Kumap: Kernel Uniform Manifold Approximation and Projection for Out-of-sample Extensions Problem

Abstract

Uniform Manifold Approximation and Projection (UMAP) is a popular dimensionality reduction and visualization algorithm recently proposed and widely used in several fields. However, UMAP encounters difficulties in mapping new samples into low-dimensional embeddings with what has been learnt from the learning process, which often referred to as the out-of-sample problem. In this paper, a kernel UMAP (KUMAP) method is proposed to address this problem, which is a kernel-based expansion technique. It uses the Laplacian kernel function to map the original samples to the low-dimensional space. In addition, to make full use of the label information in the sample data, a supervised kernel UMAP (SKUMAP) is also proposed. The KUMAP and SKUMAP methods are evaluated on different scale datasets in terms of the preservation of structure in small neighborhood data, silhouette coefficients, and classification accuracy. Compared with UMAP and other representative method, the KUMAP and SKUMAP methods have better embedding quality, higher classification accuracy, and better visualization.