2 research outputs found
ν° κ·Έλν μμμμ κ°μΈνλ νμ΄μ§ λν¬μ λν λΉ λ₯Έ κ³μ° κΈ°λ²
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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