Monte Carlo Methods for Top-k Personalized PageRank Lists and Name Disambiguation

We study a problem of quick detection of top-k Personalized PageRank lists. This problem has a number of important applications such as finding local cuts in large graphs, estimation of similarity distance and name disambiguation. In particular, we apply our results to construct efficient algorithms for the person name disambiguation problem. We argue that when finding top-k Personalized PageRank lists two observations are important. Firstly, it is crucial that we detect fast the top-k most important neighbours of a node, while the exact order in the top-k list as well as the exact values of PageRank are by far not so crucial. Secondly, a little number of wrong elements in top-k lists do not really degrade the quality of top-k lists, but it can lead to significant computational saving. Based on these two key observations we propose Monte Carlo methods for fast detection of top-k Personalized PageRank lists. We provide performance evaluation of the proposed methods and supply stopping criteria. Then, we apply the methods to the person name disambiguation problem. The developed algorithm for the person name disambiguation problem has achieved the second place in the WePS 2010 competition

Term-Specific Eigenvector-Centrality in Multi-Relation Networks

Fuzzy matching and ranking are two information retrieval techniques widely used in web search. Their application to structured data, however, remains an open problem. This article investigates how eigenvector-centrality can be used for approximate matching in multi-relation graphs, that is, graphs where connections of many different types may exist. Based on an extension of the PageRank matrix, eigenvectors representing the distribution of a term after propagating term weights between related data items are computed. The result is an index which takes the document structure into account and can be used with standard document retrieval techniques. As the scheme takes the shape of an index transformation, all necessary calculations are performed during index tim

COMPUTING APPROXIMATE CUSTOMIZED RANKING

As the amount of information grows and as users become more sophisticated, ranking techniques become important building blocks to meet user needs when answering queries. PageRank is one of the most successful link-based ranking methods, which iteratively computes the importance scores for web pages based on the importance scores of incoming pages. Due to its success, PageRank has been applied in a number of applications that require customization. We address the scalability challenges for two types of customized ranking. The first challenge is to compute the ranking of a subgraph. Various Web applications focus on identifying a subgraph, such as focused crawlers and localized search engines. The second challenge is to compute online personalized ranking. Personalized search improves the quality of search results for each user. The user needs are represented by a personalized set of pages or personalized link importance in an entity relationship graph. This requires an efficient online computation. To solve the subgraph ranking problem efficiently, we estimate the ranking scores for a subgraph. We propose a framework of an exact solution (IdealRank) and an approximate solution (ApproxRank) for computing ranking on a subgraph. Both IdealRank and ApproxRank represent the set of external pages with an external node $\Lambda$ and modify the PageRank-style transition matrix with respect to $\Lambda$. The IdealRank algorithm assumes that the scores of external pages are known. We prove that the IdealRank scores for pages in the subgraph converge to the true PageRank scores. Since the PageRank-style scores of external pages may not typically be available, we propose the ApproxRank algorithm to estimate scores for the subgraph. We analyze the $L_1$ distance between IdealRank scores and ApproxRank scores of the subgraph and show that it is within a constant factor of the $L_1$ distance of the external pages. We demonstrate with real and synthetic data that ApproxRank provides a good approximation to PageRank for a variety of subgraphs. We consider online personalization using ObjectRank; it is an authority flow based ranking for entity relationship graphs. We formalize the concept of an aggregate surfer on a data graph; the surfer's behavior is controlled by multiple personalized rankings. We prove a linearity theorem over these rankings which can be used as a tool to scale this type of personalization. DataApprox uses a repository of precomputed rankings for a given set of link weights assignments. We define DataApprox as an optimization problem; it selects a subset of the precomputed rankings from the repository and produce a weighted combination of these rankings. We analyze the $L_1$ distance between the DataApprox scores and the real authority flow ranking scores and show that DataApprox has a theoretical bound. Our experiments on the DBLP data graph show that DataApprox performs well in practice and allows fast and accurate personalized authority flow ranking

Pair-Linking for Collective Entity Disambiguation: Two Could Be Better Than All

Collective entity disambiguation aims to jointly resolve multiple mentions by linking them to their associated entities in a knowledge base. Previous works are primarily based on the underlying assumption that entities within the same document are highly related. However, the extend to which these mentioned entities are actually connected in reality is rarely studied and therefore raises interesting research questions. For the first time, we show that the semantic relationships between the mentioned entities are in fact less dense than expected. This could be attributed to several reasons such as noise, data sparsity and knowledge base incompleteness. As a remedy, we introduce MINTREE, a new tree-based objective for the entity disambiguation problem. The key intuition behind MINTREE is the concept of coherence relaxation which utilizes the weight of a minimum spanning tree to measure the coherence between entities. Based on this new objective, we design a novel entity disambiguation algorithms which we call Pair-Linking. Instead of considering all the given mentions, Pair-Linking iteratively selects a pair with the highest confidence at each step for decision making. Via extensive experiments, we show that our approach is not only more accurate but also surprisingly faster than many state-of-the-art collective linking algorithms

큰 그래프 상에서의 개인화된 페이지 랭크에 대한 빠른 계산 기법

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·컴퓨터공학부, 2020. 8. 이상구.Computation of Personalized PageRank (PPR) in graphs is an important function that is widely utilized in myriad application domains such as search, recommendation, and knowledge discovery. Because the computation of PPR is an expensive process, a good number of innovative and efficient algorithms for computing PPR have been developed. However, efficient computation of PPR within very large graphs with over millions of nodes is still an open problem. Moreover, previously proposed algorithms cannot handle updates efficiently, thus, severely limiting their capability of handling dynamic graphs. In this paper, we present a fast converging algorithm that guarantees high and controlled precision. We improve the convergence rate of traditional Power Iteration method by adopting successive over-relaxation, and initial guess revision, a vector reuse strategy. The proposed method vastly improves on the traditional Power Iteration in terms of convergence rate and computation time, while retaining its simplicity and strictness. Since it can reuse the previously computed vectors for refreshing PPR vectors, its update performance is also greatly enhanced. Also, since the algorithm halts as soon as it reaches a given error threshold, we can flexibly control the trade-off between accuracy and time, a feature lacking in both sampling-based approximation methods and fully exact methods. Experiments show that the proposed algorithm is at least 20 times faster than the Power Iteration and outperforms other state-of-the-art algorithms.그래프 내에서 개인화된 페이지랭크 (P ersonalized P age R ank, PPR 를 계산하는 것은 검색 , 추천 , 지식발견 등 여러 분야에서 광범위하게 활용되는 중요한 작업 이다 . 개인화된 페이지랭크를 계산하는 것은 고비용의 과정이 필요하므로 , 개인화된 페이지랭크를 계산하는 효율적이고 혁신적인 방법들이 다수 개발되어왔다 . 그러나 수백만 이상의 노드를 가진 대용량 그래프에 대한 효율적인 계산은 여전히 해결되지 않은 문제이다 . 그에 더하여 , 기존 제시된 알고리듬들은 그래프 갱신을 효율적으로 다루지 못하여 동적으로 변화하는 그래프를 다루는 데에 한계점이 크다 . 본 연구에서는 높은 정밀도를 보장하고 정밀도를 통제 가능한 , 빠르게 수렴하는 개인화된 페이지랭크 계산 알고리듬을 제시한다 . 전통적인 거듭제곱법 (Power 에 축차가속완화법 (Successive Over Relaxation) 과 초기 추측 값 보정법 (Initial Guess 을 활용한 벡터 재사용 전략을 적용하여 수렴 속도를 개선하였다 . 제시된 방법은 기존 거듭제곱법의 장점인 단순성과 엄밀성을 유지 하면서 도 수렴율과 계산속도를 크게 개선 한다 . 또한 개인화된 페이지랭크 벡터의 갱신을 위하여 이전에 계산 되어 저장된 벡터를 재사용하 여 , 갱신 에 드는 시간이 크게 단축된다 . 본 방법은 주어진 오차 한계에 도달하는 즉시 결과값을 산출하므로 정확도와 계산시간을 유연하게 조절할 수 있으며 이는 표본 기반 추정방법이나 정확한 값을 산출하는 역행렬 기반 방법 이 가지지 못한 특성이다 . 실험 결과 , 본 방법은 거듭제곱법에 비하여 20 배 이상 빠르게 수렴한다는 것이 확인되었으며 , 기 제시된 최고 성능 의 알고리 듬 보다 우수한 성능을 보이는 것 또한 확인되었다1 Introduction 1 2 Preliminaries: Personalized PageRank 4 2.1 Random Walk, PageRank, and Personalized PageRank. 5 2.1.1 Basics on Random Walk 5 2.1.2 PageRank. 6 2.1.3 Personalized PageRank 8 2.2 Characteristics of Personalized PageRank. 9 2.3 Applications of Personalized PageRank. 12 2.4 Previous Work on Personalized PageRank Computation. 17 2.4.1 Basic Algorithms 17 2.4.2 Enhanced Power Iteration 18 2.4.3 Bookmark Coloring Algorithm. 20 2.4.4 Dynamic Programming 21 2.4.5 Monte-Carlo Sampling. 22 2.4.6 Enhanced Direct Solving 24 2.5 Summary 26 3 Personalized PageRank Computation with Initial Guess Revision 30 3.1 Initial Guess Revision and Relaxation 30 3.2 Finding Optimal Weight of Successive Over Relaxation for PPR. 34 3.3 Initial Guess Construction Algorithm for Personalized PageRank. 36 4 Fully Personalized PageRank Algorithm with Initial Guess Revision 42 4.1 FPPR with IGR. 42 4.2 Optimization. 49 4.3 Experiments. 52 5 Personalized PageRank Query Processing with Initial Guess Revision 56 5.1 PPR Query Processing with IGR 56 5.2 Optimization. 64 5.3 Experiments. 67 6 Conclusion 74 Bibliography 77 Appendix 88 Abstract (In Korean) 90Docto