The stochastic approach for link-structure analysis (SALSA) and the TKC effect

Abstract

This article is being produced via complete electronic text/image integration, to enable full database storage. It has therefore to meet specific standards regarding structure and presentation.This proof is an automatically produced, low-resolution laser-printer output. The final product will naturally meet our high-quality standards regarding resolution and page lay-out.Please use this proof solely for checking of typesetting/editing and completeness of text and figures. Changes to the article as accepted for publication will not be considered at this stage. Elsevier Science N.L. Computer Networks 00 (2000) COMPNW2288The stochastic approach for link-structure analysis (SALSA) and the TKC effect 1 R. Lempel Ł , S. Moran Department of Computer Science, The Technion, Haifa 32000, Israel AbstractToday, when searching for information on the World Wide Web, one usually performs a query through a term-based search engine. These engines return, as the query's result, a list of Web sites whose contents match the query. For broad topic queries, such searches often result in a huge set of retrieved documents, many of which are irrelevant to the user. However, much information is contained in the link-structure of the World Wide Web. Information such as which pages are linked to others can be used to augment search algorithms. In this context, Jon Kleinberg introduced the notion of two distinct types of Web sites: hubs and authorities. Kleinberg argued that hubs and authorities exhibit a mutually reinforcing relationship: a good hub will point to many authorities, and a good authority will be pointed at by many hubs. In light of this, he devised an algorithm aimed at finding authoritative sites. We present SALSA, a new stochastic approach for link structure analysis, which examines random walks on graphs derived from the link structure. We show that both SALSA and Kleinberg's mutual reinforcement approach employ the same meta-algorithm. We then prove that SALSA is equivalent to a weighted in-degree analysis of the link-structure of World Wide Web subgraphs, making it computationally more efficient than the mutual reinforcement approach. We compare the results of applying SALSA to the results derived through Kleinberg's approach. These comparisons reveal a topological phenomenon called the TKC effect (Tightly Knit Community) which, in certain cases, prevents the mutual reinforcement approach from identifying meaningful authorities. 

Perturbation of the Hyper-Linked Environment

“…Note that this example shows that HITS fails to be stable even under small perturbation of a connected graph 6 . Therefore, the following proposition is not surprising.…”

“…As an alternative algorithm to HITS(an algorithm to avoid "topic-drift"), SALSA is proposed by Lempel and Moran [6]. SALSA performs two random walks on web pages; a random walk by following a backward-link and then a forward-link alternately, and another one by following a forward-link and then a backward-link alternately.…”

“…The transition probability matrices of the markov chains for the authorities and hubs are given byà = A t col A row ,H = A row A t col , where A col is constructed by renormalizing each column of the adjacency matrix A to sum to 1, and A row is constructed by renormalizing each row of the adjacency matrix A to sum to 1. One attractive aspect of SALSA is that its stationarity distributions have explicit forms [6].…”

“…Different attempts [6,7,3,9,10,[12][13][14] to improve these algorithms were taken. A simple evaluation of query results using human judgement is normally employed to measure the performance of algorithms.…”

“…The first class of algorithms are algebraic methods such as HITS [1],PageRank [2], SALSA [6] and various hybrid algorithms of the first two [3,9,11]. These methods essentially compute principal eigenvectors of particular matrices related to the adjacency matrix of a certain web graph to identify the most relevant pages on that web graph.…”