Locally Linear Embedding Based on Scrambled Halton Sequence Initialized Frilled Lizard Optimization

In the era of big data, the scale and complexity of data are ever increasing, traditional data dimensionality reduction methods can no longer meet the requirements of data users. In this context, manifold learning has now become an important research direction, which mainly achieves dimensionality reduction and mapping of nonlinear structural data in high-dimensional space to low-dimensional space, reduces data noise, and improves low-dimensional data representation ability. Locally linear embedding (LLE) is an important algorithm in manifold learning that projects data from high-dimensional space onto low-dimensional space while maintaining the linear relationship between data. However, the optimization objective function of LLE uses L2 norm measurement to approximate the error, which can easily amplify or reduce the error and cause oscillation in the error measurement. Therefore, in this paper, L1 norm instead of L2 norm is used to overcome this drawback, but introduces a new problem of the objective function becoming a non-smooth function. To solve this problem, in this paper, a derivative-free optimization method, which is also a swarm intelligence method called scrambled Halton sequence initialized frilled lizard optimization has been proposed, and via numerical experiment, its reliability and effectiveness has been verified.