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RandomWalk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation
March 2007 (vol. 19 no. 3)
pp. 355369
ASCII Text  x  
Fran?ois Fouss, Alain Pirotte, JeanMichel Renders, Marco Saerens, "RandomWalk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation," IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 3, pp. 355369, March, 2007.  
BibTex  x  
@article{ 10.1109/TKDE.2007.46, author = {Fran?ois Fouss and Alain Pirotte and JeanMichel Renders and Marco Saerens}, title = {RandomWalk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation}, journal ={IEEE Transactions on Knowledge and Data Engineering}, volume = {19}, number = {3}, issn = {10414347}, year = {2007}, pages = {355369}, doi = {http://doi.ieeecomputersociety.org/10.1109/TKDE.2007.46}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Knowledge and Data Engineering TI  RandomWalk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation IS  3 SN  10414347 SP355 EP369 EPD  355369 A1  Fran?ois Fouss, A1  Alain Pirotte, A1  JeanMichel Renders, A1  Marco Saerens, PY  2007 KW  Graph analysis KW  graph and database mining KW  collaborative recommendation KW  graph kernels KW  spectral clustering KW  Fiedler vector KW  proximity measures KW  statistical relational learning. VL  19 JA  IEEE Transactions on Knowledge and Data Engineering ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TKDE.2007.46
This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted and undirected graph. It is based on a Markovchain model of random walk through the database. More precisely, we compute quantities (the average commute time, the pseudoinverse of the Laplacian matrix of the graph, etc.) that provide similarities between any pair of nodes, having the nice property of increasing when the number of paths connecting those elements increases and when the "length” of paths decreases. It turns out that the square root of the average commute time is a Euclidean distance and that the pseudoinverse of the Laplacian matrix is a kernel matrix (its elements are inner products closely related to commute times). A principal component analysis (PCA) of the graph is introduced for computing the subspace projection of the node vectors in a manner that preserves as much variance as possible in terms of the Euclidean commutetime distance. This graph PCA provides a nice interpretation to the "Fiedler vector,” widely used for graph partitioning. The model is evaluated on a collaborativerecommendation task where suggestions are made about which movies people should watch based upon what they watched in the past. Experimental results on the MovieLens database show that the Laplacianbased similarities perform well in comparison with other methods. The model, which nicely fits into the socalled "statistical relational learning” framework, could also be used to compute document or word similarities, and, more generally, it could be applied to machinelearning and patternrecognition tasks involving a relational database.
Index Terms:
Graph analysis, graph and database mining, collaborative recommendation, graph kernels, spectral clustering, Fiedler vector, proximity measures, statistical relational learning.
Citation:
Fran?ois Fouss, Alain Pirotte, JeanMichel Renders, Marco Saerens, "RandomWalk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation," IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 3, pp. 355369, March 2007, doi:10.1109/TKDE.2007.46
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