Locally Linear Embedding Based on Neiderreit Sequence Randomized Rat Swarm Optimizer

In the era of big data, the scale and complexity of data continue to expand, and traditional data dimensionality reduction methods are difficult to extract low-dimensional feature representations from massive amounts of data. Thus, manifold learning, which represents nonlinear dimensionality reduction methods in the field of artificial intelligence (AI), has become a key research direction, especially playing an important role in achieving dimensionality reduction and mapping of linear structured data from high-dimensional space to low-dimensional space, reducing data noise, and improving the representation ability of low-dimensional data. However, locally linear embedding (LLE), as a typical manifold learning algorithm, has natural a flaw in its construction of the objective loss function, as the L2 norm it used is prone to amplifying and reducing errors, making it too sensitive to data. To overcome such problems, in this paper, an LLE algorithm with L1 instead of L2 norm is proposed, and, as it has made LLE loss function a non-smooth one and cannot be solved by traditional gradient dependent optimization method, a derivative-free optimization method, which is called Neiderreit sequence randomized rat swarm optimizer (NSRSO) has also been proposed. And LLE with L1 norm optimized by NSRSO has been experimentally proved to be highly effective in extracting low-dimensional representation for data.