Locally Linear Embedding Based on t-Distribution Grasshopper Optimization Algorithm

Abstract

Locally linear embedding (LLE) is a classical nonlinear dimensionality reduction algorithm for manifold learning in the field of machine learning (ML). The main idea of LLE is to pursue the linear isomorphism in the algebraic relationship between high-dimensional spatial data and low-dimensional spatial data after dimensionality reduction, and obtain the projection points of low-dimensional space by solving two optimization sub-problems. The optimization part of LLE is usually solved by gradient descent (GD) method. however, GD method has many disadvantages, such as easy to fall into the trap of local minimum, the closer to the optimal solution, the easier it is to show sawtooth effect. In order to overcome the above difficulties, in this paper, an LLE based on t-distribution grasshopper optimization algorithm has been proposed, it uses t-distribution grasshopper optimization algorithm which is a gradient independent swarm intelligence algorithm to replace GD for parameter optimization. Via numerical experiment, the effectiveness of the proposed algorithm has been proved.