非负定方差阵下的证券组合投资决策模型研究

在用于度量投资风险的方差阵为非负定时 ,本文建立并研究了允许卖空与不允许卖空情形下证券组合投资决策模型 ,同时给出了计算最优投资比例系数的方法。

几类矩阵的研究及其应用

对几类矩阵进行了刻划；对于非负阵谱半径的一个重要性质￣［１］，给出了新的简单证明；作为应用，得到有重要实际意义的某些类矩阵之逆的谱半径的界的估计。

广义置换矩阵的性质

本文给出广义置换矩阵的若干性质,证明了广义置换矩阵即是非负的所谓广义正交矩阵,并且讨论了方程AX=b当A为广义置换矩阵时的一个迭代收敛问题.

Numerical Methods for a Class of Quadratic Matrix Equations

Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.

Matrix dimensionality reduction for mining typical user profiles

Recently clustering techniques have been used to automatically discover typical user profiles. In general, it is a challenging problem to design effective similarity measure between the session vectors which are usually high-dimensional and sparse. Two approaches for mining typical user profiles, based on matrix dimensionality reduction, are presented. In these approaches, non-negative matrix factorization is applied to reduce dimensionality of the session-URL matrix, and the projecting vectors of the user-session vectors are clustered into typical user-session profiles using the spherical k -means algorithm. The results show that two algorithms are successful in mining many typical user profiles in the user sessions.

Image Fusion Based on Complex Contourlet Transform and Nonnegative Matrix Factorization

An image fusion method combining complex contourlet transform(CCT) with nonnegative matrix factorization(NMF) is proposed in this paper.After two images are decomposed by CCT,NMF is applied to their highand low-frequency components,respectively,and finally an image is synthesized.Subjective-visual-quality of the image fusion result is compared with those of the image fusion methods based on NMF and the combination of wavelet /contourlet /nonsubsampled contourlet with NMF.The experimental results are evaluated quantitatively,and the running time is also contrasted.It is shown that the proposed image fusion method can gain larger information entropy,standard deviation and mean gradient,which means that it can better integrate featured information from all source images,avoid background noise and promote space clearness in the fusion image effectively.

Minimum distance constrained nonnegative matrix factorization for hyperspectral data unmixing

This paper considers a problem of unsupervised spectral unmixing of hyperspectral data. Based on the Linear Mixing Model （ LMM）, a new method under the framework of nonnegative matrix fac- torization （NMF） is proposed, namely minimum distance constrained nonnegative matrix factoriza- tion （MDC-NMF）. In this paper, firstly, a new regularization term, called endmember distance （ED） is considered, which is defined as the sum of the squared Euclidean distances from each end- member to their geometric center. Compared with the simplex volume, ED has better optimization properties and is conceptually intuitive. Secondly, a projected gradient （PG） scheme is adopted, and by the virtue of ED, in this scheme the optimal step size along the feasible descent direction can be calculated easily at each iteration. Thirdly, a finite step （ no more than the number of endmem- bers） terminated algorithm is used to project a point on the canonical simplex, by which the abun- dance nonnegative constraint and abundance sum-to-one constraint can be accurately satisfied in a light amount of computation. The experimental results, based on a set of synthetic data and real da- ta, demonstrate that, in the same running time, MDC-NMF outperforms several other similar meth- ods proposed recently.

Orthogonal nonnegative matrix factorization based local hidden Markov model for multimode process monitoring

Traditional data driven fault detection methods assume that the process operates in a single mode so that they cannot perform well in processes with multiple operating modes. To monitor multimode processes effectively,this paper proposes a novel process monitoring scheme based on orthogonal nonnegative matrix factorization(ONMF) and hidden Markov model(HMM). The new clustering technique ONMF is employed to separate data from different process modes. The multiple HMMs for various operating modes lead to higher modeling accuracy.The proposed approach does not presume the distribution of data in each mode because the process uncertainty and dynamics can be well interpreted through the hidden Markov estimation. The HMM-based monitoring indication named negative log likelihood probability is utilized for fault detection. In order to assess the proposed monitoring strategy, a numerical example and the Tennessee Eastman process are used. The results demonstrate that this method provides efficient fault detection performance.

E-matrices and Several Necessary and Sufficient Conditions

In this paper,we define a kind of sguare matrices which is called E-matrices,and give several necessary and sufficient conditions for E-matrices.

Alzheimer’s disease classification based on sparse functional connectivity and non-negative matrix factorization

A novel framework is proposed to obtain physiologically meaningful features for Alzheimer's disease(AD)classification based on sparse functional connectivity and non-negative matrix factorization.Specifically,the non-negative adaptive sparse representation(NASR)method is applied to compute the sparse functional connectivity among brain regions based on functional magnetic resonance imaging(fMRI)data for feature extraction.Afterwards,the sparse non-negative matrix factorization(sNMF)method is adopted for dimensionality reduction to obtain low-dimensional features with straightforward physical meaning.The experimental results show that the proposed framework outperforms the competing frameworks in terms of classification accuracy,sensitivity and specificity.Furthermore,three sub-networks,including the default mode network,the basal ganglia-thalamus-limbic network and the temporal-insular network,are found to have notable differences between the AD patients and the healthy subjects.The proposed framework can effectively identify AD patients and has potentials for extending the understanding of the pathological changes of AD.

AN NMF ALGORITHM FOR BLIND SEPARATION OF CONVOLUTIVE MIXED SOURCE SIGNALS WITH LEAST CORRELATION CONSTRAINS

Most of the existing algorithms for blind sources separation have a limitation that sources are statistically independent. However, in many practical applications, the source signals are non- negative and mutual statistically dependent signals. When the observations are nonnegative linear combinations of nonnegative sources, the correlation coefficients of the observations are larger than these of source signals. In this letter, a novel Nonnegative Matrix Factorization (NMF) algorithm with least correlated component constraints to blind separation of convolutive mixed sources is proposed. The algorithm relaxes the source independence assumption and has low-complexity algebraic com- putations. Simulation results on blind source separation including real face image data indicate that the sources can be successfully recovered with the algorithm.

关于R.S.Varga书中stein-ROSenberg定理的证明的一个注解

R.S.Varga的《Matrix Iterative Analgsis》一书（以下简称原书）中,在证明Stein—Rosenberg定理（原书定理33第70页）的过程中应用了这样一个事实,即:B是一个非负,不可约的Jacobi阵,￡1是与B相属的Gauss—Seidel阵,则谱半径ρ（￡1）】o,并且￡1有一与ρ（￡1）相属的正特征矢,原书对这个事实未给证明,而作为一个易见的问题留给读者自证。这个事实的证明并不简单。

Sequences of Lower Bounds for the Perron Root of a Nonnegative Irreducible Matrix

Estimate bounds for the Perron root of a nonnegative matrix are important in theory of nonnegative matrices.It is more practical when the bounds are expressed as an easily calcu-lated function in elements of matrices.For the Perron root of nonnegative irreducible matrices,three sequences of lower bounds are presented by means of constructing shifted matrices,whose convergence is studied.The comparisons of the sequences with known ones are supplemented with a numerical example.

The Auslander-type condition of triangular matrix rings

Let R be a left and right Noetherian ring and n, k be any non-negative integers. R is said to satisfy the Auslander-type condition Gn（k） if the right fiat dimension of the （i ＋ 1）-th term in a minimal injective resolution of RR is at most i ＋ k for any 0 ≤ i ≤ n - 1. In this paper, we prove that R is Gn（k） if and only if so is a lower triangular matrix ring of any degree t over R.