LLE Score: A New Filter-Based Unsupervised Feature Selection Method Based on Nonlinear Manifold Embedding and Its Application to Image Recognition

The task of feature selection is to find the most representative features from the original high-dimensional data. Because of the absence of the information of class labels, selecting the appropriate features in unsupervised learning scenarios is much harder than that in supervised scenarios. In this paper, we investigate the potential of locally linear embedding (LLE), which is a popular manifold learning method, in feature selection task. It is straightforward to apply the idea of LLE to the graph-preserving feature selection framework. However, we find that this straightforward application suffers from some problems. For example, it fails when the elements in the feature are all equal; it does not enjoy the property of scaling invariance and cannot capture the change of the graph efficiently. To solve these problems, we propose a new filter-based feature selection method based on LLE in this paper, which is named as LLE score. The proposed criterion measures the difference between the local structure of each feature and that of the original data. Our experiments of classification task on two face image data sets, an object image data set, and a handwriting digits data set show that LLE score outperforms state-of-the-art methods, including data variance, Laplacian score, and sparsity score.