Bi-Level Spectral Feature Selection.

Unsupervised feature selection (UFS) aims to learn an indicator matrix relying on some characteristics of the high-dimensional data to identify the features to be selected. However, traditional unsupervised methods perform only at the feature level, i.e., they directly select useful features by feature ranking. Such methods do not pay any attention to the interaction information with other tasks such as classification, which severely degrades their feature selection performance. In this article, we propose an UFS method which also takes into account the classification level, and selects features that perform well both in clustering and classification. To achieve this, we design a bi-level spectral feature selection (BLSFS) method, which combines classification level and feature level. More concretely, at the classification level, we first apply the spectral clustering to generate pseudolabels, and then train a linear classifier to obtain the optimal regression matrix. At the feature level, we select useful features via maintaining the intrinsic structure of data in the embedding space with the learned regression matrix from the classification level, which in turn guides classifier training. We utilize a balancing parameter to seamlessly bridge the classification and feature levels together to construct a unified framework. A series of experiments on 12 benchmark datasets are carried out to demonstrate the superiority of BLSFS in both clustering and classification performance.

Symmetric positive definite manifold learning and its application in fault diagnosis.

Locally linear embedding (LLE) is an effective tool to extract the significant features from a dataset. However, most of the relevant existing algorithms assume that the original dataset resides on a Euclidean space, unfortunately nearly all the original data space is non-Euclidean. In addition, the original LLE does not use the discriminant information of the dataset, which will degrade its performance in feature extraction. To address these problems raised in the conventional LLE, we first employ the original dataset to construct a symmetric positive definite manifold, and then estimate the tangent space of this manifold. Furthermore, the local and global discriminant information are integrated into the LLE, and the improved LLE is operated in the tangent space to extract the important features. We introduce Iris dataset to analyze the capability of the proposed method to extract features. Finally, several experiments are performed on five machinery datasets, and experimental results indicate that our proposed method can extract the excellent low-dimensional representations of the original dataset. Compared with the state-of-the-art methods, the proposed algorithm shows a strong capability for fault diagnosis.