653 research outputs found
TPA: Fast, Scalable, and Accurate Method for Approximate Random Walk with Restart on Billion Scale Graphs
Given a large graph, how can we determine similarity between nodes in a fast
and accurate way? Random walk with restart (RWR) is a popular measure for this
purpose and has been exploited in numerous data mining applications including
ranking, anomaly detection, link prediction, and community detection. However,
previous methods for computing exact RWR require prohibitive storage sizes and
computational costs, and alternative methods which avoid such costs by
computing approximate RWR have limited accuracy. In this paper, we propose TPA,
a fast, scalable, and highly accurate method for computing approximate RWR on
large graphs. TPA exploits two important properties in RWR: 1) nodes close to a
seed node are likely to be revisited in following steps due to block-wise
structure of many real-world graphs, and 2) RWR scores of nodes which reside
far from the seed node are proportional to their PageRank scores. Based on
these two properties, TPA divides approximate RWR problem into two subproblems
called neighbor approximation and stranger approximation. In the neighbor
approximation, TPA estimates RWR scores of nodes close to the seed based on
scores of few early steps from the seed. In the stranger approximation, TPA
estimates RWR scores for nodes far from the seed using their PageRank. The
stranger and neighbor approximations are conducted in the preprocessing phase
and the online phase, respectively. Through extensive experiments, we show that
TPA requires up to 3.5x less time with up to 40x less memory space than other
state-of-the-art methods for the preprocessing phase. In the online phase, TPA
computes approximate RWR up to 30x faster than existing methods while
maintaining high accuracy.Comment: 12pages, 10 figure
Approximate Computation and Implicit Regularization for Very Large-scale Data Analysis
Database theory and database practice are typically the domain of computer
scientists who adopt what may be termed an algorithmic perspective on their
data. This perspective is very different than the more statistical perspective
adopted by statisticians, scientific computers, machine learners, and other who
work on what may be broadly termed statistical data analysis. In this article,
I will address fundamental aspects of this algorithmic-statistical disconnect,
with an eye to bridging the gap between these two very different approaches. A
concept that lies at the heart of this disconnect is that of statistical
regularization, a notion that has to do with how robust is the output of an
algorithm to the noise properties of the input data. Although it is nearly
completely absent from computer science, which historically has taken the input
data as given and modeled algorithms discretely, regularization in one form or
another is central to nearly every application domain that applies algorithms
to noisy data. By using several case studies, I will illustrate, both
theoretically and empirically, the nonobvious fact that approximate
computation, in and of itself, can implicitly lead to statistical
regularization. This and other recent work suggests that, by exploiting in a
more principled way the statistical properties implicit in worst-case
algorithms, one can in many cases satisfy the bicriteria of having algorithms
that are scalable to very large-scale databases and that also have good
inferential or predictive properties.Comment: To appear in the Proceedings of the 2012 ACM Symposium on Principles
of Database Systems (PODS 2012
μ€μΈκ³ κ·Έλν νΉμ§μ νμ©ν λλ€ μν¬ κΈ°λ° λκ·λͺ¨ κ·Έλν λ§μ΄λ
νμλ
Όλ¬Έ(λ°μ¬)--μμΈλνκ΅ λνμ :곡과λν μ»΄ν¨ν°κ³΅νλΆ,2020. 2. κ°μ .Numerous real-world relationships are represented as graphs such as social networks, hyperlink networks, and protein interaction networks. Analyzing those networks is important to understand the real-life phenomena. Among various graph analysis techniques, random walk has been widely used in many applications with satisfactory results. However, various real-world graphs are large and complicated with diverse labels. Traditional random walk based methods require heavy computational cost, and disregards those labels for performing random walks; thus, its utilization has been limited in such large and complicated graphs.
In this thesis, I handle the technical challenges of mining large real-world graphs based on random walk. Real-world graphs have distinct structural properties which become a basis to increase the performance of the random walk in terms of speed and quality. Based upon this idea, I develop fast, scalable, and exact methods for node ranking using random walk in large-scale plain networks. I also design accurate models using random walks for node ranking and relational reasoning in labeled graphs such as signed networks and knowledge bases.
Through extensive experiments on various real-world graphs, I demonstrate the effectiveness of the methods and models proposed by this thesis. The proposed methods process 100 times larger graphs, and require up to 130 times less memory with up to 9 times faster speed compared to other existing methods, successfully scaling to billion-scale graphs. Also, the proposed models substantially improve the predictive performance of a variety of tasks in labeled graphs such as signed networks and knowledge bases.λ€μν μ€μΈκ³ μμ° νμμμμ κ΄κ³λ€μ μμ
λ€νΈμν¬, νμ΄νΌλ§ν¬ λ€νΈμν¬μ λ¨λ°±μ§ μνΈμμ© λ€νΈμν¬μ κ°μ΄ μ μ κ³Ό κ°μμ κ·Έλνλ‘ ννλλ€. μ΄λ¬ν λ€νΈμν¬λ₯Ό λΆμνλ κ²μ μ€μΈκ³μ νμμ μ΄ν΄νλλ° λ§€μ° μ€μνλ€. λ€μν κ·Έλν λΆμ κΈ°λ²μ€μ λλ€ μν¬λΌλ κΈ°λ²μ΄ λ§μ‘±μ€λ¬μ΄ μ±λ₯κ³Ό ν¨κ» λ§μ κ·Έλν λ§μ΄λ μμ©μ λ리 νμ©λμ΄ μλ€. κ·Έλ¬λ λλ€μμ μ€μΈκ³ κ·Έλνλ κ·Έ κ·λͺ¨κ° κ΅μ₯ν ν¬κ³ λ€μν λΌλ²¨ μ 보μ ν¨κ» 볡μ‘νκ² ννλλ€. μ ν΅μ μΈ λλ€ μν¬ κΈ°λ°μ κΈ°λ²λ€μ κ³μ°λμ΄ λ§μ΄ μꡬλκ³ , λλ€ μν¬λ₯Ό νλλ° μμ΄μ λ€μν λΌλ²¨ μ 보λ₯Ό μ ν κ³ λ €νμ§ μμ λΌλ²¨λ‘ ννλλ κ·Έλνμ κ³ μ ν νΉμ±μ΄ 무μλκ² λλ€. κ·Έλμ μ΄μ κ°μ΄ 볡μ‘νλ©΄μ λκ·λͺ¨ κ·Έλνμμλ λλ€ μν¬μ μ€μ§μ νμ©μ΄ μ νλμ΄μλ€.
λ³Έ νμ λ
Όλ¬Έμμλ λλ€ μν¬ κΈ°λ°μ λκ·λͺ¨ μ€μΈκ³ κ·Έλν λΆμμ κΈ°μ μ νκ³λ₯Ό ν΄κ²°νκ³ μ νλ€. μ€μΈκ³ κ·Έλνλ κ³ μ ν ꡬ쑰μ νΉμ§λ€μ κ°μ§κ³ μμΌλ©° μ΄λ¬ν ꡬ쑰μ νΉμ§λ€μ μλμ νμ§μ μΈ‘λ©΄μμ λλ€ μν¬μ μ±λ₯μ ν₯μμν€λλ° κΈ°λ°μ΄ λ μ μλ€. μ΄λ¬ν μμ΄λμ΄λ₯Ό νμ©νμ¬, λκ·λͺ¨μ λΌλ²¨μ΄ μλ μΌλ°μ μΈ λ€νΈμν¬μμ λλ€ μν¬ κΈ°λ°μ κ°μΈνλ μ μ λνΉ κ³μ°μ λΉ λ₯΄κ³ , νμ₯μ± μκ³ μ ννκ² κ΅¬νλ κΈ°λ²μ μ μνλ€. λν λΆνΈνλ λ€νΈμν¬ λλ μ§μ λ² μ΄μ€μ κ°μ λΌλ²¨μ΄ μλ κ·Έλνμμ κ°μΈνλ μ μ λνΉκ³Ό κ΄κ³ μΆλ‘ μ μν λλ€ μν¬ κΈ°λ°μ λͺ¨λΈμ μ μνλ€.
λ€μν μ€μΈκ³ κ·Έλνμμ κ΄λ²μν μ€νμ ν΅ν΄ λ³Έ νμ λ
Όλ¬Έμ μν΄ μ μλ λ°©λ²κ³Ό λͺ¨λΈμ ν¨κ³Όμ±μ 보μΈλ€. μ μνλ λ°©λ²μ λ€λ₯Έ κ²½μ κΈ°λ²λ€κ³Ό λΉκ΅νμ λ μ΅λ 100λ°° λ ν° κ·Έλνλ₯Ό μ²λ¦¬ν μ μκ³ , μ΅λ 130λ°° μ κ² λ©λͺ¨λ¦¬λ₯Ό μ¬μ©νλ©΄μ, μ΅λ 9λ°° λΉ λ₯Έ μλλ₯Ό 보μ΄λ©°, κ²°κ³Όμ μΌλ‘ μ μμ΅ κ·λͺ¨μ κ·Έλνμμ λλ€ μν¬ κΈ°λ°μ κ°μΈνλ μ μ λνΉμ μ±κ³΅μ μΌλ‘ ꡬν μ μλ€. λν, μ μνλ λλ€ μν¬ κΈ°λ°μ λͺ¨λΈλ€μ λΆνΈνλ λ€νΈμν¬μ μ§μ λ² μ΄μ€μ κ°μ λΌλ²¨μ΄ μλ κ·Έλνμμ λΆνΈ μμΈ‘, κ°μ μμΈ‘, μ΄μ νμ νμ§, κ΄κ³ μΆλ‘ λ±μ λ€μν μμ©μμ λ€λ₯Έ κ²½μ λͺ¨λΈλ€λ³΄λ€ λ μ’μ μμΈ‘ μ±λ₯μ 보μΈλ€.Chapter1 Overview .... 1
1.1 Motivation .... 1
1.2 Research Statement .... 4
1.2.1 Research Goals and Importance .... 4
1.2.2 Technical Challenges .... 6
1.2.3 Main Approaches .... 7
1.2.4 Contributions .... 9
1.2.5 Overall Impact .... 10
1.3 Thesis Organization .... 11
Chapter2 Background .... 12
2.1 Definitions .... 12
2.1.1 Notations on Graphs .... 12
2.1.2 Random Walk with Restart .... 13
2.2 Related Works .... 15
2.2.1 Previous Methods for RWR in Plain Graphs .... 15
2.2.2 Ranking Models in Signed Networks .... 17
2.2.3 Relational Reasoning Models in Edge-labeled Graphs .... 19
Chapter 3 Fast and Scalable Ranking in Large-scale Plain Graphs .... 21
3.1 Introduction .... 21
3.2 Preliminaries .... 23
3.2.1 Iterative Methods for RWR .... 24
3.2.2 Preprocessing Methods for RWR .... 25
3.3 Proposed Method .... 26
3.3.1 Overview .... 26
3.3.2 BePI-B: Exploiting Graph Characteristics for Node Reordering and Block Elimination .... 28
3.3.3 BePI-B: Incorporating an Iterative Method into Block Elimination .... 32
3.3.4 BePI-S: Sparsifying the Schur Complement .... 34
3.3.5 BePI: Preconditioning a Linear System for the Iterative Method .... 36
3.4 Theoretical Results .... 39
3.4.1 Time Complexity .... 39
3.4.2 Space Complexity .... 40
3.4.3 Accuracy Bound .... 41
3.4.4 Lemmas and Proofs .... 43
3.5 Experiments .... 48
3.5.1 Experimental Settings .... 49
3.5.2 Preprocessing Cost .... 51
3.5.3 Query Cost .... 53
3.5.4 Scalability .... 53
3.5.5 Effects of Sparse Schur Complement and Preconditioning .... 54
3.5.6 Effects of the Hub Selection Ratio .... 57
3.5.7 Accuracy .... 58
3.5.8 Comparison with the-State-of-the-Art Method .... 59
3.6 Summary .... 60
Chapter 4 Personalized Ranking in Signed Graphs .... 61
4.1 Introduction .... 61
4.2 Problem Definition .... 65
4.3 Proposed Method .... 65
4.3.1 Signed Random Walk with Restart Model .... 66
4.3.2 SRWR-Iter: Iterative Algorithm for Signed Random Walk with Restart .... 76
4.3.3 SRWR-Pre: Preprocessing Algorithm for Signed Random Walk with Restart .... 82
4.4 Experiments .... 93
4.4.1 Experimental Settings .... 94
4.4.2 Link Prediction Task .... 96
4.4.3 User Preference Preservation Task .... 99
4.4.4 Troll Identification Task .... 100
4.4.5 Sign Prediction Task .... 104
4.4.6 Effectiveness of Balance Attenuation Factors .... 109
4.4.7 Performance of SRWR-Pre .... 110
4.5 Summary .... 113
Chapter 5 Relational Reasoning in Edge-labeled Graphs .... 114
5.1 Introduction .... 114
5.2 Preliminary .... 116
5.3 Proposed Method .... 118
5.3.1 Label Transition Observation .... 120
5.3.2 Learning Label Transition Probabilities .... 121
5.3.3 Multi-Labeled Random Walk with Restart .... 123
5.3.4 Formulation for MuRWR .... 125
5.3.5 Algorithm for MuRWR .... 127
5.4 Theoretical Results .... 131
5.4.1 Lemma for Solution of Label Transition Probabilities and Convexity .... 131
5.4.2 Lemma for Recursive Equation of MuRWR Score Matrix .... 134
5.4.3 Lemma for Spectral Radius in Convergence Theorem .... 136
5.4.4 Lemma for Complexity Analysis .... 137
5.5 Experiment .... 138
5.5.1 Experimental Settings .... 139
5.5.2 Relation Inference Task .... 140
5.5.3 Effects of Label Weights in MuRWR .... 142
5.5.4 Effects of Restart Probability in MuRWR .... 143
5.5.5 Convergence of MuRWR .... 144
5.6 Summary .... 145
Chapter6 Future Works .... 146
6.1 Fast and Accurate Pseudoinverse Computation .... 146
6.2 Fast and Scalable Signed Network Generation .... 147
6.3 Disk-based Algorithms for Random Walk .... 147
Chapter7 Conclusion .... 149
References .... 151
Appendix .... 166
A.1 Hub-and-Spoke Reordering Method .... 166
A.2 Time Complexity of Sparse Matrix Multiplication .... 167
A.3 Details of Preconditioned GMRES .... 167
A.4 Detailed Description of Evaluation Metrics .... 170
A.4.1 Link Prediction .... 170
A.4.2 Troll Identification .... 171
A.5 Discussion on Relative Trustworthiness of SRWR .... 173
Abstract in Korean .... 176Docto
Efficient Node Proximity and Node Significance Computations in Graphs
abstract: Node proximity measures are commonly used for quantifying how nearby or otherwise related to two or more nodes in a graph are. Node significance measures are mainly used to find how much nodes are important in a graph. The measures of node proximity/significance have been highly effective in many predictions and applications. Despite their effectiveness, however, there are various shortcomings. One such shortcoming is a scalability problem due to their high computation costs on large size graphs and another problem on the measures is low accuracy when the significance of node and its degree in the graph are not related. The other problem is that their effectiveness is less when information for a graph is uncertain. For an uncertain graph, they require exponential computation costs to calculate ranking scores with considering all possible worlds.
In this thesis, I first introduce Locality-sensitive, Re-use promoting, approximate Personalized PageRank (LR-PPR) which is an approximate personalized PageRank calculating node rankings for the locality information for seeds without calculating the entire graph and reusing the precomputed locality information for different locality combinations. For the identification of locality information, I present Impact Neighborhood Indexing (INI) to find impact neighborhoods with nodes' fingerprints propagation on the network. For the accuracy challenge, I introduce Degree Decoupled PageRank (D2PR) technique to improve the effectiveness of PageRank based knowledge discovery, especially considering the significance of neighbors and degree of a given node. To tackle the uncertain challenge, I introduce Uncertain Personalized PageRank (UPPR) to approximately compute personalized PageRank values on uncertainties of edge existence and Interval Personalized PageRank with Integration (IPPR-I) and Interval Personalized PageRank with Mean (IPPR-M) to compute ranking scores for the case when uncertainty exists on edge weights as interval values.Dissertation/ThesisDoctoral Dissertation Computer Science 201
ν° κ·Έλν μμμμ κ°μΈνλ νμ΄μ§ λν¬μ λν λΉ λ₯Έ κ³μ° κΈ°λ²
νμλ
Όλ¬Έ (λ°μ¬) -- μμΈλνκ΅ λνμ : 곡과λν μ κΈ°Β·μ»΄ν¨ν°κ³΅νλΆ, 2020. 8. μ΄μꡬ.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.κ·Έλν
λ΄μμ κ°μΈνλ νμ΄μ§λν¬ (P ersonalized P age R ank, PPR λ₯Ό κ³μ°νλ κ²μ κ²μ , μΆμ² , μ§μλ°κ²¬ λ± μ¬λ¬ λΆμΌμμ κ΄λ²μνκ² νμ©λλ μ€μν μμ
μ΄λ€ . κ°μΈνλ νμ΄μ§λν¬λ₯Ό κ³μ°νλ κ²μ κ³ λΉμ©μ κ³Όμ μ΄ νμνλ―λ‘ , κ°μΈνλ νμ΄μ§λν¬λ₯Ό κ³μ°νλ ν¨μ¨μ μ΄κ³ νμ μ μΈ λ°©λ²λ€μ΄ λ€μ κ°λ°λμ΄μλ€ . κ·Έλ¬λ μλ°±λ§ μ΄μμ λ
Έλλ₯Ό κ°μ§ λμ©λ κ·Έλνμ λν ν¨μ¨μ μΈ κ³μ°μ μ¬μ ν ν΄κ²°λμ§ μμ λ¬Έμ μ΄λ€ . κ·Έμ λνμ¬ , κΈ°μ‘΄ μ μλ μκ³ λ¦¬λ¬λ€μ κ·Έλν κ°±μ μ ν¨μ¨μ μΌλ‘ λ€λ£¨μ§ λͺ»νμ¬ λμ μΌλ‘ λ³ννλ κ·Έλνλ₯Ό λ€λ£¨λ λ°μ νκ³μ μ΄ ν¬λ€ . λ³Έ μ°κ΅¬μμλ λμ μ λ°λλ₯Ό 보μ₯νκ³ μ λ°λλ₯Ό ν΅μ κ°λ₯ν , λΉ λ₯΄κ² μλ ΄νλ κ°μΈνλ νμ΄μ§λν¬ κ³μ° μκ³ λ¦¬λ¬μ μ μνλ€ . μ ν΅μ μΈ κ±°λμ κ³±λ² (Power μ μΆμ°¨κ°μμνλ² (Successive Over Relaxation) κ³Ό μ΄κΈ° μΆμΈ‘ κ° λ³΄μ λ² (Initial Guess μ νμ©ν λ²‘ν° μ¬μ¬μ© μ λ΅μ μ μ©νμ¬ μλ ΄ μλλ₯Ό κ°μ νμλ€ . μ μλ λ°©λ²μ κΈ°μ‘΄ κ±°λμ κ³±λ²μ μ₯μ μΈ λ¨μμ±κ³Ό μλ°μ±μ μ μ§ νλ©΄μ λ μλ ΄μ¨κ³Ό κ³μ°μλλ₯Ό ν¬κ² κ°μ νλ€ . λν κ°μΈνλ νμ΄μ§λν¬ λ²‘ν°μ κ°±μ μ μνμ¬ μ΄μ μ κ³μ° λμ΄ μ μ₯λ 벑ν°λ₯Ό μ¬μ¬μ©ν μ¬ , κ°±μ μ λλ μκ°μ΄ ν¬κ² λ¨μΆλλ€ . λ³Έ λ°©λ²μ μ£Όμ΄μ§ μ€μ°¨ νκ³μ λλ¬νλ μ¦μ κ²°κ³Όκ°μ μ°μΆνλ―λ‘ μ νλμ κ³μ°μκ°μ μ μ°νκ² μ‘°μ ν μ μμΌλ©° μ΄λ νλ³Έ κΈ°λ° μΆμ λ°©λ²μ΄λ μ νν κ°μ μ°μΆνλ μνλ ¬ κΈ°λ° λ°©λ² μ΄ κ°μ§μ§ λͺ»ν νΉμ±μ΄λ€ . μ€ν κ²°κ³Ό , λ³Έ λ°©λ²μ κ±°λμ κ³±λ²μ λΉνμ¬ 20 λ°° μ΄μ λΉ λ₯΄κ² μλ ΄νλ€λ κ²μ΄ νμΈλμμΌλ©° , κΈ° μ μλ μ΅κ³ μ±λ₯ μ μκ³ λ¦¬ λ¬ λ³΄λ€ μ°μν μ±λ₯μ 보μ΄λ κ² λν νμΈλμλ€1 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
- β¦