Link Prediction via Matrix Completion

Inspired by practical importance of social networks, economic networks, biological networks and so on, studies on large and complex networks have attracted a surge of attentions in the recent years. Link prediction is a fundamental issue to understand the mechanisms by which new links are added to the networks. We introduce the method of robust principal component analysis (robust PCA) into link prediction, and estimate the missing entries of the adjacency matrix. On one hand, our algorithm is based on the sparsity and low rank property of the matrix, on the other hand, it also performs very well when the network is dense. This is because a relatively dense real network is also sparse in comparison to the complete graph. According to extensive experiments on real networks from disparate fields, when the target network is connected and sufficiently dense, whatever it is weighted or unweighted, our method is demonstrated to be very effective and with prediction accuracy being considerably improved comparing with many state-of-the-art algorithms

Temporal effects in trend prediction: identifying the most popular nodes in the future

Prediction is an important problem in different science domains. In this paper, we focus on trend prediction in complex networks, i.e. to identify the most popular nodes in the future. Due to the preferential attachment mechanism in real systems, nodes' recent degree and cumulative degree have been successfully applied to design trend prediction methods. Here we took into account more detailed information about the network evolution and proposed a temporal-based predictor (TBP). The TBP predicts the future trend by the node strength in the weighted network with the link weight equal to its exponential aging. Three data sets with time information are used to test the performance of the new method. We find that TBP have high general accuracy in predicting the future most popular nodes. More importantly, it can identify many potential objects with low popularity in the past but high popularity in the future. The effect of the decay speed in the exponential aging on the results is discussed in detail

링크 예측을 이용한 금융시장 복잡계 네트워크 분석

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2020. 8. 장우진.Financial risk sets off a chain reaction in the market and leads to a collapse of the system, called a domino effect. Since the U.S. subprime mortgage crisis in 2008 hit economies across the world, it has emerged important research fields to understand and analyze the financial system properly to deal with financial risk. Econophysics is an interdisciplinary research field to explain the stylized facts in financial systems that are unexplainable by traditional financial theories. In particular, the complex network models that represent a system by nodes and links are widely applied regardless of research areas. However, since the existing complex network models for financial markets usually end up in confirming empirical results such as a structural change in the network and diffusion paths of risk, based on historical data, it has limitations to suggest direct alternatives. To cope with these limitations, this dissertation proposes a link prediction model based on the real effective exchange rate (REER) that reveals the relationships clearly between the compositions. At first, it is confirmed that the network successfully mimics the market to ensure the validity of the network structure prediction. The results show that the return of REER has fat-tailed distributions whose tails are not exponentially bounded and follow a power-law. Also, for the analysis, the changes are focused on cross-sectional topology and time-varying properties of the network during the U.S. subprime mortgage crisis, the European debt crisis, and the Chinese stock market turbulence. The result implies that the network appropriately describes the market by showing the significant increments in out-degrees and in-degrees of the originating continents of the crises. Secondly, the Weighted Causality Link Prediction (WCLP) model is proposed to predict future possible links by measuring the similarities between different nodes. This model has differentiations that it measures the strength of directed Granger causality directions as effect sizes based on $F$-statistics, while the existing models are based on correlations. The experiment is conducted under the hypothesis that the intensity of connections is different from each other and maintains longer when the effect size is larger. The higher prediction accuracy is observed rather than that of unweighted or correlation-based weighted models by showing the statistical significance of higher Area Under Curve (AUC) in every aspects. Finally, a decision making model for investment is proposed based on the results of the link prediction. Once the portfolio is composed of stocks located in the periphery of the PMFG, it distributes the risk due to the low correlation between assets. However, the correlation does not represent the relationship by time lags since it implies only the extent of association between them. Therefore, this dissertation proposes the Weighted Causality Planar Graph (WCPG) that is improved from the Planar Correlation Planar Graph (PCPG) model. It differs from the existing models in that it considers directions and strength of links based on the similarity score between assets. As a result, the proposed model improves the performance in terms of risk-adjusted return compared to the benchmarks. Especially, it has an advantage in long-term investment for over 6 months. In conclusion, the contributions of this dissertation involve the development of an effective link prediction model based on the effect size and the attempt to suggest a decision-making model for investment.금융 시장에서 발생하는 위험은 하나의 금융 체계(System)에서 연쇄 작용으로 이어지며 이것은 곧 시스템의 붕괴로 이어진다. 세계 경제에 큰 타격을 주었던 미국의 서브프라임 모기지 사태 이후 위기 대처 능력 제고를 위해 금융 체계를 올바르게 이해하고 분석하는 것이 매우 중요한 과제로 떠올랐다. 전통적인 금융 위험 관리 이론으로 설명되지 않는 정형화된 사실(stylized facts)들의 발견으로 새롭게 등장한 연구 분야가 경제물리학(Econophysics)이다. 특히, 점(노드)과 선(링크)으로 하나의 체계를 나타내는 복잡계 네트워크 모형은 분야를 막론하고 다양하게 응용되고 있다. 하지만 금융 시장에 대한 기존의 복잡계 네트워크 모형은 대부분 과거 데이터를 기반으로 네트워크 구조 변화, 위험의 확산 경로와 같은 실증적 연구결과를 확인하는 데 그쳐 위험에 대비한 능동적인 대안을 제시하는데 제약이 존재한다. 본 학위논문은 이러한 결점을 보완하고자 네트워크 구성 요소 간 관계가 명확하게 드러나는 환율 데이터 기반의 네트워크 링크 예측 모형을 제시하였다. 먼저, 네트워크 구조 예측의 타당성을 확보하기 위해 네트워크가 시장을 성공적으로 모방하는지 확인하였다. 그 결과 실질실효환율 데이터는 두꺼운 꼬리(Fat-tailed) 분포를 가지며 꼬리 분포가 멱함수(Power-law) 분포를 따르는 것을 확인하였다. 또한, 미국의 서브프라임 모기지 사태, 유럽 부채 위기, 중국 주식 시장 위기 동안 네트워크의 단면(cross-sectional) 토폴로지와 시간에 따라 변화하는 성질을 관찰하였다. 위기 발생 대륙에서 증가하는 링크의 수량을 봤을 때 제시된 그레인저-인과관계(Granger causality) 네트워크가 시장을 적절히 나타내고 있었다. 두 번째로, 네트워크에서 새롭게 생겨날 수 있는 링크를 예측하기 위해 구성 요소 간 유사도를 측정하는 Weighted Causality Link Prediction (WCLP) 모형을 제시하였다. 기존의 많은 네트워크 모형이 구성 요소 간 상관관계에 기반하였다면, 본 모형은 그레인저 인과관계를 측정하여 네트워크의 방향성을 함께 고려하고, 연결 강도를 통계량에 기반한 효과 크기(Effect size)로 나타내었다는 점에서 그 차별성이 있다. 네트워크의 링크는 서로 다른 연결 강도를 가지며 효과 크기가 클 수록 오래 유지된다는 가설 하에 실험을 진행하였다. 그 결과, 높은 수신자 조작 특성 곡선의 면적 (Area Under the receiver operating characteristic Curve, AUC) 값을 가져 비가중치(Unweighted) 또는 상관관계 기반 유클리드 거리(Euclidean distance)를 가중치를 이용한 기존 모형들에 비해 통계적으로 개선된 예측 성능을 보였다. 마지막으로, 네트워크 링크 예측 결과를 기반으로 미국 금융 시장에서의 투자 의사 결정 모형을 제시하였다. PMFG의 주변부에 위치하는 종목으로 포트폴리오가 구성되면, 자산 간의 낮은 상관관계는 포트폴리오 위험의 분산화를 가능하게 한다. 하지만 상관관계는 두 변수 간 연관된 정도만을 나타내므로 시차를 두고 나타나는 인과관계를 나타내지 못한다는 단점이 있다. 따라서 본 학위논문에서는 기존의 Partial Correlation Planar Graph (PCPG) 모형에서 개선 된 새로운 그래프를 제시하고, Weighted Causality Planar Graph (WCPG)라고 명명한다. WCPG는 링크 예측을 통해 얻은 자산 간 유사도를 이용하여 만들어지며 방향성과 세기가 함께 고려된다는 점에서 기존 모형과 차별성이 있다. 그 결과, 위험 조정 수익률 측면에서 제시된 모형이 기존의 네트워크 모형 대비 개선된 성능을 보이며 특히 6개월 이상의 장기 투자에서 강점을 가졌다. 결론적으로 본 학위논문은 효과적인 링크 예측 모형을 효과 크기와 결부하여 개선된 모형을 제시하고 투자 의사 결정을 위한 모형에 응용하였다는 점에서 그 의의를 찾을 수 있다.Chapter 1 Introduction 1 1.1 Problem Description 1 1.2 Motivations of Research 5 1.3 Organization of the Thesis 7 Chapter 2 Literature Review 9 2.1 Network models 9 2.2 Link Prediction 11 2.3 Portfolio optimization 12 Chapter 3 Time-varying Granger Causality Network 15 3.1 Overview 15 3.2 Architecture of Time-varying Granger Causality Network 16 3.2.1 Granger Causality Direction 16 3.2.2 Granger Causality Network 18 3.2.3 Measures of Granger Causality Network 20 3.3 Data description 21 3.4 Results 25 3.4.1 Cross-sectional Topology of REER Networks 25 3.4.2 Time-varying Properties of REER Networks 38 3.5 Summary and Discussion 44 Chapter 4 Link Prediction 47 4.1 Overview 47 4.2 Benchmarks for Link Prediction 48 4.2.1 Unweighted Measures 48 4.2.2 Weighted Measures 57 4.3 Proposed measures 59 4.4 Results 61 4.4.1 Evaluation of Link Prediction 61 4.4.2 Result of Link Prediction 63 4.5 Summary and Discussion 69 Chapter 5 Application of Link Prediction 71 5.1 Overview 71 5.2 Benchmark models 72 5.2.1 Classical models 72 5.2.2 Planar Maximally Filtered Graph(PMFG) 73 5.3 Weighted Causality Planar Graph(WCPG) 76 5.3.1 Realization of WCPG 76 5.4 Data description 78 5.5 Results 79 5.5.1 Evaluation measures 79 5.5.2 Evaluation of portfolio strategies 82 5.6 Summary and Discussion 92 Chapter 6 Concluding Remarks 95 6.1 Contributions and Limitations 95 6.2 Future Work 98 Bibliography 101 Appendix 117 국문초록 125Docto