In many applications, we need to measure similarity between nodes in a large network based on features of their neighborhoods. Although in-network node similarity based on proximity has been well investigated, surprisingly, measuring in-network node similarity based on neighborhoods remains a largely untouched problem in literature. One challenge is that in different applications we may need different measurements that manifest different meanings of similarity. Furthermore, we often want to make trade-offs between specificity of neighborhood matching and efficiency. In this paper, we investigate the problem in a principled and systematic manner. We develop a unified parametric model and a series of four instance measures. Those instance similarity measures not only address a spectrum of various meanings of similarity, but also present a series of trade-offs between computational cost and strictness of matching between neighborhoods of nodes being compared. By extensive experiments and case studies, we demonstrate the effectiveness of the proposed model and its instances.
Node proximity is widely adopted as similarity measures in many data mining and machine learning tasks. Koutra @cite_18 proposed a unified framework of Guilt-by-Association. A wide range of popular proximity measures, such as Personalized PageRank @cite_9 , Random Walk with Restart @cite_10 and Generalized Belief Propagation @cite_28 , are special cases or can be approximated by Guilt-by-Association. The basic assumption behind those proximity-based measures is that nodes in a network influence each other through edges and paths. Thus, nodes within the same community are often more similar than those from different communities. Apparently, proximity-based measures cannot be used to solve the problems demonstrated in Example .
@cite_28 @cite_9 @cite_18 @cite_10
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Many recommendation and retrieval tasks can be represented as proximity queries on a labeled directed graph, with typed nodes representing documents, terms, and metadata, and labeled edges representing the relationships between them. Recent work has shown that the accuracy of the widely-used random-walk-based proximity measures can be improved by supervised learning - in particular, one especially effective learning technique is based on Path-Constrained Random Walks (PCRW), in which similarity is defined by a learned combination of constrained random walkers, each constrained to follow only a particular sequence of edge labels away from the query nodes. The PCRW based method significantly outperformed unsupervised random walk based queries, and models with learned edge weights. Unfortunately, PCRW query systems are expensive to evaluate. In this study we evaluate the use of approximations to the computation of the PCRW distributions, including fingerprinting, particle filtering, and truncation strategies. In experiments on several recommendation and retrieval problems using two large scientific publications corpora we show speedups of factors of 2 to 100 with little loss in accuracy. Scientific literature with rich metadata can be represented as a labeled directed graph. This graph representation enables a number of scientific tasks such as ad hoc retrieval or named entity recognition (NER) to be formulated as typed proximity queries in the graph. One popular proximity measure is called Random Walk with Restart (RWR), and much work has been done on the supervised learning of RWR measures by associating each edge label with a parameter. In this paper, we describe a novel learnable proximity measure which instead uses one weight per edge label sequence: proximity is defined by a weighted combination of simple "path experts", each corresponding to following a particular sequence of labeled edges. Experiments on eight tasks in two subdomains of biology show that the new learning method significantly outperforms the RWR model (both trained and untrained). We also extend the method to support two additional types of experts to model intrinsic properties of entities: query-independent experts, which generalize the PageRank measure, and popular entity experts which allow rankings to be adjusted for particular entities that are especially important. The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). Proximity measures quantify the closeness or similarity between nodes in a social network and form the basis of a range of applications in social sciences, business, information technology, computer networks, and cyber security. It is challenging to estimate proximity measures in online social networks due to their massive scale (with millions of users) and dynamic nature (with hundreds of thousands of new nodes and millions of edges added daily). To address this challenge, we develop two novel methods to efficiently and accurately approximate a large family of proximity measures. We also propose a novel incremental update algorithm to enable near real-time proximity estimation in highly dynamic social networks. Evaluation based on a large amount of real data collected in five popular online social networks shows that our methods are accurate and can easily scale to networks with millions of nodes. To demonstrate the practical values of our techniques, we consider a significant application of proximity estimation: link prediction, i.e., predicting which new edges will be added in the near future based on past snapshots of a social network. Our results reveal that (i) the effectiveness of different proximity measures for link prediction varies significantly across different online social networks and depends heavily on the fraction of edges contributed by the highest degree nodes, and (ii) combining multiple proximity measures consistently yields the best link prediction accuracy.