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

On construction, performance, and diversification for structured queries on the semantic desktop

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Diverse and proportional size-1 object summaries for keyword search

The abundance and ubiquity of graphs (e.g., Online Social Networks such as Google+ and Facebook; bibliographic graphs such as DBLP) necessitates the effective and efficient search over them. Given a set of keywords that can identify a Data Subject (DS), a recently proposed relational keyword search paradigm produces, as a query result, a set of Object Summaries (OSs). An OS is a tree structure rooted at the DS node (i.e., a tuple containing the keywords) with surrounding nodes that summarize all data held on the graph about the DS. OS snippets, denoted as size-l OSs, have also been investigated. Size-l OSs are partial OSs containing l nodes such that the summation of their importance scores results in the maximum possible total score. However, the set of nodes that maximize the total importance score may result in an uninformative size-l OSs, as very important nodes may be repeated in it, dominating other representative information. In view of this limitation, in this paper we investigate the effective and efficient generation of two novel types of OS snippets, i.e. diverse and proportional size-l OSs, denoted as DSize-l and PSize-l OSs. Namely, apart from the importance of each node, we also consider its frequency in the OS and its repetitions in the snippets. We conduct an extensive evaluation on two real graphs (DBLP and Google+). We verify effectiveness by collecting user feedback, e.g. by asking DBLP authors (i.e. the DSs themselves) to evaluate our results. In addition, we verify the efficiency of our algorithms and evaluate the quality of the snippets that they produce.postprin

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