Random-Walk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation
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...Saerens and coworkers (Fouss and Renders, 2007; Saerens et al., 2004; Yen et al., 2007, 2009) have extensively studied and used the commutetime (and variants thereof) as (dis)similarity measure: the larger the time, the farther (less similar) the vertices....
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...Here the cost function is the total intra-cluster distance, or squared error function k∑ i=1 ∑ xj∈Si ||xj − ci||2, (23) where Si indicates the subset of points of the i-th cluster and ci its centroid....
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...Accordingly, the cosine similarity is defined as the cosine of the node vectors, namely [71]...
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...Also, elements in a set can be assigned a category provided by elements from another set....
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...Analysis (PCA) in the sense that the projection of the node vectors in this subspace has maximal variance (in terms of ECTD) among all the possible candidate projections (see [58]; see also Appendix F). This is related, in a number of interesting ways, with both spectral clustering (see, e.g., [ 62 ], [20], and our work [58]), kernel PCA [60], and spectral embedding [6], [7]....
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...the sparseness of the transition-probability matrix [30], [56], is one alternative (based on (1) or (2))....
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