Fast Single-Pair SimRank Computation

Abstract

SimRank is an intuitive and effective measure for link-based similarity that scores similarity between two nodes as the first-meeting probability of two random surfers, based on the random surfer model. However, when a user queries the similarity of a given node-pair based on SimRank, the existing approaches need to compute the similarities of other node-pairs beforehand, which we call an all-pair style. In this paper, we propose a Single-Pair SimRank approach. Without accuracy loss, this approach performs an iterative computation to obtain the similarity of a single node-pair. The time cost of our Single-Pair SimRank is always less than All-Pair SimRank and obviously efficient when we only need to assess similarity of one or a few node-pairs. We confirm the accuracy and efficiency of our approach in extensive experimental studies over synthetic and real datasets. IntroductionThe measure of similarity between objects plays a significant role in many real-world applications, including clustering, classification, information retrieval, and recommendation systems. The current similarity measures can be generalized into two broad categories: content-based similarity measures and link-based similarity measures [14]. The former is based on the content using a vector space model [16], and the latter is based on a link graph in which objects and relationships are modeled as nodes and edges. Examples of link graphs include citations between papers, social relationships in human or web hyperlinks. Effective and efficient similarity measures between objects in a link graph can greatly assist users for searching and analyzing information [20,9,19,6,5,13], in particular when the relationships among objects are complex.Among the link-based similarity measures in the literature, SimRank [9] has attracted a considerable attention due to its intuition and sturdy theoretical foundation. The basic intuition behind SimRank is "two objects are similar if they are referenced by similar

Geographic knowledge extraction and semantic similarity in OpenStreetMap

“…observe the performance of co-citation algorithms by exploring the result space of P-Rank. In this context, we propose a linear algebra formulation of P-Rank, discussing in detail the meaning and impact of its parameters (K, λ, and C), largely left implicit in the literature [62,29,33]. P-Rank is a recursive measure of similarity, based on the combination of two recursive assumptions: (1) two entities are similar if they are referenced by similar entities; (2) two entities are similar if they reference similar entities.…”

“…The underlying recursive assumption is that "two objects are similar if they are referenced by similar objects" [29, p. 541]. Given its generality and effectiveness, SimRank has attracted notable research interest [37,33].…”

Efficient partial-pairs simrank search on large networks

“…We refer to this phenomenon as "high iteration coupling". To the best of our knowledge, there are several pioneering works trying to break the "high iteration coupling" barrier, such as single-pair SimRank [3,6,12], and top-K single-source SimRank [4,9,10], but they still require excessive time and memory, or deliver probabilistic results. (see Related Work section for a detailed comparison).…”

“…First, it is a unified model, containing as special cases the existing all-pairs [13,16], single-source [4,10], and single-pair [6,12] SimRank, when (A, B) is taken to be (V, V ), (V, {j}), and ({i}, {j}), respectively, with queries i and j. Thus, it is applicable to any domains where all-pairs, single-source, and single-pair SimRank apply.…”

“…(1) Due to "high iteration coupling", it is difficult to break the holistic nature of the conventional iterative models for retrieving only partial-pairs SimRank in a self-contained style. (2) It is a grand challenge to improve both time and memory for partial-pairs SimRank without loss of accuracy, since even for computing a single-pair score, the prior works [6,12] have comparable complexities of all-pairs SimRank [13,16].…”