TAKES: a fast method to select features in the kernel space

Feature selection is an effective tool to deal with the "curse of dimensionality". To cope with the non-separable problem, feature selection in the kernel space has been investigated. However, previous study cannot adequately estimate the intrinsic dimensionality of the kernel space. Thus, it is difficult to accurately preserve the sketch of the kernel space using the learned basis, and the feature selection performance is affected. Moreover, the computing load of the algorithm reaches at least cubic with the number of training data. In this paper, we propose a fast framework to conduct feature selection in the kernel space. By designing a fast kernel subspace learning method, we automatically learn the intrinsic dimensionality and construct an orthogonal basis set of kernel space. The learned basis can accurately preserve the sketch of kernel space. Then backed by the constructed basis, we directly select features in kernel space. The whole proposed framework has a quadratic complexity with the number of training data, which is faster than existing kernel methods for feature selection. We evaluate our work under several typical datasets and find it not only preserves the sketch of the kernel space more accurately but also achieves better classification performance compared with many state-of-the-art methods.