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.

中文翻译：

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同时学习亲和矩阵和数据表示，以进行机器故障诊断。

近来，在学习表示的同时保留数据的几何信息已经在智能机器故障诊断中引起了越来越多的关注。现有的几何保留方法要求预先定义原始数据空间中数据点之间的相似性。然后，在表示学习的过程中，将预定义的亲和力矩阵（也称为相似度矩阵）用于保存几何信息。因此，在固定和已知的先验知识（即数据点之间的相似性）的假设下学习数据表示。但是，假定的先验知识很难精确地确定数据点之间的实际关系，尤其是在高维空间中。还，使用两个分离的步骤来学习亲和度矩阵和数据表示对于数据分类而言可能不是最佳且通用的方法。本文基于极限学习机自动编码器（ELM-AE），建议同时学习数据表示和亲和矩阵。亲和矩阵被视为变量，并统一在ELM-AE的目标函数中。代替预先定义和固定亲和力矩阵，所提出的方法通过考虑其在原始数据空间和非线性映射的表示空间中捕获几何信息的能力来调整相似性。同时，借助于亲和矩阵可以将原始数据的几何信息保留在嵌入的表示中。