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This work presents a novel procedure for computing (1) distances between nodes of a weighted, undirected, graph, called the Euclidean Commute Time Distance (ECTD), and (2) a subspace projection of the nodes of the graph that preserves as much variance as possible, in terms of the ECTD – a principal components analysis of the graph. It is based on a(More)
This 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(More)
This work presents a systematic comparison between seven kernels (or similarity matrices) on a graph, namely the exponential diffusion kernel, the Laplacian diffusion kernel, the von Neumann kernel, the regularized Laplacian kernel, the commute time kernel, and finally the Markov diffusion kernel and the cross-entropy diffusion matrix - both introduced in(More)
This work proposes a simple way to improve a clustering algorithm. The idea is to exploit a new distance metric called the “Euclidian Commute Time” (ECT) distance, based on a random walk model on a graph derived from the data. Using this distance measure instead of the usual Euclidean distance in a k-means algorithm allows to retrieve wellseparated clusters(More)
This work presents a kernel method for clustering the nodes of a weighted, undirected, graph. The algorithm is based on a two-step procedure. First, the sigmoid commute-time kernel (KCT), providing a similarity measure between any couple of nodes by taking the indirect links into account, is computed from the adjacency matrix of the graph. Then, the nodes(More)
This work introduces a link-based covariance measure between the nodes of a weighted directed graph, where a cost is associated with each arc. To this end, a probability distribution on the (usually infinite) countable set of paths through the graph is defined by minimizing the total expected cost between all pairs of nodes while fixing the total relative(More)
This work addresses the problem of detecting clusters in a weighted, undirected, graph by using kernel-based clustering methods, directly partitioning the graph according to a welldefined similarity measure between the nodes (a kernel on a graph). The proposed algorithms are based on a two-step procedure. First, a kernel or similarity matrix, providing a(More)
This letter addresses the problem of designing the transition probabilities of a finite Markov chain (the policy) in order to minimize the expected cost for reaching a destination node from a source node while maintaining a fixed level of entropy spread throughout the network (the exploration). It is motivated by the following scenario. Suppose you have to(More)
This work introduces a new family of link-based dissimilarity measures between nodes of a weighted directed graph. This measure, called the randomized shortest-path (RSP) dissimilarity, depends on a parameter <i>&#952;</i> and has the interesting property of reducing, on one end, to the standard shortest-path distance when <i>&#952;</i> is large and, on the(More)
This paper presents a framework allowing to tune continual exploration in an optimal way. It first quantifies the rate of exploration by defining the degree of exploration of a state as the probability-distribution entropy for choosing an admissible action. Then, the exploration/exploitation tradeoff is stated as a global optimization problem: find the(More)