All-pairs SimRank calculation is a classic SimRank problem. However, all-pairs algorithms suffer from efficiency issues and accuracy issues. In this paper, we convert the non-linear simrank calculation into a new simple closed formulation of linear system. And we come up with a sequence of novel algorithms to efficiently solve the linear system with accuracy guarantees. To reduce the memory consumption and improve the computational efficiency, we build a hierarchical framework to calculate the all-pairs SimRank scores, which includes locally coarse calculation and globally refine calculation. We first solve the local linear systems generated from the subgraphs, then we refine the SimRank scores on the full graph from the residuals of the local structures. We also show that our algorithms outperform the state-of-the-art all-pairs SimRank computation algorithms on real graphs.

SimRank is a model that measures the structural similarity between any two nodes in a directed graph. Its main idea is that if two nodes in the graph are referenced by similar nodes, then these two nodes are similar. SimRank model calculates the similarity based on the full graph structure information of two nodes. According to SimRank’s definition, SimRank is a nonlinear and recursive model. In recent years, research on the SimRank algorithms has mainly focused on rapid updates of All-Pairs SimRank on dynamic graphs. However, existing algorithms now have the following problems: algorithms based on random walk cannot update quickly based on existing results, and they need to recalculate for each changes; at the same time, most iterative algorithms cannot guarantee the maximum calculation error, because they are approximate algorithms. In this paper, we first derive a close formed linear system from the SimRank definition on dynamic graphs, then we design an algorithm to get the numerical solution of the linear system, finally through experiments in real graphs, it has been shown that this algorithm performs better in terms of time and spatial complexity than the state-of-the-art algorithms on dynamic graphs.

Although much effort has been made to implement Factorization Machine (FM) on distributed frameworks, most of them achieve bad model performance or low efficiency. In this paper, we propose a new distributed block coordinate descent algorithm to learn FM. In addition, a distributed pre-computation mechanism incorporated with an optimized Parameter Server framework is designed to avoid the massive repetitive calculations and further reduce the communication cost. Systematically, we evaluate the proposed distributed algorithm on three different genres of datasets for prediction. The experimental results show that the proposed algorithm achieves significantly better performance (3.8

传统矩阵分解方法因其算法的高可扩展性和较好的性能等特点,在预测、推荐等领域有着广泛的应用.然而大数据环境下,更多上下文因素的获取变得可能,传统矩阵分解方法缺乏对上下文信息的有效利用.在此背景下,因子分解机模型提出并流行.为了更好地把握因子分解机模型的发展脉络,促进因子分解机模型与应用相结合,针对因子分解机模型及其算法进行了综述.首先,对因子分解机模型的提出进行了溯源,介绍了从传统矩阵分解到因子分解机模型的演化过程;其次,从模型准确率和效率两方面对因子分解机模型存在的基本问题和近年来的研究进展进行了总结,然后综述了适用于因子分解机模型求解的4种代表性优化算法;最后分析了因子分解机模型目前仍存在的问题,提出了可能的解决思路,并对未来的研究方向进行了展望.

SimRank是一种衡量有向图中任意两节点间结构相似度的模型,其主要思想为,若图中两个节点被相似节点引用,则这两个节点相似.SimRank计算的相似度被广泛应用到网络图聚类、近似查询和协同过滤等领域.SimRank计算模型是一个递归模型,其计算时间、空间复杂度非常高,很难应用于大规模图计算.过去十几年,研究者们针对大规模图提出了许多高效或近似计算的SimRank计算算法.本文首先介绍SimRank模型的描述,以及常见的SimRank计算问题定义,然后按照计算方式将这些算法分为迭代法、非迭代法与随机游走法三类;将非迭代法分为基于矩阵运算求解、基于节点对图求解以及基于线性表示求解,将随机游走法分为基于不同索引结构求解、基于不同抽样方式求解以及其他随机游走算法;介绍了这些算法的基本概念、计算原理以及算法特点;分析了随机游走法与迭代法、非迭代法之间的关系;对各种算法的时间复杂度、空间复杂度、计算精确度以及可扩展性进行了论述;在此基础总结了这些SimRank算法所对应的计算场景,主要包括单点对/单源(Single Pair/Single Source)查询问题、全体/部分节点对(All Pair/Partial Pair)计算问题以及查询问题.最后对不同算法实验中图的规模进行了总结,并对大规模图上的SimRank计算方法进行了总结和展望.

The edges of a network can be divided into positive and negative relationships according to their potential meanings.When the edges of a network are signed with plus or minus signs respectively,a signed network can be formed.Signed networks are widely used in many fields such as sociology,informatics and biology.Hence,the sign prediction problem in signed networks has become one of research hot spots.In large dataset,the scalability of sign prediction algorithm is still a great challenge.There are many related works in the distributed design of signed network prediction methods,however,the computation efficiency is still limited by the fundamental server/client framework.This paper proposes client to client distributed framework (C2CDF).Compared with traditional server/client framework,C2CDF is a completely new client-to-client framework which can release the bandwidth pressure by abandoning the server node and allowing the communications between the client nodes.The Experiments on sign prediction in signed social networks,prediction in click-through rate and prediction in forest type show that C2CDF is a general approach which can not only be applied in sign prediction in signed network but also be used in the other prediction areas.In these three datasets,C2CDF can achieve better performance than FM inferred by the traditional SGD algorithm.C2CDF also achieves a 2.3-3.3x speed-up over the method implemented under the server/client framework while obtains a better accuracy performance than the method compared against.

Factorization Machines (FMs) offers attractive performance by combining low-rank data vectors and heuristic features. However, it suffers from the growth of the dataset and the model complexity. Although much efforts have been made to distribute FMs over multiple machines, the computation efficiency is still limited by the foundational master-slave framework. In this paper, we propose CDSFM, which leverages Stochastic Gradient Langevin Dynamics (SGLD) to optimize FMs, and is distributed into a completely new circular framework. Experiments on two genres of datasets show that CDSFM can achieves a 2.3–4.7 × speed-up over the comparison methods while obtains better performance.