Uniform Manifold Approximation with Two-phase Optimization
Authors: Hyung-Kwon Ko, Jaemin Jo, Yung-Kyun Noh, Jinwook Seo
Keywords: Dimensionality Reduction, Manifold Learning, Visualization, Topological Data Analysis, UMAP
Abstract: We present a dimensionality reduction algorithm called Uniform Manifold Approximation with Two-phase Optimization (UMATO) which produces less biased global structures in the embedding results and is robust over diverse initialization methods than previous methods such as $t$-SNE and UMAP. We divide the optimization into two phases to alleviate the bias by establishing the global structure early using the representatives of the high-dimensional structures. The phases are 1) global optimization to obtain the overall skeleton of data and 2) local optimization to identify the regional characteristics of local areas. In our experiments with one synthetic and three real-world datasets, UMATO outperformed widely-used baseline algorithms, such as PCA, red, $t$-SNE, UMAP, topological autoencoders and Anchor $t$-SNE, in terms of quality metrics and 2D projection results.