基于受约束偏置的概率矩阵分解算法

在概率矩阵分解(PMF)模型拟合之后,评分较少用户的特征趋近于先验分布的平均值,导致对其评分预测接近物品的平均评分.受约束概率矩阵分解(CPMF)未考虑到不同评分系统的整体差异以及数据集内部用户与物品存在的固有属性.针对以上问题,提出将传统矩阵分解中的用户和物品偏置项以及全局平均分结合受约束概率矩阵分解来建立新的矩阵分解算法.算法利用整体平均分衡量不同评分系统,在采用偏置来表示用户以及物品之间相互独立的属性的同时,引入约束使行为相近用户拥有相近的用户偏置,从而提高预测精度.在两个真实数据集上的实验结果表明,该算法相对于PMF和CPMF算法预测精度得到了提高.     

基于大整数分解可公开验证的秘密共享方案

基于不定方程整数解的存在性及大整数分解的困难性,以Shamir(t,n)门限方案为基础,提出了一种可公开验证的秘密共享方案.方案利用大整数分解的困难性为共享者建立秘密份额,通过不定方程整数解的存在性计算方程的特解组合,共享秘密由共享者的秘密份额和特解组合元素共同计算恢复;方案实现了对秘密份额、参与者之间及参与者对分发者的有效性验证.安全分析表明,该方案是安全的,具有一定的实际应用价值.     

Set‐based fault detection and isolation for detectable linear parameter‐varying systems

In the context of fault detection and isolation of linear parameter‐varying systems, a challenging task appears when the dynamics and the available measurements render the model unobservable, which invalidates the use of standard set‐valued observers. Two results are obtained in this paper, namely, using a left‐coprime factorization, one can achieve set‐valued estimates with ultimately bounded hyper‐volume and convergence dependent on the slowest unobservable mode; and by rewriting the set‐valued observer equations and taking advantage of a coprime factorization, it is possible to have a low‐complexity fault detection and isolation method. Performance is assessed through simulation, illustrating, in particular, the detection time for various types of faults. Copyright © 2017 John Wiley & Sons, Ltd.     

基于矩阵分解的个性化推荐系统研究

随着社交网络的快速发展,用户在使用社交应用时会产生大量有价值的数据。通过对社交网络进行数据挖掘,发现隐藏在数据中关联用户与物品之间的偏好关系。然后对用户建模分析,选择合适的推荐引擎进行个性化物品推荐,这是一个非常有价值的研究方向。该文重点研究矩阵分解算法对处理大规模用户与物品评分矩阵的推荐效果,为了提高推荐的准确度展开了对用户社交关系和隐性反馈的研究,在组合预测模型中加入社交关系、人口统计学信息配置项、用户的消费记录等隐因子项,通过实验验证了扩展之后的混合预测模型在RMSE值上比SVD算法降低了0.259 475,在推荐性能有较大幅度的提高。     

LBP与LNMF特征融合的人脸识别

提出一种融合局部二值模式(LBP)和局部非负矩阵分解(LNMF)进行人脸识别的方法,采用LBP算子提取分块人脸图像的LBP直方图序列(LBPHS),根据每块的贡献度,得到权重的直方图序列(WeightLBPHS),采用LNMF方法提取其非负子空间及其系数矩阵,根据最近邻原则进行识别。在ORL和YALE标准人脸数据库上的实验表明,该方法具有较高的识别率。     

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

We illustrate procedures to identify a state-space representation of a lossless or dissipative system from a given noise-free trajectory; important special cases are passive systems and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; the state-space equations are then computed by solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order model.     

Enhanced clustering of biomedical documents using ensemble non-negative matrix factorization

Searching and mining biomedical literature databases are common ways of generating scientific hypotheses by biomedical researchers. Clustering can assist researchers to form hypotheses by seeking valuable information from grouped documents effectively. Although a large number of clustering algorithms are available, this paper attempts to answer the question as to which algorithm is best suited to accurately cluster biomedical documents. Non-negative matrix factorization (NMF) has been widely applied to clustering general text documents. However, the clustering results are sensitive to the initial values of the parameters of NMF. In order to overcome this drawback, we present the ensemble NMF for clustering biomedical documents in this paper. The performance of ensemble NMF was evaluated on numerous datasets generated from the TREC Genomics track dataset. With respect to most datasets, the experimental results have demonstrated that the ensemble NMF significantly outperforms classical clustering algorithms of bisecting K-means, and hierarchical clustering. We compared four different methods for constructing an ensemble NMF. For clustering biomedical documents, this research is the first to compare ensemble NMF with typical classical clustering algorithms, and validates ensemble NMF constructed from different graph-based ensemble algorithms. This is also the first work on ensemble NMF with Hybrid Bipartite Graph Formulation for clustering biomedical documents.     

Reflections on the evolution of implicit Navier–Stokes algorithms

This article gives a historical perspective on the evolution of implicit algorithms for the Navier–Stokes equations that utilize time or Newton linearizations and various forms of approximate factorization including alternating-direction, lower/upper, and symmetric relaxation schemes. A theme of the paper is how progress in implicit Navier–Stokes algorithms has been influenced and enabled by the introduction of characteristic-based upwind approximations, unstructured-grid discretizations, parallelization, and by advances in computer performance and architecture. Historical examples of runtime, problem size, and estimated cost are given for actual and hypothetical Navier–Stokes flow cases from the past 40 years.     

Computing monodromy via continuation methods on random Riemann surfaces

We consider a Riemann surface X defined by a polynomial f(x,y) of degree d, whose coefficients are chosen randomly. Hence, we can suppose that X is smooth, that the discriminant δ(x) of f has d(d−1) simple roots, Δ, and that δ(0)≠0, i.e. the corresponding fiber has d distinct points {y₁,…,y_d}. When we lift a loop 0∈γ⊂C−Δ by a continuation method, we get d paths in X connecting {y₁,…,y_d}, hence defining a permutation of that set. This is called monodromy.Here we present experimentations in Maple to get statistics on the distribution of transpositions corresponding to loops around each point of Δ. Multiplying families of “neighbor” transpositions, we construct permutations and the subgroups of the symmetric group they generate. This allows us to establish and study experimentally two conjectures on the distribution of these transpositions and on transitivity of the generated subgroups.Assuming that these two conjectures are true, we develop tools allowing fast probabilistic algorithms for absolute multivariate polynomial factorization, under the hypothesis that the factors behave like random polynomials whose coefficients follow uniform distributions.     

A note on Gao’s algorithm for polynomial factorization

Shuhong Gao (2003) [6] has proposed an efficient algorithm to factor a bivariate polynomial f over a field F. This algorithm is based on a simple partial differential equation and depends on a crucial fact: the dimension of the polynomial solution space G associated with this differential equation is equal to the number r of absolutely irreducible factors of f. However, this holds only when the characteristic of F is either zero or sufficiently large in terms of the degree of f. In this paper we characterize a vector subspace of G for which the dimension is r, regardless of the characteristic of F, and the properties of Gao’s construction hold. Moreover, we identify a second vector subspace of G that leads to an analogous theory for the rational factorization of f.