识别表达不稳定的基因

提出集成分析来自相同研究问题的不同数据集来识别表达不稳定的基因.把这一问题形式化为一个非线性整数规划问题,三个启发式的算法被提出来求解这一优化问题;进一步地设计了一个统计量来度量基因的不稳定表达程度.提出的方法应用于两个真实数据,实验结果显示:所识别的不稳定基因在两个数据中的表达不一致;利用表达不稳定基因可以提高差异表达基因的筛选结果,而去除表达不稳定基因可以有效地提高微阵列数据分类.实验结果表明,提出的方法是有效的,并且表达不稳定基因可以为微阵列数据分析提供有价值的信息.     

Rank 1 weighted factorization for 3D structure recovery: algorithms and performance analysis

The paper describes the rank 1 weighted factorization solution to the structure from motion problem. This method recovers the 3D structure from the factorization of a data matrix that is rank 1 rather than rank 3. This matrix collects the estimates of the 2D motions of a set of feature points of the rigid object. These estimates are weighted by the inverse of the estimates error standard deviation so that the 2D motion estimates for "sharper" features, which are usually well-estimated, are given more weight, while the noisier motion estimates for "smoother" features are weighted less. We analyze the performance of the rank 1 weighted factorization algorithm to determine what are the most suitable 3D shapes or the best 3D motions to recover the 3D structure of a rigid object from the 2D motions of the features. Our approach is developed for the orthographic camera model. It avoids expensive singular value decompositions by using the power method and is suitable to handle dense sets of feature points and long video sequences. Experimental studies with synthetic and real data illustrate the good performance of our approach.     

Incorporating non-motion cues into 3D motion segmentation

We address the problem of segmenting an image sequence into rigidly moving 3D objects. An elegant solution to this problem in the case of orthographic projection is the multibody factorization approach in which the measurement matrix is factored into lower rank matrices. Despite progress in factorization algorithms, their performance is still far from satisfactory and in scenes with missing data and noise, most existing algorithms fail.In this paper we propose a method for incorporating 2D non-motion cues (such as spatial coherence) into multibody factorization. We show the similarity of the problem to constrained factor analysis and use the EM algorithm to find the segmentation. We show that adding these cues improves performance in real and synthetic sequences.     

Estimating 3D shape from degenerate sequences with missing data

Reconstructing a 3D scene from a moving camera is one of the most important issues in the field of computer vision. In this scenario, not all points are known in all images (e.g. due to occlusion), thus generating missing data. On the other hand, successful 3D reconstruction algorithms like Tomasi & Kanade’s factorization method, require an orthographic model for the data, which is adequate in close-up views. The state-of-the-art handles the missing points in this context by enforcing rank constraints on the point track matrix. However, quite frequently, close-up views tend to capture planar surfaces producing degenerate data. Estimating missing data using the rank constraint requires that all known measurements are “full rank” in all images of the sequence. If one single frame is degenerate, the whole sequence will produce high errors on the reconstructed shape, even though the observation matrix verifies the rank 4 constraint. In this paper, we propose to solve the structure from motion problem with degenerate data, introducing a new factorization algorithm that imposes the full scaled-orthographic model in one single optimization procedure. By imposing all model constraints, a unique (correct) 3D shape is estimated regardless of the data degeneracies. Experiments show that remarkably good reconstructions are obtained with an approximate models such as orthography.     

Using underapproximations for sparse nonnegative matrix factorization

Nonnegative matrix factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g., text mining, image processing, microarray data analysis, collaborative filtering, etc.We introduce a novel approach to solve NMF problems, based on the use of an underapproximation technique, and show its effectiveness to obtain sparse solutions. This approach, based on Lagrangian relaxation, allows the resolution of NMF problems in a recursive fashion. We also prove that the underapproximation problem is NP-hard for any fixed factorization rank, using a reduction of the maximum edge biclique problem in bipartite graphs.We test two variants of our underapproximation approach on several standard image datasets and show that they provide sparse part-based representations with low reconstruction error. Our results are comparable and sometimes superior to those obtained by two standard sparse nonnegative matrix factorization techniques.     

基于多近似模型的交互式遗传算法

人的疲劳向题是交互式遗传算法的核心问题,它制约了交互式遗传算法在复杂优化问题中的应用.为了解决该问题,本文提出基于多近似模型的交互式遗传算法.该算法首先将搜索空间划分,然后利用传统交互式遗传算法得到的数据,在不同子空间生成不同的近似模型,最后采用该模型近似人对进化个体的评价,从而减少人评价的数量,有效解决人的疲劳问题.算法性能分析及在服装进化设计系统中的应用验证了其有效性.     

Multi-Manifold Concept Factorization for Data Clustering

Clustering plays an important role in many fields, such as pattern recognition and data mining. Its goal is to group the collected data points into their respective clusters. To this end, a number of matrix factorization based methods have been developed to obtain satisfying clustering results by extracting the latent concepts in the data, e.g., concept factorization (CF) and locally consistent concept factorization (LCCF). LCCF takes into account the local manifold structure of the data, but it is nontrivial to estimate the intrinsic manifold, reflecting the true data structure. To address this issue, we in this paper present a novel method called Multi-Manifold Concept Factorization (MMCF) to derive more promising clustering performance. Specifically, we assume the intrinsic manifold lies in a convex hull of some predefined candidate manifolds. The basic idea is to learn a convex combination of a group of candidate manifolds, which is utilized to approximate the intrinsic manifold of the data. In this way, the low-dimensional data representation derived from MMCF is able to better preserve the locally geometrical structure of the data. To optimize the objective function, we develop an alternating algorithm and learn the manifold coefficients using the entropic mirror descent algorithm. The effectiveness of the proposed approach has been demonstrated through a set of evaluations on several real-world data sets.     

Optimal Kullback–Leibler approximation of Markov chains via nuclear norm regularisation

This paper is concerned with model reduction for Markov chain models. The goal is to obtain a low-rank approximation to the original Markov chain. The Kullback–Leibler divergence rate is used to measure the similarity between two Markov chains; the nuclear norm is used to approximate the rank function. A nuclear-norm regularised optimisation problem is formulated to approximately find the optimal low-rank approximation. The proposed regularised problem is analysed and performance bounds are obtained through the convex analysis. An iterative fixed point algorithm is developed based on the proximal splitting technique to compute the optimal solutions. The effectiveness of this approach is illustrated via numerical examples.     

基于Schatten-p范数和特征自表示的无监督特征选择

特征选择是去除不相关和冗余特征,找到具有良好泛化能力的原始特征的紧凑表示,同时,数据中含有的噪声和离群点会使学习获得的系数矩阵的秩变大,使得算法无法捕捉到高维数据中真实的低秩结构。因此,利用Schatten-p范数逼近秩最小化问题和特征自表示重构无监督特征选择问题中的系数矩阵,建立一个基于Schatten-p范数和特征自表示的无监督特征选择（SPSR）算法,并使用增广拉格朗日乘子法和交替方向法乘子法框架进行求解。最后在6个公开数据集上与经典无监督特征选择算法进行实验比较,SPSR算法的聚类精度更高,可以有效地识别代表性特征子集。     

非负子空间聚类指导下的非负矩阵分解

非负矩阵分解作为一种有效的数据表示方法被广泛应用于模式识别和机器学习领域。为了得到原始数据紧致有效的低维数据表示,无监督非负矩阵分解方法在特征降维的过程中通常需要同时发掘数据内部隐含的几何结构信息。通过合理建模数据样本间的相似性关系而构建的相似度图,通常被用来捕获数据样本的空间分布结构信息。子空间聚类可以有效发掘数据内部的子空间结构信息,其获得的自表达系数矩阵可用于构建相似度图。该文提出了一种非负子空间聚类算法来发掘数据的子空间结构信息,同时利用该信息指导非负矩阵分解,从而得到原始数据有效的非负低维表示。同时,该文还提出了一种有效的迭代求解方法来求解非负子空间聚类问题。在两个图像数据集上的聚类实验结果表明,利用数据的子空间结构信息可以有效改善非负矩阵分解的性能。     

基于附加间隔Softmax特征的人脸聚类算法

针对数据量巨大、类别多、真实类别数未知、样本数量不均衡、类内变化多的无标签人脸图像分类问题,提出基于附加间隔Softmax特征的近似等级排序人脸聚类算法。使用附加间隔Softmax损失结合Inception-ResNet-V1网络训练人脸识别模型来提取深度人脸特征,并应用于近似等级排序聚类。在LFW人脸数据集、LFW与视频模糊人脸的混合数据集上进行实验,结果表明该模型在人脸识别准确率、误识率为0.1%时的验证率均优于其他模型,近似等级排序聚类在F1度量得分优于其他聚类算法,具有更强的鲁棒性和应用价值。     

一种谱分解降维的模糊有监督局部保持投影策略

提出一种谱分解降维的模糊有监督局部保持投影策略。首先针对监督局部保持投影SLPP存在过学习和不能较好地保持图像空间的差异信息等问题,通过最小化局部离散度和最大化差异离散度准则提取投影方向,找到一种线性鉴别分析的等价形式。其次,通过采用模糊k近邻(FKNN)方法得到相应的样本分布隶属度信息,同时考虑到离群样本对整个分类结果的不利影响,提出一种模糊化方法,根据样本的隶属度对样本分布矩阵重定义所做的贡献,将每个样本的隶属度融入到SLPP特征抽取的过程中,从而得到完整有效的模糊样本特征向量集,有效解决了小样本问题的特征抽取问题。第三,提出一种谱分解的矩阵分析方法,在SLPP投影准则下,对散布矩阵实现降维。在ORL和NUST603人脸库上的实验结果验证了该方法的有效性。     

Fuzzy clustering to estimate the parameters of block mixture models

Finite mixture models are being increasingly used to provide model-based cluster analysis. To tackle the problem of block clustering which aims to organize the data into homogeneous blocks, recently we have proposed a block mixture model; we have considered this model under the classification maximum likelihood approach and we have developed a new algorithm for simultaneous partitioning based on the classification EM algorithm. From the estimation point of view, classification maximum likelihood approach yields inconsistent estimates of the parameters and in this paper we consider the block clustering problem under the maximum likelihood approach; unfortunately, the application of the classical EM algorithm for the block mixture model is not direct: difficulties arise due to the dependence structure in the model and approximations are required. Considering the block clustering problem under a fuzzy approach, we propose a fuzzy block clustering algorithm to approximate the EM algorithm. To illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.     

一种优化标签的矩阵分解推荐算法

个性化推荐研究中,垃圾标签不仅会导致数据稀疏性问题,同时影响推荐的实时性和精确性。因此提出一种优化标签的矩阵分解推荐算法OTMFR,该算法分为两个阶段：首先优化标签,在建立三部网络图的基础上提出一种标签排序算法,利用互增强的关系得到关于标签流行度的排序,去除排序靠后的垃圾标签;然后在此基础上利用用户和资源对标签的偏好信息构建用户-资源偏好矩阵,并从矩阵分解的角度为用户产生推荐。在Delicious数据集上的实验结果表明,该算法在推荐精准度上有较为明显的效果。     

结合个体影响力和信任传递的推荐算法

针对推荐系统中存在的数据稀疏性和推荐准确性问题,利用信任传递思想,融合个体影响力计算模型和用户评分预测模型,使用结构投影非负矩阵分解推荐算法,采用随机梯度下降逼近方法,提出了一种以保留原始数据结构特征为目的、融合个体影响力和信任传递的结构投影非负矩阵分解推荐算法TP-SPNMF。通过多组对比实验证明,相比其他算法,TP-SPNMF算法不仅降低了MAE和RMSE,还提高了系统的预测准确性。     

满秩仿Hermite多项式矩阵的J-谱分解计算

基于仿等价变换实现了满秩仿Hermite多项式矩阵的J-谱分解计算.对于一个满秩的 仿Hermite多项式矩阵,首先用仿等价变换将其变换为单模的满秩仿Hermite多项式矩阵,进 一步再用仿等价变换将其变换为常数满秩矩阵,最后变换为J-矩阵.将这些变换矩阵积累起 来,得到满秩仿Hermite多项式矩阵的J-谱分解.在作者发展的多项式矩阵运算程序库的基础 上,给出了实现所提出的计算方法的算法.数例表明,该方法是有效的.     

非负矩阵分解在微阵列数据分类和聚类发现中的应用

基因芯片是微阵列技术的典型代表,它具有高通量的特性和同时检测全部基因组基因表达水平的能力。应用微阵列芯片的一个主要目的是基因表达模式的发现,即在基因组水平发现功能相似,生物学过程相关的基因簇;或者将样本分类,发现样本的各种亚型。例如根据基因表达水平对癌症样本进行分类,发现疾病的分子亚型。非负矩阵分解NMF方法是一种非监督的、非正交的、基于局部表示的矩阵分解方法。近年来这种方法被越来越多地应用在微阵列数据的分类分析和聚类发现中。系统地介绍了非负矩阵分解的原理、算法和应用,分解结果的生物学解释,分类结果的质量评估和基于NMF算法的分类软件。总结并评估了NMF方法在微阵列数据分类和聚类发现应用中的表现。     

Numerical computation of a coprime factorization of a transfer function matrix

A new algorithm is presented for computing a coprime factorization of a transfer function matrix. The method is based on reformulating the problem as a problem of constructing a minimal basis of the right nullspace of a matrix pencil λB - A. Due to the special structure and rank properties of the pencil obtained after transforming λB - A to generalized Schur form, the original problem can be easily solved in a numerically reliable way.     

A sparse nonnegative matrix factorization technique for graph matching problems

Graph matching problem that incorporates pairwise constraints can be cast as an Integer Quadratic Programming (IQP). Since it is NP-hard, approximate methods are required. In this paper, a new approximate method based on nonnegative matrix factorization with sparse constraints is presented. Firstly, the graph matching is formulated as an optimization problem with nonnegative and sparse constraints, followed by an efficient algorithm to solve this constrained problem. Then, we show the strong relationship between the sparsity of the relaxation solution and its effectiveness for graph matching based on our model. A key benefit of our method is that the solution is sparse and thus can approximately impose the one-to-one mapping constraints in the optimization process naturally. Therefore, our method can approximate the original IQP problem more closely than other approximate methods. Extensive and comparative experimental results on both synthetic and real-world data demonstrate the effectiveness of our graph matching method.     

The unitary interactor matrix and its estimation using closed-loop data

This paper is concerned with the factorization and estimation of the unitary interactor matrix or the time-delay matrix of multivariable systems. The important properties of the unitary interactor matrix for minimum variance control are discussed. An algorithm for factorization of the unitary interactor matrix from the Markov parameters is introduced. A method for direct estimation of the interactor matrix from closed-loop data is proposed. The proposed algorithm is evaluated by application to a simulated example, pilot-scale experiment and actual industrial data.