A fast algorithm for local feature selection in data classification

Typical feature selection methods select a global feature subset that is applied over all regions of the sample space. In localized feature selection (LFS), each region of the sample space is associated with its own optimized feature subset. This allows the feature subset to adapt to local variations in the sample space. Feature subsets are selected such that within a localized region, within‐class distances are minimized and between‐class distances are maximized. LFS outperforms global feature selection methods. LFS is solved using a randomized rounding approach when weights of regions are fixed. Randomized rounding is a too time‐consuming algorithm. In this paper, we show that LFS has a closed‐form solution when weights of regions are fixed. Using this closed‐form solution can decrease the runtime of solving LFS substantially. Experimental results on real datasets confirm that the classification error rate of our proposed method and the randomized rounding‐based method are the same; the runtime of our proposed method is much better than that of the randomized rounding‐based method; and the classification error rate of our proposed method and the randomized rounding‐based method outperforms the state‐of‐the‐art feature selection methods.