t-SNE Based on Halton Sequence Initialized Mountaineering Team-Based Optimization Algorithm

t-distributed stochastic neighbor embedding (t-SNE) is a classic manifold learning algorithm in the field of machine learning (ML), and it is a non-linear data dimensionality reduction method. Manifold learning generally constructs homeomorphic mappings from high-dimensional spaces to low dimensional spaces based on different mathematical ideas. The idea of t-SNE is to pursue the probability isomorphism of data distribution before and after projection from high-dimensional space to low dimensional space. Thus, its essence can be seen as solving the minimization problem of Kullback-Leibler (KL) divergence that measures the similarity of probability distribution before and after projection. t-SNE algorithm usually uses gradient dependent line search optimization methods to solve, but gradient dependent optimization methods are often prone to fall into the trap of local optimal solutions and unable to find the global one. To address this issue, in this paper, a non-derivative optimization method, which is called Halton sequence initiated mountaineering team-based optimization (HSMTBO) has been proposed to realize the parameter optimization of t-SNE, and its feasibility and advantages can be verified through numerical experiments.