Unsupervised feature selection with least-squares quadratic mutual information

We propose the feature selection method based on the dependency between features in an unsupervised manner. The underlying assumption is that the most important feature should provide high dependency between itself and the rest of the features. Therefore, the top m features with maximum dependency scores should be selected, but the redundant features should be ignored. To deal with this problem, the objective function that is applied to evaluate the dependency between features plays a crucial role. However, previous methods mainly used the mutual information (MI), where the MI estimator based on the k-nearest neighbor graph, resulting in its estimation dependent on the selection of parameter, k, without a systematic way to select it. This implies that the MI estimator tends to be less reliable. Here, we introduce the leastsquares quadratic mutual information (LSQMI) that is more sensible because its tuning parameters can be selected by cross-validation. We show through the experiments that the use of LSQMI performed better than that of MI. In addition, we compared the proposed method to the three counterpart methods using six UCI benchmark datasets. The results demonstrated that the proposed method is useful for selecting the informative features as well as discarding the redundant ones.