这一部分结果的论证建立在非负矩阵的理论基础上。
提出一种带有正则约束的非负矩阵分解算法(RCNMF)。
An algorithm with regularization constrains for nonnegative matrix factorization (RCNMF) is proposed.
非负矩阵分解具有非负性和局部性的特点，是一种新型的特征提取方法。
Non-negative matrix factorization has non-negative and local characteristics, and it is a new feature extraction method.
非负矩阵分解算法简单，易于实现，并且具有降维、收敛和稀疏等特性。
Moreover, NMF algorithm is simple and easy to implement and it has features such as dimension-lowering and sparse convergence.
本文主要是论述稀疏非负矩阵分解算法在矿产资源定量预测中的应用研究。
In this article, the sparse non-negative matrix factorization algorithm is applied to quantitative predict the mineral resources.
一个著名的结果是一个非负矩阵的最大特征值在它的最小行和与最大行和之间。
One of well-known results is that the greatest eigenvalue of a nonnegative matrix lies between the smallest and the largest row sum.
非负矩阵分解过程中，适当地选取特征空间的维数能够获得原始数据的局部特征。
The local feature based representation could be obtained by choosing suitable dimension of the feature subspace in NMF.
本文借助于非负矩阵分解算法，提出了一种基于非负因子分析的模糊文本聚类方法。
Inspired by the nonnegative matrix factorization algorithm, we put forward an fuzzy text clustering method based on nonnegative factor analysis.
摘要：非负矩阵分解方法是基于局部特征的特征提取方法，已经成功用于人脸识别。
Absrtact: Non - negative matrix factorization (NMF) is a method of parts - based feature extraction, it has been already applied to face recognition successfully.
并在特征提取环节，提出CSVD算法与非负矩阵因子算法特征数据相融合的人脸识别算法。
And in the feature extraction process, a new face recognition method based on CSVD and non Negative Matrix Factorization (NMF) is presented.
其次，在第二章中，我们讨论了将一个非负矩阵分解成有限多个完全不可分非负阵的乘积的问题。
Secondly, we discuss the problem of decomposing a nonnegative matrix into a product of fully indecomposable nonnegative matrices in chapter 2.
实验结果表明提出的两种特征提取方法在识别率方面整体上好于原非负矩阵分解特征提取（NMF）方法。
The experimental results on Olivetti Research Laboratory (ORL) face database and YALE face database show that the new methods are better than original NMF in terms of recognition rate.
本文对一个矩阵的最小示性数进行了研究，并证明了一个矩阵的最小示性数等于其对应的非负矩阵的谱半径。
It is proved in this paper that the minimal characterizing number of a matrix is equal to the spectral radius of the corresponding non-negative matrix.
非负矩阵分解（NMF）要求分解得到的左矩阵为列满秩，这限制了它在欠定盲分离（UBSS）中的应用。
The decomposed left matrix of Non-negative Matrix Factorization (NMF) is required to be full column rank, which limits of its application to Underdetermined Blind Source Separation (UBSS).
目的：研究非负矩阵因子分解算法(NMF)用于手性药物HPLC - DAD二维数据解析的可行性及其影响因素。
Aim: to study the feasibility and influential factors for the resolution of HPLC-DAD data of chiral drugs by non-negative matrix factorization (NMF) algorithm.
竞赛矩阵和竞赛图由于具有固定行和向量及列和向量的非负矩阵类的计数，是组合数学的一个非常困难的问题，因此对具有固定得分向量的竞赛矩阵的计数问题也比较困难。
But it is very difficult to compute the number of non-negative matrix with fixed score row or column vectors, so to compute the number of tournament matrix with fixed score vector is also difficult.
作为本文的主要结果，关于交换环上矩阵的正点定理，零点定理和非负点定理被建立。
As the main results, it gives a Positivstellensatz, a Nullstellensatz and a Nichtnegativstellensatz for matrices over a commutative ring.
刻画了在非负无零因子交换半环上强保持可逆矩阵的线性算子。
The linear operators that strongly preserve invertible matrices over some antinegative commutative semirings with no zero divisors were characterized.
刻画了在非负无零因子交换半环上强保持可逆矩阵的线性算子。
Then T is an invertible linear operator preserving rank - partial ordering on Sn(F) if and only if there exists an invertible matrix (F) such that where .
讨论了L-非负定矩阵的广义B-D逆的代数扰动问题，并给出了它的代数扰动表达式。
In this paper, the algebraic perturbation theory of generalized B-D Inverse of L-nonnegative definite matrix is discussed. and the expressions of the algebraic perturbation are presented.
本文给出了一般非负广义幂等矩阵的充要条件。
In this paper, we study nonnegative generalized idempotent matrices in detail.
本文给出了一般非负广义幂等矩阵的充要条件。
In this paper, we study nonnegative generalized idempotent matrices in detail.
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