矩阵补全模型及其算法研究综述

近年来,随着压缩感知技术在信号处理领域的巨大成功,由其衍生而来的矩阵补全技术也日益成为机器学习领域的研究热点,诸多研究者针对矩阵补全问题展开了大量卓有成效的研究.为了更好地把握矩阵补全技术的发展规律,促进矩阵补全理论与工程应用相结合,本文针对矩阵补全模型及其算法进行综述.首先对矩阵补全技术进行溯源,介绍了从压缩感知到矩阵补全的自然演化历程,指出压缩感知理论的发展为矩阵补全理论的形成奠定了基础;其次从非凸非光滑秩函数松弛的角度将现有矩阵补全模型进行分类,旨在为面向具体应用的矩阵补全问题建模提供思路;接着综述了适用于矩阵补全模型求解的代表性优化算法,其目的在于从本质上理解各种矩阵补全模型优化技巧,从而有利于面向应用问题的矩阵补全新模型求解;最后分析了矩阵补全模型及其算法目前存在的问题,提出了这些问题可能的解决思路,并对未来研究方向进行了展望.     

基于矩阵分解的社交网络正则化推荐模型

社交网站的快速发展和普及使得实现高效的好友推荐成为了一个热点问题,而矩阵分解算法是被业界广泛采用的方法.虽然传统的矩阵分解算法能够带来良好的效果,但是仍然存在一些问题.首先,算法没有充分利用用户之间的社交网络结构化关系;其次,算法依赖的用户-物品评分矩阵只有二级评分不能充分表达用户的喜好.提出了一种基于矩阵分解的社交网络正则化推荐模型,利用社交网络中用户的近邻关系进行建模,并将其作为一种辅助信息融合到矩阵分解模型当中,该模型能够解决传统矩阵分解面临的问题.通过在腾讯微博数据集上进行实验对比,验证了本文提出的方法与传统的推荐方法相比能取得更高的推荐平均准确度.     

基于用户聚类和移动上下文的矩阵分解推荐算法研究

随着移动互联网技术的快速发展,越来越多的用户通过移动设备获取移动信息和服务,导致信息过载问题日益凸出。针对目前上下文感知推荐算法中存在的数据稀疏性差、上下文信息融入不够、用户相似性度量被忽略等问题,提出一种基于用户聚类和移动上下文的矩阵分解推荐算法。该算法通过利用k-means对用户聚类找到偏好相似的用户簇,求出每簇中并对 用户所处上下文之间的相似度并对其进行排序,由此找出与目标用户偏好和上下文均相似的用户集合,借助该集合改进传统矩阵分解模型损失函数,并以此为基准进行评分预测和推荐。仿真实验结果表明,所提算法可有效提高预测评分的准确度。     

融合多种数据信息的餐馆推荐模型

餐馆推荐可以利用用户的签到信息、时间上下文、地理上下文、餐馆属性信息以及用户的人口统计信息等挖掘用户的饮食偏好,为用户生成餐馆推荐列表.为了更加有效地融合这些数据信息,提出一种融合了多种数据信息的餐馆推荐模型,该模型首先利用签到信息和时间上下文构建“用户-餐馆-时间片”的三维张量,同时利用其他数据信息挖掘若干用户相似关系矩阵和餐馆相似关系矩阵;然后,在概率张量分解的基础上同时对这些关系矩阵进行分解,并利用BPR优化准则和梯度下降算法进行模型求解;最后得到预测张量,从而为目标用户在不同时间片生成相应的餐馆推荐列表.通过在两个真实数据集上的实验结果表明：相比于目前存在的餐馆推荐模型,所提出的模型有着更好的推荐效果和可接受的运行时间,并且缓解了数据稀疏性对推荐效果的影响.     

基于高阶偏差的因子分解机推荐算法

在推荐系统中,因评分尺度差异而造成的偏差问题一直影响着协同过滤算法的预测准确性。其中针对矩阵因子分解算法中的偏差问题,本文提出一种基于高阶偏差的因子分解机算法。该算法首先按照评分偏差的现实特征对用户和项目进行划分,再将偏差类别作为辅助特征集成到因子分解机中,实现了评分预测中不同偏差用户、项目的高阶交互。在Movielens数据集上的实验结果表明,相比传统矩阵因子分解算法,本文提出的算法具有更低的预测误差,体现了其更好的推荐性能。     

基于词项关联关系与归一化割加权的微博用户兴趣模型

提出一种基于词项关联关系与归一化割加权非负矩阵分解的微博用户兴趣模型构建方法.该方法首先基于词分布上下文语义相关性来建立词项关联关系矩阵刻画词项间相似度,然后应用归一化割加权非负矩阵分解算法获取用户—主题矩阵,产生用户感兴趣的微博主题聚类结果.实验表明,此方法能有效地进行微博主题聚类,并支持微博用户兴趣模型构建.     

融合社交信息的矩阵分解推荐方法研究综述

随着社交网络的发展,融合社交信息的推荐成为推荐领域中的一个研究热点.基于矩阵分解的协同过滤推荐方法（简称为矩阵分解推荐方法）因其算法可扩展性好及灵活性高等诸多特点,成为研究人员在其基础之上进行社交推荐模型构建的重要原因.本文围绕基于矩阵分解的社交推荐模型,依据模型的构建方式对社交推荐模型进行综述.在实际数据上对已有代表性社交推荐方法进行对比,分析各种典型社交推荐模型在不同视角下的性能（如整体用户、冷启动用户、长尾物品）.最后,分析基于矩阵分解的社交推荐模型及其求解算法存在的问题,并对未来研究方向与发展趋势进行了展望.     

基于上下文多维度的移动用户偏好动态分析方法

移动用户偏好的动态分析由于引入了上下文数据,使得原有的用户-项目二维矩阵将扩展为用户-项目-上下文的三维矩阵。根据多维矩阵中低秩分解理论,可以简化数据的分析,但是其移动用户偏好动态分析的自学习方法没有充分利用多维矩阵的低秩分解性质。针对此问题,提出了基于多维度上下文的张量低秩分解的自学习方法,此方法基于张量的平行因子分解性质,加快了算法的收敛速度,降低了数据分析的复杂度。仿真结果验证了算法在移动用户偏好估计精度方面的有效性。     

融合评论文本和社交网络的矩阵分解推荐方法

基于矩阵分解的推荐方法易受到数据稀疏性问题的影响,常见的解决办法是向矩阵分解模型中融入评论文本信息,但是这类方法通常假设用户是独立存在的,忽略了用户之间的社交关系.现实世界中用户的行为与喜好往往会受到其信任好友的影响,因此本文提出一种融合评论文本和社交网络的矩阵分解推荐方法(Review and social probabilistic matrix factorization, RSPMF).首先设计了深度神经网络模型用于学习评论文本的上下文特征;其次,设计了信任传播模型用于根据社交好友的特征修正用户的潜在隐特征;最后将上述两种模型以正则化方式融入概率矩阵分解模型,通过训练模型获取用户与物品之间的内在关系并实现物品推荐.在公开的真实数据集Yelp上进行了实验,并与多种前沿的算法进行了性能对比,结果表明本文提出的RSPMF方法具有良好的推荐性能.     

基于边界矩阵低阶近似和近邻模型的协同过滤算法

为解决矩阵分解应用到协同过滤算法的局限性和准确率等问题,提出基于边界矩阵低阶近似（BMA）和近邻模型的协同过滤算法（BMAN-CF）来提高物品评分预测的准确率。首先,引入BMA的矩阵分解算法,挖掘子矩阵的隐含特征信息,提高近邻集合查找的准确率;然后,根据传统基于用户和基于物品的协同过滤算法分别预测出目标用户对目标物品的评分,利用平衡因子和控制因子动态平衡两个预测结果,得到目标用户对物品的评分;最后,利用MapReduce计算框架的特点,对数据进行分块,将该算法在Hadoop环境下并行化。实验结果表明,BMAN-CF比其他矩阵分解算法有更高的评分预测准确率,且加速比实验验证了该算法具有较好的可扩展性。     

基于差分进化的因子分解机算法

因子分解机(Factorization Machine,FM) 算法是一种基于矩阵分解的机器学习算法,可用于求解回归、分类和排序等问题。FM模型中的参数求解使用的是基于梯度的优化方法,然而在样本较少的情况下,该优化方法收敛速度慢,且易陷入局部最优。差分进化算法(Differential Evolution,DE)是一种启发式的全局优化算法,具有收敛速度快等特性。为提高FM模型的训练速度,利用DE计算FM模型参数,提出了DE-FM算法。在数据集Diabetes、HorseColic以及音乐分类数据集Music上的实验结果表明,改进后的基于差分进化的因子分解机算法DE-FM在训练速度和准确性上均有所提高。     

Binary matrix factorization for analyzing gene expression data

The advent of microarray technology enables us to monitor an entire genome in a single chip using a systematic approach. Clustering, as a widely used data mining approach, has been used to discover phenotypes from the raw expression data. However traditional clustering algorithms have limitations since they can not identify the substructures of samples and features hidden behind the data. Different from clustering, biclustering is a new methodology for discovering genes that are highly related to a subset of samples. Several biclustering models/methods have been presented and used for tumor clinical diagnosis and pathological research. In this paper, we present a new biclustering model using Binary Matrix Factorization (BMF). BMF is a new variant rooted from non-negative matrix factorization (NMF). We begin by proving a new boundedness property of NMF. Two different algorithms to implement the model and their comparison are then presented. We show that the microarray data biclustering problem can be formulated as a BMF problem and can be solved effectively using our proposed algorithms. Unlike the greedy strategy-based algorithms, our proposed algorithms for BMF are more likely to find the global optima. Experimental results on synthetic and real datasets demonstrate the advantages of BMF over existing biclustering methods. Besides the attractive clustering performance, BMF can generate sparse results (i.e., the number of genes/features involved in each biclustering structure is very small related to the total number of genes/features) that are in accordance with the common practice in molecular biology.     

基于加权的不完备非负矩阵分解算法

非负矩阵分解(NMF)作为一种特征提取与数据降维的新方法,相较于一些传统算法,具有实现上的简便性,分解形式和分解结果上的可解释性等优点。但当样本矩阵不完备时,NMF无法对其进行直接分解。提出一种基于加权的不完备非负矩阵分解(NMFI)算法,该算法在处理不完备样本矩阵时,先采用随机修复的方法降低误差,再利用加权来控制各样本的权重,尽量削弱缺损数据对分解结果产生的干扰。此外,NMFI算法使用区域权重来进一步减少关键区域数据缺损对分解产生的影响。实验结果表明,NMFI算法能有效提取样本中残余数据的信息,减少缺损数据对分解结果的影响。     

融合层次聚类和粒子群优化的鲁棒推荐算法

针对现有的推荐算法面对托攻击时鲁棒性差的情况,提出一种融合层次聚类和粒子群优化的鲁棒推荐算法.首先,根据用户评分矩阵,使用层次聚类将用户聚为两类,并根据平均类内距离进行类别判定,对攻击概貌进行标记;然后,基于矩阵分解技术,引入粒子群优化技术进行特征矩阵初始化,为模型训练提供初始最优解;最后,根据攻击概貌标识结果构造标记函数,降低对模型训练过程的影响,实现对目标用户的鲁棒推荐.在公共数据集上将本文提出的算法和其他算法进行了实验对比分析,结果显示提出的算法在鲁棒性方面有很大的提升,推荐精度也有提高.     

基于半自动编码器的协同过滤推荐算法

为高效利用推荐系统中用户和物品的交互历史和辅助信息,提出一种改进的协同过滤推荐算法。利用半自动编码器对用户和物品的辅助信息进行特征提取,将提取出的特征映射到矩阵分解模型中,通过反向传播算法实现半自动编码器与矩阵分解模型的联合更新以提升推荐效果。在MovieLens-100K和Book-Crossing公开数据集上的实验结果表明,与融合偏置的奇异值分解、概率矩阵分解等传统推荐算法相比,该算法具有更低的均方根误差和更好的推荐性能。     

DCFM：基于深度学习的混合推荐模型

传统推荐算法大多都仅考虑用户-商品评级信息来进行推荐,这种忽略了用户属性和商品属性信息的推荐模型准确率不高。因子分解机可在数据稀疏情况下挖掘用户与商品的关联关系,交叉网络可挖掘属性特征与其高阶特征的线性组合关系,以及深度神经网络有效识别高阶非线性关联关系,基于三种模型的优势,提出了一种基于深度学习的混合推荐模型（Deep and Cross Factorization Machine,DCFM）。三部分并联组合,共享输入层,各部分结果线性组合后作为模型整体输出。通过在MovieLens电影数据集上仿真实验,并与因子分解机（FM）、深度因子分解机（DeepFM）、深度交叉网络（DCN）模型做比较,结果证明该模型在准确率、F1-Score和AUC值上均得到了提高和改善。     

Recommender systems based on ranking performance optimization

The rapid development of online services and information overload has inspired the fast development of recommender systems, among which collaborative filtering algorithms and model-based recommendation approaches are wildly exploited. For instance, matrix factorization (MF) demonstrated successful achievements and advantages in assisting internet users in finding interested information. These existing models focus on the prediction of the users’ ratings on unknown items. The performance is usually evaluated by the metric root mean square error (RMSE). However, achieving good performance in terms of RMSE does not always guarantee a good ranking performance. Therefore, in this paper, we advocate to treat the recommendation as a ranking problem. Normalized discounted cumulative gain (NDCG) is chosen as the optimization target when evaluating the ranking accuracy. Specifically, we present three ranking-oriented recommender algorithms, NSMF, AdaMF and AdaNSMF. NSMF builds a NDCG approximated loss function for Matrix Factorization. AdaMF is based on an algorithm by adaptively combining component MF recommenders with boosting method. To combine the advantages of both algorithms, we propose AdaNSMF, which is a hybird of NSMF and AdaMF, and show the superiority in both ranking accuracy and model generalization. In addition, we compare our proposed approaches with the state-of-the-art recommendation algorithms. The comparison studies confirm the advantage of our proposed approaches.     

A novel social network hybrid recommender system based on hypergraph topologic structure

With the advent and popularity of social network, more and more people like to share their experience in social network. However, network information is growing exponentially which leads to information overload. Recommender system is an effective way to solve this problem. The current research on recommender systems is mainly focused on research models and algorithms in social networks, and the social networks structure of recommender systems has not been analyzed thoroughly and the so-called cold start problem has not been resolved effectively. We in this paper propose a novel hybrid recommender system called Hybrid Matrix Factorization(HMF) model which uses hypergraph topology to describe and analyze the interior relation of social network in the system. More factors including contextual information, user feature, item feature and similarity of users ratings are all taken into account based on matrix factorization method. Extensive experimental evaluation on publicly available datasets demonstrate that the proposed hybrid recommender system outperforms the existing recommender systems in tackling cold start problem and dealing with sparse rating datasets. Our system also enjoys improved recommendation accuracy compared with several major existing recommendation approaches.     

Bounded matrix factorization for recommender system

Matrix factorization has been widely utilized as a latent factor model for solving the recommender system problem using collaborative filtering. For a recommender system, all the ratings in the rating matrix are bounded within a pre-determined range. In this paper, we propose a new improved matrix factorization approach for such a rating matrix, called Bounded Matrix Factorization (BMF), which imposes a lower and an upper bound on every estimated missing element of the rating matrix. We present an efficient algorithm to solve BMF based on the block coordinate descent method. We show that our algorithm is scalable for large matrices with missing elements on multicore systems with low memory. We present substantial experimental results illustrating that the proposed method outperforms the state of the art algorithms for recommender system such as stochastic gradient descent, alternating least squares with regularization, SVD++ and Bias-SVD on real-world datasets such as Jester, Movielens, Book crossing, Online dating and Netflix.     

Leveraging clustering to improve collaborative filtering

Extensive work on matrix factorization (MF) techniques have been done recently as they provide accurate rating prediction models in recommendation systems. Additional extensions, such as neighbour-aware models, have been shown to improve rating prediction further. However, these models often suffer from a long computation time. In this paper, we propose a novel method that applies clustering algorithms to the latent vectors of users and items. Our method can capture the common interests between the cluster of users and the cluster of items in a latent space. A matrix factorization technique is then applied to this cluster-level rating matrix to predict the future cluster-level interests. We then aggregate the traditional user-item rating predictions with our cluster-level rating predictions to improve the rating prediction accuracy. Our method is a general “wrapper” that can be applied to all collaborative filtering methods. In our experiments, we show that our new approach, when applied to a variety of existing matrix factorization techniques, improves their rating predictions and also results in better rating predictions for cold-start users. Above all, in this paper we show that better quality and more quantity of these clusters achieve a better rating prediction accuracy.