Graph regularization multidimensional projection

This paper introduces a novel multidimensional projection method of datasets. Our method called Graph Regularization Multidimensional Projection (GRMP) is based on a technique from the graph signal processing theory, the graph regularization. Initially, a similarity graph is built on the high-dimensional space where the dataset lies. A two-dimensional distribution of points is then created in the visual space using a phyllotactic distribution. The similarity graph is copied properly over the phyllotactic distribution and the graph regularization is applied to their coordinates, which are interpreted as graph signals. The graph regularization reorganizes the phyllotactic distribution by bringing together points that represent similar data in the high-dimensional space. We employ synthetic and real datasets to demonstrate the effectiveness of our method. Furthermore, since the solution of the graph regularization can still be approximated using a fast approximation mechanism based on the Chebyshev polynomials, our method is computationally efficient even for large graphs.

Automated summary

This paper presents a novel multidimensional projection method called Graph Regularization Multidimensional Projection (GRMP), which utilizes the graph regularization technique from the graph signal processing theory. The method constructs a similarity graph in the high-dimensional space and creates a two-dimensional distribution using a phyllotactic distribution in the visual space. The graph regularization reorganizes the distribution by bringing together similar data points. The effectiveness of the method is demonstrated using synthetic and real datasets, and its computational efficiency is highlighted by its fast approximation mechanism based on Chebyshev polynomials.