Correntropy based feature selection using binary projection

Most feature selection algorithms based on information-theoretic learning (ITL) adopt ranking process or greedy search as their searching strategies. The former selects features individually so that it ignores feature interaction and dependencies. The latter heavily relies on the search paths, as only one path will be explored with no possible back-track. In addition, both strategies typically lead to heuristic algorithms. To cope with these problems, this article proposes a novel feature selection framework based on correntropy in ITL, namely correntropy based feature selection using binary projection (BPFS). Our framework selects features by projecting the original high-dimensional data to a low-dimensional space through a special binary projection matrix. The formulated objective function aims at maximizing the correntropy between selected features and class labels. And this function can be efficiently optimized via standard mathematical tools. We apply the half-quadratic method to optimize the objective function in an iterative manner, where each iteration reduces to an assignment subproblem which can be highly efficiently solved with some off-the-shelf toolboxes. Comparative experiments on six real-world datasets indicate that our framework is effective and efficient.

► Our searching strategy is better justified theoretically in feature selection.
► Our framework is more theoretically justified with strong convergence guarantee.
► Our objective function can be efficiently solved by existing optimization techniques.