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

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

PLAZA 4.0 : an integrative resource for functional, evolutionary and comparative plant genomics

PLAZA (https://bioinformatics.psb.ugent.be/plaza) is a plant-oriented online resource for comparative, evolutionary and functional genomics. The PLAZA platform consists of multiple independent instances focusing on different plant clades, while also providing access to a consistent set of reference species. Each PLAZA instance contains structural and functional gene annotations, gene family data and phylogenetic trees and detailed gene colinearity information. A user-friendly web interface makes the necessary tools and visualizations accessible, specific for each data type. Here we present PLAZA 4.0, the latest iteration of the PLAZA framework. This version consists of two new instances (Dicots 4.0 and Monocots 4.0) providing a large increase in newly available species, and offers access to updated and newly implemented tools and visualizations, helping users with the ever-increasing demands for complex and in-depth analyzes. The total number of species across both instances nearly doubles from 37 species in PLAZA 3.0 to 71 species in PLAZA 4.0, with a much broader coverage of crop species (e.g. wheat, palm oil) and species of evolutionary interest (e.g. spruce, Marchantia). The new PLAZA instances can also be accessed by a programming interface through a RESTful web service, thus allowing bioinformaticians to optimally leverage the power of the PLAZA platform

AUC Optimisation and Collaborative Filtering

In recommendation systems, one is interested in the ranking of the predicted items as opposed to other losses such as the mean squared error. Although a variety of ways to evaluate rankings exist in the literature, here we focus on the Area Under the ROC Curve (AUC) as it widely used and has a strong theoretical underpinning. In practical recommendation, only items at the top of the ranked list are presented to the users. With this in mind, we propose a class of objective functions over matrix factorisations which primarily represent a smooth surrogate for the real AUC, and in a special case we show how to prioritise the top of the list. The objectives are differentiable and optimised through a carefully designed stochastic gradient-descent-based algorithm which scales linearly with the size of the data. In the special case of square loss we show how to improve computational complexity by leveraging previously computed measures. To understand theoretically the underlying matrix factorisation approaches we study both the consistency of the loss functions with respect to AUC, and generalisation using Rademacher theory. The resulting generalisation analysis gives strong motivation for the optimisation under study. Finally, we provide computation results as to the efficacy of the proposed method using synthetic and real data