DCMDS-RV: density-concentrated multi-dimensional scaling for relation visualization

Abstract

This paper proposes a novel unsupervised multi-dimensional scaling (MDS) method to visualize high-dimensional data and their relations in a low-dimensional (e.g., 2D) space. Different from traditional MDS approaches where the main purpose is to embed high-dimensional data into a low-dimensional space, this study aims to both embed data into a low-dimensional space and reveal data relations, thus providing better visualization as graph. By taking into account the density relationships inherent in data, this paper proposes a new density-concentrated multi-dimensional scaling algorithm DCMDS-RV to perform visualization of high-dimensional data and their relations. One benefit of the proposed DCMDS-RV algorithm is the ability to embed data more accurately than traditional MDS techniques by using second-order gradient optimization instead of first-order gradient. A key advantage of the presented DCMDS-RV algorithm is the capability to show relations as categorical information. In the resulting embedding, data are compact in clusters. The results demonstrate that the proposed DCMDS-RV algorithm outperforms conventional MDS methods regarding Kruskal stress factor and ACC value. The relations between data as graph are clearly viewed as well.