Semi-metric Networks for Recommender Systems

Simas, Tiago; Rocha, Luís M.

doi:10.1109/wi-iat.2012.245

Cited by 10 publications

(13 citation statements)

References 19 publications

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“…Additionally, using proximity networks to capture and extract knowledge in the biomedical literature led to very high performance on various information extraction tasks (Verspoor et al, 2005;Abi-Haidar et al, 2008;Kolchinsky et al, 2010) of the BioCreative text mining competition (Hirschman et al, 2005). We have also tested recommendation of movies based on the clusters of the proximity network of users obtained from the MovieLens benchmark with very good results (Simas and Rocha, 2012). This exemplifies how proximity networks can be seen as effective, knowledge and social structure representations.…”

Section: Representing and Fusing Knowledge In Proximity Networkmentioning

confidence: 78%

Distance closures on complex networks

Simas

Rocha

2015

Net Sci

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149

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To expand the toolbox available to network science, we study the isomorphism between distance and Fuzzy (proximity or strength) graphs. Distinct transitive closures in Fuzzy graphs lead to closures of their isomorphic distance graphs with widely different structural properties. For instance, the All Pairs Shortest Paths (APSP) problem, based on the Dijkstra algorithm, is equivalent to a metric closure, which is only one of the possible ways to calculate shortest paths in weighted graphs. We show that different closures lead to different distortions of the original topology of weighted graphs. Therefore, complex network analyses that depend on the calculation of shortest paths on weighted graphs should take into account the closure choice and associated topological distortion. We characterise the isomorphism using the max-min and Dombi disjunction/conjunction pairs. This allows us to: (1) study alternative distance closures, such as those based on diffusion, metric, and ultra-metric distances; (2) identify the operators closest to the metric closure of distance graphs (the APSP), but which are logically consistent; and (3) propose a simple method to compute alternative distance closures using existing algorithms for the APSP. In particular, we show that a specific diffusion distance is promising for community detection in complex networks, and is based on desirable axioms for logical inference or approximate reasoning on networks; it also provides a simple algebraic means to compute diffusion processes on networks. Based on these results, we argue that choosing different distance closures can lead to different conclusions about indirect associations on network data, as well as the structure of complex networks, and are thus important to consider.

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Section: Representing and Fusing Knowledge In Proximity Networkmentioning

confidence: 78%

Distance closures on complex networks

Simas

Rocha

2015

Net Sci

Self Cite

149

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“…Metric and Semi-metric edges and paths. As defined in [13,12,9,11,15,14,10], an edge in a weighted graph is metric if the shortest path is equal to the edge by itself (direct connection). Otherwise the edge is considered semi-metric, which means that there is at least one alternative path that involves other nodes.…”

Section: Food-pairing Food-bridging and Flavour Networkmentioning

confidence: 99%

“…The hypothesis of food-bridging stems from the combination of the theory of complex networks and gastronomy [1,2,3,5,8,9,12,13]. It assumes that if two ingredients do not share a strong molecular or empirical affinity, they may become affine through a chain of pairwise affinities.…”

Section: Introductionmentioning

confidence: 99%

Food-Bridging: A New Network Construction to Unveil the Principles of Cooking

et al. 2017

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In this manuscript, we propose, analyze, and discuss a possible new principle behind traditional cuisine: the Food-bridging hypothesis and its comparison with the food-pairing hypothesis using the same dataset and graphical models employed in the food-pairing study by Ahn et al. (2011). The Food-bridging hypothesis assumes that if two ingredients do not share a strong molecular or empirical affinity, they may become affine through a chain of pairwise affinities. That is, in a graphical model as employed by Ahn et al., a chain represents a path that joints the two ingredients, the shortest path represents the strongest pairwise chain of affinities between the two ingredients. Food-pairing and Food-bridging are different hypotheses that may describe possible mechanisms behind the recipes of traditional cuisines. Food-pairing intensifies flavor by mixing ingredients in a recipe with similar chemical compounds, and food-bridging smoothes contrast between ingredients. Both food-pairing and food-bridging are observed in traditional cuisines, as shown in this work. We observed four classes of cuisines according to food-pairing and food-bridging: (1) East Asian cuisines, at one extreme, tend to avoid food-pairing as well as food-bridging; and (4) Latin American cuisines, at the other extreme, follow both principles. For the two middle classes: (2) Southeastern Asian cuisines, avoid foodpairing and follow food-bridging; and (3) Western cuisines, follow food-pairing and avoid food-bridging.

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“…The concept of semi-metricity in weighted graphs has been first used in complex network analysis. Semi-metricity was introduced in weighted graphs by Rocha [45,46], showing that semi-metric edges in a weighted graph encode some latent information between a pair of nodes, which may be useful for information discovery [45,46,48,44,49]. Simas et al introduce in [49] a new mathematical framework to the study of networks in general and specifically semi-metric networks.…”

Section: Related Workmentioning

confidence: 99%

“…Effectively, the metric backbone is a reduced representation of a graph, that preserves information about shortest paths. This property has been used to improve recommendation algorithms [46,44,48] and more recently, to improve the modularity in community detection [49].…”

Section: Introductionmentioning

confidence: 99%

The shortest path is not always a straight line

2016

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In this paper, we leverage the concept of the metric backbone to improve the efficiency of large-scale graph analytics. The metric backbone is the minimum subgraph that preserves the shortest paths of a weighted graph. We use the metric backbone in place of the original graph to compute various graph metrics exactly or with good approximation. By computing on a smaller graph, we improve the performance of graph analytics applications on two different systems, a batch graph processing system and a graph database. Further, we provide an algorithm for the computation of the metric backbone on large graphs. While one can compute the metric backbone by solving the all-pairs-shortestpaths problem, this approach incurs prohibitive time and space complexity for big graphs. Instead, we propose a heuristic that makes computing the metric backbone practical even for large graphs. Additionally, we analyze several real datasets of different sizes and domains and we show that we can approximate the metric backbone by removing only first-order semi-metric edges; edges for which a shorter two-hop path exists. We provide a distributed implementation of our algorithm and apply it in large scale scenarios. We evaluate our algorithm using a variety of real graphs, including a Facebook social network subgraph of ∼50 billion edges. We measure the impact of using the metric backbone on runtime performance in two graph management systems. We achieve query speedups of up to 6.7x in the Neo4j commercial graph database and job speedups of up to 6x in the Giraph graph processing system.

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Semi-metric Networks for Recommender Systems

Cited by 10 publications

References 19 publications

Distance closures on complex networks

Distance closures on complex networks

Food-Bridging: A New Network Construction to Unveil the Principles of Cooking

The shortest path is not always a straight line

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