Abstract: Locally linear embedding (LLE) can be used to approximate the global non-linearity via local linearity, and it has the advantages of preserving the data structure after dimension reduction, and short time cost for calculation. However, it is sensitive to the number of nearest neighbors, which affects the performance on dimension reduction. Therefore, a variable K-nearest neighbor local linear embedding algorithm is proposed based on the value of residual error before and after dimension reduction, which can be regarded as a measure of data structure preservation. For a given maximum value of the nearest neighbor number, the optimal number of nearest neighbors can be selected according to the smaller residual error, which making the number of nearest neighbors of each sample adjustable. Simulation analysis of the mixing national institute of standards and technology(MNIST) data sets verified the effectiveness and accuracy of the proposed approach, and the computational complexity is decreased. Experiment on bearing vibration signal analysis also demonstrates that the method can provide a better representation after dimension reduction and improve the classification.

Key words: Bearing, Locally linear embedding (LLE), Pattern recognition, Variable nearest neighbor, Early fault diagnosis, Pulse coupled neural network, Time-time domain transform, Rolling bearing