evaluate our proposed algorithm based on extensive simulations of real world datasets. The results show our proposed method is able to deliver marked improvements over other supervised and unsupervised algorithms.