Locally Linear Embedding Based on Neiderreit Sequence Initialized Ali Baba and The Forty Thieves Algorithm

Manifold learning is a nonlinear dimensionality reduction technique that reveals the essential features and structure of data through dimensionality reduction. This technique has enormous theoretical research and industry application value in fields such as data visualization, denoising, and anomaly detection. Locally linear embedding (LLE) is a classic algorithm in manifold learning, which projects high-dimensional data into a low-dimensional space while maintaining the same algebraic structure. However, the optimization objective function of LLE uses L2 norm to measure linear approximation error, which can easily amplify and reduce the error. Therefore, in this paper, L1 norm is used instead of L2 norm to overcome this deficiency, but it also brings about the problem of non-smoothness in the optimization objective function. To address this issue, in this paper, a derivative-free optimization method called Neiderreit sequence initialize Ali Baba and the forty thieves (NSAFT) algorithm has been proposed, and demonstrates its effectiveness in finding the optimal solution for the objective function of LLE through numerical experiments.