Simultaneously learning affinity matrix and data representations for machine fault diagnosis.

Recently, preserving geometry information of data while learning representations have attracted increasing attention in intelligent machine fault diagnosis. Existing geometry preserving methods require to predefine the similarities between data points in the original data space. The predefined affinity matrix, which is also known as the similarity matrix, is then used to preserve geometry information during the process of representations learning. Hence, the data representations are learned under the assumption of a fixed and known prior knowledge, i.e., similarities between data points. However, the assumed prior knowledge is difficult to precisely determine the real relationships between data points, especially in high dimensional space. Also, using two separated steps to learn affinity matrix and data representations may not be optimal and universal for data classification. In this paper, based on the extreme learning machine autoencoder (ELM-AE), we propose to learn the data representations and the affinity matrix simultaneously. The affinity matrix is treated as a variable and unified in the objective function of ELM-AE. Instead of predefining and fixing the affinity matrix, the proposed method adjusts the similarities by taking into account its capability of capturing the geometry information in both original data space and non-linearly mapped representation space. Meanwhile, the geometry information of original data can be preserved in the embedded representations with the help of the affinity matrix. Experimental results on several benchmark datasets demonstrate the effectiveness of the proposed method, and the empirical study also shows it is an efficient tool on machine fault diagnosis.