Semi-supervised Learning with Regularized Laplacian

International audienceWe study a semi-supervised learning method based on the similarity graph and Regularized Laplacian. We give convenient optimization formulation of the Regularized Laplacian method and establish its various properties. In particular, we show that the kernel of the method can be interpreted in terms of discrete and continuous time random walks and possesses several important properties of proximity measures. Both optimization and linear algebra methods can be used for efficient computation of the classification functions. We demonstrate on numerical examples that the Regularized Laplacian method is robust with respect to the choice of the regularization parameter and outperforms the Laplacian-based heat kernel methods

The Perception of Graph Properties In Graph Layouts

abstract: When looking at drawings of graphs, questions about graph density, community structures, local clustering and other graph properties may be of critical importance for analysis. While graph layout algorithms have focused on minimizing edge crossing, symmetry, and other such layout properties, there is not much known about how these algorithms relate to a user’s ability to perceive graph properties for a given graph layout. This study applies previously established methodologies for perceptual analysis to identify which graph drawing layout will help the user best perceive a particular graph property. A large scale (n = 588) crowdsourced experiment is conducted to investigate whether the perception of two graph properties (graph density and average local clustering coefficient) can be modeled using Weber’s law. Three graph layout algorithms from three representative classes (Force Directed - FD, Circular, and Multi-Dimensional Scaling - MDS) are studied, and the results of this experiment establish the precision of judgment for these graph layouts and properties. The findings demonstrate that the perception of graph density can be modeled with Weber’s law. Furthermore, the perception of the average clustering coefficient can be modeled as an inverse of Weber’s law, and the MDS layout showed a significantly different precision of judgment than the FD layout.Dissertation/ThesisMasters Thesis Computer Science 201