t-SNE Based on Halton Sequence Initialized Butterfly Optimization Algorithm

t-distributed stochastic neighbor embedding (t-SNE), as a type of dimensionality reduction algorithm, is usually used to visualize and explore high-dimensional data. By comparing with other dimensionality reduction algorithms, t-SNE has the best effect for data visualization. If it is applied to n-dimensional data, intelligent mapping can be successfully done from n-dimensional data to 3-dimensional data, or even 2-dimensional data, and the probability distribution of the original data can be properly kept even after the dimensionality reduction process. t-SNE is not a linear dimensionality reduction technique, and it is good at processing nonlinear structural data, thus, it is easy for t-SNE algorithm to obtain complex manifold structures from high-dimensional data. Usually, t-SNE does not have a unique optimal solution, and the number of iterations and the convergence of its objective function are the main factors which can affect its visualization effect. Generally, gradient descent (GD) method is used to solve the problem of minimum Kullback-Leiber (KL) divergence of the objective function. However, due to the disadvantage of GD method that can easily fall into local optimal value, in this paper, Halton sequence initialized butterfly optimization algorithm (HSBOA) has been combined with traditional t-SNE algorithm so as to improve the optimization accuracy and convergence speed, and to effectively help t-SNE jump out of the local optimal value trap during the optimization process.