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.