We propose a generalization of SimRank similarity measure for heterogeneous information networks. Given the information network, the intraclass similarity score s(a, b) is high if the set of objects that are related with a and the set of objects that are related with b are pair-wise similar according to all imposed relations.
The basic graph structure similarity measure is the classical SimRank @cite_7 over a homogeneous graph @math which is defined as follows: @math @math The main drawback of this approach is that we cannot induce multiple relations or object types, so the only option is mixing them up into blobs "relation exists" and "all objects" that is completely not applicable in the case we have multiple relations with different semantics, for example the OpenCyc ontology node of the concept "Game" (see Figure ) cannot be easily expressed via a single type of relations and objects.
@cite_7
2117831564 1545879303 2147579672 2104812688
The problem of measuring "similarity" of objects arises in many applications, and many domain-specific measures have been developed, e.g., matching text across documents or computing overlap among item-sets. We propose a complementary approach, applicable in any domain with object-to-object relationships, that measures similarity of the structural context in which objects occur, based on their relationships with other objects. Effectively, we compute a measure that says "two objects are similar if they are related to similar objects:" This general similarity measure, called SimRank, is based on a simple and intuitive graph-theoretic model. For a given domain, SimRank can be combined with other domain-specific similarity measures. We suggest techniques for efficient computation of SimRank scores, and provide experimental results on two application domains showing the computational feasibility and effectiveness of our approach. Similarity assessment is one of the core tasks in hyperlink analysis. Recently, with the proliferation of applications, e.g., web search and collaborative filtering, SimRank has been a well-studied measure of similarity between two nodes in a graph. It recursively follows the philosophy that "two nodes are similar if they are referenced (have incoming edges) from similar nodes", which can be viewed as an aggregation of similarities based on incoming paths. Despite its popularity, SimRank has an undesirable property, i.e., "zero-similarity": It only accommodates paths with equal length from a common "center" node. Thus, a large portion of other paths are fully ignored. This paper attempts to remedy this issue. (1) We propose and rigorously justify SimRank*, a revised version of SimRank, which resolves such counter-intuitive "zero-similarity" issues while inheriting merits of the basic SimRank philosophy. (2) We show that the series form of SimRank* can be reduced to a fairly succinct and elegant closed form, which looks even simpler than SimRank, yet enriches semantics without suffering from increased computational cost. This leads to a fixed-point iterative paradigm of SimRank* in O(Knm) time on a graph of n nodes and m edges for K iterations, which is comparable to SimRank. (3) To further optimize SimRank* computation, we leverage a novel clustering strategy via edge concentration. Due to its NP-hardness, we devise an efficient and effective heuristic to speed up SimRank* computation to O(Knm) time, where m is generally much smaller than m. (4) Using real and synthetic data, we empirically verify the rich semantics of SimRank*, and demonstrate its high computation efficiency. Many real-world objects described by multiple attributes or features can be decomposed as multiple "views" (e.g., an image can be described by a color view or a shape view), which often provides complementary information to each other. Learning a metric (similarity measures) for multi-view data is primary due to its wide applications in practices. However, leveraging multi-view information to produce a good metric is a great challenge and existing techniques are concerned with pairwise similarities, leading to undesirable fusion metric and high computational complexity. In this paper, we propose a novel Metric Fusion technique via cross-view graph Random Walk, named MFRW, regarding a multi-view based similarity graphs (with each similarity graph constructed under each view). Instead of using pairwise similarities, we seek a high-order metric yielded by graph random walks over constructed similarity graphs. Observing that outlier views" may exist in the fusion process, we incorporate the coefficient matrices representing the correlation strength between any two views into MFRW, named WMFRW. The principle of WMFRW is implemented by exploring the common latent structure" between views. The empirical studies conducted on real-world databases demonstrate that our approach outperforms the state-of-the-art competitors in terms of effectiveness and efficiency. Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degree distribution, clustering coefficient, diameter, and relative graphlet frequency distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it is that the networks will truly be similar. Results: We introduce a new systematic measure of a network's local structure that imposes a large number of similarity constraints on networks being compared. In particular, we generalize the degree distribution, which measures the number of nodes 'touching' k edges, into distributions measuring the number of nodes 'touching' k graphlets, where graphlets are small connected non-isomorphic subgraphs of a large network. Our new measure of network local structure consists of 73 graphlet degree distributions of graphlets with 2--5 nodes, but it is easily extendible to a greater number of constraints (i.e. graphlets), if necessary, and the extensions are limited only by the available CPU. Furthermore, we show a way to combine the 73 graphlet degree distributions into a network 'agreement' measure which is a number between 0 and 1, where 1 means that networks have identical distributions and 0 means that they are far apart. Based on this new network agreement measure, we show that almost all of the 14 eukaryotic PPI networks, including human, resulting from various high-throughput experimental techniques, as well as from curated databases, are better modeled by geometric random graphs than by Erdos--Reny, random scale-free, or Barabasi--Albert scale-free networks. Availability: Software executables are available upon request. Contact: natasha@ics.uci.edu