An Experimental Investigation of Graph Kernels on a Collaborative Recommendation Task

Abstract

a b s t r a c tThis paper presents a survey as well as an empirical comparison and evaluation of seven kernels on graphs and two related similarity matrices, that we globally refer to as ''kernels on graphs'' for simplicity. They are the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regularized Laplacian kernel, the commute-time (or resistance-distance) kernel, the randomwalk-with-restart similarity matrix, and finally, a kernel first introduced in this paper (the regularized commute-time kernel) and two kernels defined in some of our previous work and further investigated in this paper (the Markov diffusion kernel and the relative-entropy diffusion matrix). The kernel-ongraphs approach is simple and intuitive. It is illustrated by applying the nine kernels to a collaborativerecommendation task, viewed as a link prediction problem, and to a semisupervised classification task, both on several databases. The methods compute proximity measures between nodes that help study the structure of the graph. Our comparisons suggest that the regularized commute-time and the Markov diffusion kernels perform best on the investigated tasks, closely followed by the regularized Laplacian kernel.

Link prediction in complex networks: A survey

“…This index has been applied to quantify the similarity between nodes on collaborative recommendation task [71]. The results indicate that a simple nearestneighbors rule based on similarity measured by MFI performs best.…”

A Comprehensive Survey of Neighborhood-Based Recommendation Methods

“…Among these are the average first-passage time and the average commute time [19,20]. The average first-passage time m( j|i) [56] is the average number of steps needed by a random walker to reach a node j for the first time, when starting from a node i = j.…”

Within-Network Classification Using Local Structure Similarity

“…However, these kernels tend to evaluate the affinity (proximity) between two nodes of a network indirectly based on the number and length of the paths between these nodes [9], thus subscribing to the homophily assumption. Other kernels that compare the structure of two graphs have also been proposed [10,16].…”

“…Kernels on graphs Also related to our approach are classification methods based on graph kernels, including exponential and diffusion kernels [18], kernels using regularization operators [30], and kernels based on random walks [5,9,11,35]. However, these kernels tend to evaluate the affinity (proximity) between two nodes of a network indirectly based on the number and length of the paths between these nodes [9], thus subscribing to the homophily assumption.…”

“…The task of recovering the missing types of entities and links (i.e. node and edge labels) based on the available information, known as within-network classification, is a semi-supervised learning problem key to several applications like image processing [2,12], classifying document and web pages [5,6,21,32], classifying protein interaction and gene expression data [28], part-ofspeech tagging [19], detecting malicious or fraudulent activities [26], and recommending items to consummers [9,14].…”