5,995 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
Fast and Accurate Random Walk with Restart on Dynamic Graphs with Guarantees
Given a time-evolving graph, how can we track similarity between nodes in a
fast and accurate way, with theoretical guarantees on the convergence and the
error? Random Walk with Restart (RWR) is a popular measure to estimate the
similarity between nodes and has been exploited in numerous applications. Many
real-world graphs are dynamic with frequent insertion/deletion of edges; thus,
tracking RWR scores on dynamic graphs in an efficient way has aroused much
interest among data mining researchers. Recently, dynamic RWR models based on
the propagation of scores across a given graph have been proposed, and have
succeeded in outperforming previous other approaches to compute RWR
dynamically. However, those models fail to guarantee exactness and convergence
time for updating RWR in a generalized form. In this paper, we propose OSP, a
fast and accurate algorithm for computing dynamic RWR with insertion/deletion
of nodes/edges in a directed/undirected graph. When the graph is updated, OSP
first calculates offset scores around the modified edges, propagates the offset
scores across the updated graph, and then merges them with the current RWR
scores to get updated RWR scores. We prove the exactness of OSP and introduce
OSP-T, a version of OSP which regulates a trade-off between accuracy and
computation time by using error tolerance {\epsilon}. Given restart probability
c, OSP-T guarantees to return RWR scores with O ({\epsilon} /c ) error in O
(log ({\epsilon}/2)/log(1-c)) iterations. Through extensive experiments, we
show that OSP tracks RWR exactly up to 4605x faster than existing static RWR
method on dynamic graphs, and OSP-T requires up to 15x less time with 730x
lower L1 norm error and 3.3x lower rank error than other state-of-the-art
dynamic RWR methods.Comment: 10 pages, 8 figure
Supervised Random Walks: Predicting and Recommending Links in Social Networks
Predicting the occurrence of links is a fundamental problem in networks. In
the link prediction problem we are given a snapshot of a network and would like
to infer which interactions among existing members are likely to occur in the
near future or which existing interactions are we missing. Although this
problem has been extensively studied, the challenge of how to effectively
combine the information from the network structure with rich node and edge
attribute data remains largely open.
We develop an algorithm based on Supervised Random Walks that naturally
combines the information from the network structure with node and edge level
attributes. We achieve this by using these attributes to guide a random walk on
the graph. We formulate a supervised learning task where the goal is to learn a
function that assigns strengths to edges in the network such that a random
walker is more likely to visit the nodes to which new links will be created in
the future. We develop an efficient training algorithm to directly learn the
edge strength estimation function.
Our experiments on the Facebook social graph and large collaboration networks
show that our approach outperforms state-of-the-art unsupervised approaches as
well as approaches that are based on feature extraction
The Minimum Wiener Connector
The Wiener index of a graph is the sum of all pairwise shortest-path
distances between its vertices. In this paper we study the novel problem of
finding a minimum Wiener connector: given a connected graph and a set
of query vertices, find a subgraph of that connects all
query vertices and has minimum Wiener index.
We show that The Minimum Wiener Connector admits a polynomial-time (albeit
impractical) exact algorithm for the special case where the number of query
vertices is bounded. We show that in general the problem is NP-hard, and has no
PTAS unless . Our main contribution is a
constant-factor approximation algorithm running in time
.
A thorough experimentation on a large variety of real-world graphs confirms
that our method returns smaller and denser solutions than other methods, and
does so by adding to the query set a small number of important vertices
(i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International
Conference on Management of Dat
ํฐ ๊ทธ๋ํ ์์์์ ๊ฐ์ธํ๋ ํ์ด์ง ๋ญํฌ์ ๋ํ ๋น ๋ฅธ ๊ณ์ฐ ๊ธฐ๋ฒ
ํ์๋
ผ๋ฌธ (๋ฐ์ฌ) -- ์์ธ๋ํ๊ต ๋ํ์ : ๊ณต๊ณผ๋ํ ์ ๊ธฐยท์ปดํจํฐ๊ณตํ๋ถ, 2020. 8. ์ด์๊ตฌ.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.๊ทธ๋ํ
๋ด์์ ๊ฐ์ธํ๋ ํ์ด์ง๋ญํฌ (P ersonalized P age R ank, PPR ๋ฅผ ๊ณ์ฐํ๋ ๊ฒ์ ๊ฒ์ , ์ถ์ฒ , ์ง์๋ฐ๊ฒฌ ๋ฑ ์ฌ๋ฌ ๋ถ์ผ์์ ๊ด๋ฒ์ํ๊ฒ ํ์ฉ๋๋ ์ค์ํ ์์
์ด๋ค . ๊ฐ์ธํ๋ ํ์ด์ง๋ญํฌ๋ฅผ ๊ณ์ฐํ๋ ๊ฒ์ ๊ณ ๋น์ฉ์ ๊ณผ์ ์ด ํ์ํ๋ฏ๋ก , ๊ฐ์ธํ๋ ํ์ด์ง๋ญํฌ๋ฅผ ๊ณ์ฐํ๋ ํจ์จ์ ์ด๊ณ ํ์ ์ ์ธ ๋ฐฉ๋ฒ๋ค์ด ๋ค์ ๊ฐ๋ฐ๋์ด์๋ค . ๊ทธ๋ฌ๋ ์๋ฐฑ๋ง ์ด์์ ๋
ธ๋๋ฅผ ๊ฐ์ง ๋์ฉ๋ ๊ทธ๋ํ์ ๋ํ ํจ์จ์ ์ธ ๊ณ์ฐ์ ์ฌ์ ํ ํด๊ฒฐ๋์ง ์์ ๋ฌธ์ ์ด๋ค . ๊ทธ์ ๋ํ์ฌ , ๊ธฐ์กด ์ ์๋ ์๊ณ ๋ฆฌ๋ฌ๋ค์ ๊ทธ๋ํ ๊ฐฑ์ ์ ํจ์จ์ ์ผ๋ก ๋ค๋ฃจ์ง ๋ชปํ์ฌ ๋์ ์ผ๋ก ๋ณํํ๋ ๊ทธ๋ํ๋ฅผ ๋ค๋ฃจ๋ ๋ฐ์ ํ๊ณ์ ์ด ํฌ๋ค . ๋ณธ ์ฐ๊ตฌ์์๋ ๋์ ์ ๋ฐ๋๋ฅผ ๋ณด์ฅํ๊ณ ์ ๋ฐ๋๋ฅผ ํต์ ๊ฐ๋ฅํ , ๋น ๋ฅด๊ฒ ์๋ ดํ๋ ๊ฐ์ธํ๋ ํ์ด์ง๋ญํฌ ๊ณ์ฐ ์๊ณ ๋ฆฌ๋ฌ์ ์ ์ํ๋ค . ์ ํต์ ์ธ ๊ฑฐ๋ญ์ ๊ณฑ๋ฒ (Power ์ ์ถ์ฐจ๊ฐ์์ํ๋ฒ (Successive Over Relaxation) ๊ณผ ์ด๊ธฐ ์ถ์ธก ๊ฐ ๋ณด์ ๋ฒ (Initial Guess ์ ํ์ฉํ ๋ฒกํฐ ์ฌ์ฌ์ฉ ์ ๋ต์ ์ ์ฉํ์ฌ ์๋ ด ์๋๋ฅผ ๊ฐ์ ํ์๋ค . ์ ์๋ ๋ฐฉ๋ฒ์ ๊ธฐ์กด ๊ฑฐ๋ญ์ ๊ณฑ๋ฒ์ ์ฅ์ ์ธ ๋จ์์ฑ๊ณผ ์๋ฐ์ฑ์ ์ ์ง ํ๋ฉด์ ๋ ์๋ ด์จ๊ณผ ๊ณ์ฐ์๋๋ฅผ ํฌ๊ฒ ๊ฐ์ ํ๋ค . ๋ํ ๊ฐ์ธํ๋ ํ์ด์ง๋ญํฌ ๋ฒกํฐ์ ๊ฐฑ์ ์ ์ํ์ฌ ์ด์ ์ ๊ณ์ฐ ๋์ด ์ ์ฅ๋ ๋ฒกํฐ๋ฅผ ์ฌ์ฌ์ฉํ ์ฌ , ๊ฐฑ์ ์ ๋๋ ์๊ฐ์ด ํฌ๊ฒ ๋จ์ถ๋๋ค . ๋ณธ ๋ฐฉ๋ฒ์ ์ฃผ์ด์ง ์ค์ฐจ ํ๊ณ์ ๋๋ฌํ๋ ์ฆ์ ๊ฒฐ๊ณผ๊ฐ์ ์ฐ์ถํ๋ฏ๋ก ์ ํ๋์ ๊ณ์ฐ์๊ฐ์ ์ ์ฐํ๊ฒ ์กฐ์ ํ ์ ์์ผ๋ฉฐ ์ด๋ ํ๋ณธ ๊ธฐ๋ฐ ์ถ์ ๋ฐฉ๋ฒ์ด๋ ์ ํํ ๊ฐ์ ์ฐ์ถํ๋ ์ญํ๋ ฌ ๊ธฐ๋ฐ ๋ฐฉ๋ฒ ์ด ๊ฐ์ง์ง ๋ชปํ ํน์ฑ์ด๋ค . ์คํ ๊ฒฐ๊ณผ , ๋ณธ ๋ฐฉ๋ฒ์ ๊ฑฐ๋ญ์ ๊ณฑ๋ฒ์ ๋นํ์ฌ 20 ๋ฐฐ ์ด์ ๋น ๋ฅด๊ฒ ์๋ ดํ๋ค๋ ๊ฒ์ด ํ์ธ๋์์ผ๋ฉฐ , ๊ธฐ ์ ์๋ ์ต๊ณ ์ฑ๋ฅ ์ ์๊ณ ๋ฆฌ ๋ฌ ๋ณด๋ค ์ฐ์ํ ์ฑ๋ฅ์ ๋ณด์ด๋ ๊ฒ ๋ํ ํ์ธ๋์๋ค1 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
Adaptive image retrieval using a graph model for semantic feature integration
The variety of features available to represent multimedia data constitutes a rich pool of information. However, the plethora of data poses a challenge in terms of feature selection and integration for effective retrieval. Moreover, to further improve effectiveness, the
retrieval model should ideally incorporate context-dependent feature representations to allow for retrieval on a higher semantic level. In this paper we present a retrieval model and learning framework for the purpose of interactive information retrieval. We describe
how semantic relations between multimedia objects based on user interaction can be learnt and then integrated with visual and textual features into a unified framework. The framework models both feature similarities and semantic relations in a single graph. Querying in this model is implemented using the theory of random walks. In addition, we present ideas to implement short-term learning from relevance feedback. Systematic experimental results validate the effectiveness of the proposed approach for image retrieval. However, the model is not restricted to the image domain and could easily be employed for retrieving multimedia data (and even a combination of different domains, eg images, audio and text documents)
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
์ค์ธ๊ณ ๊ทธ๋ํ ํน์ง์ ํ์ฉํ ๋๋ค ์ํฌ ๊ธฐ๋ฐ ๋๊ท๋ชจ ๊ทธ๋ํ ๋ง์ด๋
ํ์๋
ผ๋ฌธ(๋ฐ์ฌ)--์์ธ๋ํ๊ต ๋ํ์ :๊ณต๊ณผ๋ํ ์ปดํจํฐ๊ณตํ๋ถ,2020. 2. ๊ฐ์ .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.๋ค์ํ ์ค์ธ๊ณ ์์ฐ ํ์์์์ ๊ด๊ณ๋ค์ ์์
๋คํธ์ํฌ, ํ์ดํผ๋งํฌ ๋คํธ์ํฌ์ ๋จ๋ฐฑ์ง ์ํธ์์ฉ ๋คํธ์ํฌ์ ๊ฐ์ด ์ ์ ๊ณผ ๊ฐ์์ ๊ทธ๋ํ๋ก ํํ๋๋ค. ์ด๋ฌํ ๋คํธ์ํฌ๋ฅผ ๋ถ์ํ๋ ๊ฒ์ ์ค์ธ๊ณ์ ํ์์ ์ดํดํ๋๋ฐ ๋งค์ฐ ์ค์ํ๋ค. ๋ค์ํ ๊ทธ๋ํ ๋ถ์ ๊ธฐ๋ฒ์ค์ ๋๋ค ์ํฌ๋ผ๋ ๊ธฐ๋ฒ์ด ๋ง์กฑ์ค๋ฌ์ด ์ฑ๋ฅ๊ณผ ํจ๊ป ๋ง์ ๊ทธ๋ํ ๋ง์ด๋ ์์ฉ์ ๋๋ฆฌ ํ์ฉ๋์ด ์๋ค. ๊ทธ๋ฌ๋ ๋๋ค์์ ์ค์ธ๊ณ ๊ทธ๋ํ๋ ๊ทธ ๊ท๋ชจ๊ฐ ๊ต์ฅํ ํฌ๊ณ ๋ค์ํ ๋ผ๋ฒจ ์ ๋ณด์ ํจ๊ป ๋ณต์กํ๊ฒ ํํ๋๋ค. ์ ํต์ ์ธ ๋๋ค ์ํฌ ๊ธฐ๋ฐ์ ๊ธฐ๋ฒ๋ค์ ๊ณ์ฐ๋์ด ๋ง์ด ์๊ตฌ๋๊ณ , ๋๋ค ์ํฌ๋ฅผ ํ๋๋ฐ ์์ด์ ๋ค์ํ ๋ผ๋ฒจ ์ ๋ณด๋ฅผ ์ ํ ๊ณ ๋ คํ์ง ์์ ๋ผ๋ฒจ๋ก ํํ๋๋ ๊ทธ๋ํ์ ๊ณ ์ ํ ํน์ฑ์ด ๋ฌด์๋๊ฒ ๋๋ค. ๊ทธ๋์ ์ด์ ๊ฐ์ด ๋ณต์กํ๋ฉด์ ๋๊ท๋ชจ ๊ทธ๋ํ์์๋ ๋๋ค ์ํฌ์ ์ค์ง์ ํ์ฉ์ด ์ ํ๋์ด์๋ค.
๋ณธ ํ์ ๋
ผ๋ฌธ์์๋ ๋๋ค ์ํฌ ๊ธฐ๋ฐ์ ๋๊ท๋ชจ ์ค์ธ๊ณ ๊ทธ๋ํ ๋ถ์์ ๊ธฐ์ ์ ํ๊ณ๋ฅผ ํด๊ฒฐํ๊ณ ์ ํ๋ค. ์ค์ธ๊ณ ๊ทธ๋ํ๋ ๊ณ ์ ํ ๊ตฌ์กฐ์ ํน์ง๋ค์ ๊ฐ์ง๊ณ ์์ผ๋ฉฐ ์ด๋ฌํ ๊ตฌ์กฐ์ ํน์ง๋ค์ ์๋์ ํ์ง์ ์ธก๋ฉด์์ ๋๋ค ์ํฌ์ ์ฑ๋ฅ์ ํฅ์์ํค๋๋ฐ ๊ธฐ๋ฐ์ด ๋ ์ ์๋ค. ์ด๋ฌํ ์์ด๋์ด๋ฅผ ํ์ฉํ์ฌ, ๋๊ท๋ชจ์ ๋ผ๋ฒจ์ด ์๋ ์ผ๋ฐ์ ์ธ ๋คํธ์ํฌ์์ ๋๋ค ์ํฌ ๊ธฐ๋ฐ์ ๊ฐ์ธํ๋ ์ ์ ๋ญํน ๊ณ์ฐ์ ๋น ๋ฅด๊ณ , ํ์ฅ์ฑ ์๊ณ ์ ํํ๊ฒ ๊ตฌํ๋ ๊ธฐ๋ฒ์ ์ ์ํ๋ค. ๋ํ ๋ถํธํ๋ ๋คํธ์ํฌ ๋๋ ์ง์ ๋ฒ ์ด์ค์ ๊ฐ์ ๋ผ๋ฒจ์ด ์๋ ๊ทธ๋ํ์์ ๊ฐ์ธํ๋ ์ ์ ๋ญํน๊ณผ ๊ด๊ณ ์ถ๋ก ์ ์ํ ๋๋ค ์ํฌ ๊ธฐ๋ฐ์ ๋ชจ๋ธ์ ์ ์ํ๋ค.
๋ค์ํ ์ค์ธ๊ณ ๊ทธ๋ํ์์ ๊ด๋ฒ์ํ ์คํ์ ํตํด ๋ณธ ํ์ ๋
ผ๋ฌธ์ ์ํด ์ ์๋ ๋ฐฉ๋ฒ๊ณผ ๋ชจ๋ธ์ ํจ๊ณผ์ฑ์ ๋ณด์ธ๋ค. ์ ์ํ๋ ๋ฐฉ๋ฒ์ ๋ค๋ฅธ ๊ฒฝ์ ๊ธฐ๋ฒ๋ค๊ณผ ๋น๊ตํ์ ๋ ์ต๋ 100๋ฐฐ ๋ ํฐ ๊ทธ๋ํ๋ฅผ ์ฒ๋ฆฌํ ์ ์๊ณ , ์ต๋ 130๋ฐฐ ์ ๊ฒ ๋ฉ๋ชจ๋ฆฌ๋ฅผ ์ฌ์ฉํ๋ฉด์, ์ต๋ 9๋ฐฐ ๋น ๋ฅธ ์๋๋ฅผ ๋ณด์ด๋ฉฐ, ๊ฒฐ๊ณผ์ ์ผ๋ก ์ ์ญ์ต ๊ท๋ชจ์ ๊ทธ๋ํ์์ ๋๋ค ์ํฌ ๊ธฐ๋ฐ์ ๊ฐ์ธํ๋ ์ ์ ๋ญํน์ ์ฑ๊ณต์ ์ผ๋ก ๊ตฌํ ์ ์๋ค. ๋ํ, ์ ์ํ๋ ๋๋ค ์ํฌ ๊ธฐ๋ฐ์ ๋ชจ๋ธ๋ค์ ๋ถํธํ๋ ๋คํธ์ํฌ์ ์ง์ ๋ฒ ์ด์ค์ ๊ฐ์ ๋ผ๋ฒจ์ด ์๋ ๊ทธ๋ํ์์ ๋ถํธ ์์ธก, ๊ฐ์ ์์ธก, ์ด์ ํ์ ํ์ง, ๊ด๊ณ ์ถ๋ก ๋ฑ์ ๋ค์ํ ์์ฉ์์ ๋ค๋ฅธ ๊ฒฝ์ ๋ชจ๋ธ๋ค๋ณด๋ค ๋ ์ข์ ์์ธก ์ฑ๋ฅ์ ๋ณด์ธ๋ค.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
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