Locally Linear Embedding Based on Sobol Sequence Initialized Black Widow Optimization Algorithm

Abstract

Locally linear embedding (LLE) algorithm is a nonlinear dimensionality reduction algorithm for manifold learning in the field of artificial intelligence (AI), it can learn locally linear low-dimensional manifolds in high-dimensional space, which means that its core idea is to seek a continuous homeomorphism from high-dimensional space to low-dimensional space, and mainly achieves the purpose of nonlinear dimensionality reduction by keeping the linear algebraic structure of high-dimensional space unchanged in low-dimensional space. The loss function of LLE algorithm is generally solved by gradient descent (GD) method or stochastic gradient descent (SGD) method, but the gradient dependent optimization method is often easy to fall into the trap of local minimum, and as closer it is to the best solution, there is often the sawtooth effect of violent oscillation. In order to overcome the above shortcomings, a Sobol sequence initialized black widow optimization algorithm (SBWOA) is proposed to improve the global optimality, randomness and robustness of the optimization algorithm, and the effectiveness of the algorithm is verified by numerical experiments.