A novel local linear embedding algorithm via local mutual representation for bearing fault diagnosis

The locally linear embedding algorithm (LLE) mainly extracts significant features by mining the local neighborhood structure of the data. However, when the data exhibit strong nonlinearity in high-dimensional space, the single neighborhood structure of the LLE algorithm may not accurately capture the local linear relationships between instances, which degrades the performances of the LLE. Therefore, we propose a multi-structure neighborhood locally linear embedding algorithm via local mutual representation (LMR-LLE). Firstly, in each neighborhood, multiple local neighborhood structures of one instance are mined via local mutual representation to enhance the interconnectivity between the instances. Furthermore, the multiple neighborhood structures are fused in the low-dimensional space to construct a global reconstruction model, and the ultimate significant features are acquired by determining the model's optimal solution. Finally, the extracted features are fed into a classifier for bearing fault diagnosis. Extensive experiments on two rolling bearing datasets illustrate that the LMR-LLE based diagnosis method has better performance accuracy than conventional LLE-based algorithms.