独立成分分析与主成分分析在股票市场上的运用

展示了分析及认识金融市场结构的一种新方法.将这种方法实例应用在了股票指数CAC40的一篮子股票中,对股票价格走势进行分析,并将独立成分分析（ICA）方法与传统的主成分分析（PCA）方法进行了比较.     

小鼠视觉刺激相关的脑电波分离研究

脑电波信号是无数神经元放电的混合,而实际测量所得到的脑电波信号又是由许许多多构成不同想法和控制行为的脑信号合成的.只有将脑电波信号很好地分离,才能从中确定某种脑电波与某种行为之间的关系.由于采集到的脑电信号强度很微弱,信号的强弱差别很大,所以传统的盲源分离模型很难凑效.结合独立成分分析(Independent Component Analyse,ICA)方法,首先对原始脑电信号进行去噪处理、然后,分离出呼吸相关的脑电信号,接着,根据视觉刺激对分离后的脑电信号进行时域对齐,最终在对齐的脑电信号片段上分离出与视觉相关的脑电信号.     

基于ICA模型的投资组合稳健VaR方法研究

针对参数VaR方法在测度庞大复杂的投资组合风险时,存在模型参数多估计困难和需要设定风险因子联合分布容易使风险计量产生较大偏差等问题,本文提出了基于独立成分分析(ICA)技术的半参数IC-SP-VaR模型,给出了模型的参数估计方法,并对模型进行了模拟研究和实证分析。模拟研究表明新方法在不同情形下的估计都是有效的,在非线性经济序列中优势尤其明显。实证分析验证了新方法能够提高资产组合风险计量模型的稳定性和准确性。     

三种统计分析方法在数学建模中的应用

独立成分分析是近十年来兴起的一种新的数据处理方法.它与主成分分析,因子分析都隶属于多元统计分析方法,并且这三种方法都可以用于处理多变量大样本的数据.目前数学建模竞赛越来越受到各大高校的重视,而在数学建模中,大部分赛题都首先需要进行大样本数据的统计预处理.因此将从模型上对这三种方法进行分析与解释,并通过数学建模实例来说明这三种方法在数学建模中的应用.     

基于一维搜索的ICA自适应算法及其在股票分析中的应用

在固定步长的ICA极大似然估计自适应算法的基础上,通过一维搜索引入了步长修正方案,使新算法可在收敛速度和稳定状态时的失调误差这两个性能指标上达到最佳结合点,具有较好的时变系统跟踪能力。仿真结果证实了本文所提出的算法可以有效地提高ICA的自适应性,能够更准确地完成盲源分离。在此基础上将算法用在时变性很强的股票数据上,以验证该算法的有效性和可行性。     

基于临床与基因图谱的结肠癌基因标签提取

由于基因间的调控和相互作用表现为功能基因组合的形式,在对样本的分类能力是以特征集合的形式整体体现出来的.由此,考察由多个基因构成的基因簇作为区分常人和癌症患者的分类因素,利用独立成分分析(ICA)技术最大程度地降低基因之间的相互影响,从而获得基因簇信息.随后采用了支持向量机,依据提取出的基因簇进行分类,筛选出致病的癌症基因.为了能够得到最好的分类因素,将问题转化为稀疏表示的优化问题.此外,还利用含噪声的ICA和带松弛因子的非光滑优化模型来研究含噪声的基因图谱.最后,借助于条件概率模型,将临床结论与基因图谱相结合,对病人数据进行了筛选.     

基于ICA的时间序列聚类方法及其在股票数据分析中的应用

时间序列聚类分析是时间序列数据挖掘中的重要任务之一，通常由于时间序列数据的特殊结构，导致一般的聚类算法不能直接应用于时间序列数据。本文提出了一种基于独立成分分析与改进^一均值算法相结合的时间序列聚类算法，该算法首先利用独立成分分析对时间序列数据进行特征提取，然后利用改进￡．均值聚类算法完成对时间序列特征数据的聚类分析，从而得到了一种新的基于特征的时间序列聚类方法。为了验证该方法的有效性和可行性，将其应用于实际的股票时间序列数据聚类分析中，取得了较好的数值结果。     

股指期货套利中的最优现货组合构建策略研究

针对如何构建与股指期货联动性较好的现货组合问题,本文提出采用两阶段优化策略以提高组合的跟踪准确度。第一阶段,利用基于独立成分分析与模糊C均值算法相结合的时间序列聚类方法将沪深300股指期货对应的成分股进行聚类;第二阶段,对聚类之后的结果进行指数优化复制,以跟踪误差最小为目标,确定跟踪组合的成分股权重。实证研究表明,本文所提出的两阶段优化策略可以较好地改进指数跟踪效果。     

独立状态排序问题及独立系统方法

本文提出一个基本的排序问题类－独立状态排序问题，并探讨运用拟阵及独立系统的研究方法，一些已有算法得到概括和提炼，同时一系列新算法被产生出来。     

基于主成分分析的朴素贝叶斯算法在垃圾短信用户识别中的应用

在垃圾短信用户的识别问题中,参与建模的用户行为消费数据存在极强的相关性,直接使用朴素贝叶斯算法建模准确率极低.为满足朴素贝叶斯算法要求建模属性条件独立的基本假定,利用主成分分析对数据进行处理,从而达到降维和属性独立的双重目的,继而利用朴素贝叶斯算法进行建模.结果表明,基于主成分分析和朴素贝叶斯算法的组合模型效果显著.可见在垃圾短信算法的识别中具有一定的实用价值和现实意义.     

A new constrained fixed-point algorithm for ordering independent components

Independent component analysis (ICA) aims to recover a set of unknown mutually independent components (ICs) from their observed mixtures without knowledge of the mixing coefficients. In the classical ICA model there exists ICs’ indeterminacy on permutation and dilation. Constrained ICA is one of methods for solving this problem through introducing constraints into the classical ICA model. In this paper we first present a new constrained ICA model which composed of three parts: a maximum likelihood criterion as an objective function, statistical measures as inequality constraints and the normalization of demixing matrix as equality constraints. Next, we incorporate the new fixed-point (newFP) algorithm into this constrained ICA model to construct a new constrained fixed-point algorithm. Computation simulations on synthesized signals and speech signals demonstrate that this combination both can eliminate ICs’ indeterminacy to a certain extent, and can provide better performance. Moreover, comparison results with the existing algorithm verify the efficiency of our new algorithm furthermore, and show that it is more simple to implement than the existing algorithm due to its advantage of not using the learning rate. Finally, this new algorithm is also applied for the real-world fetal ECG data, experiment results further indicate the efficiency of the new constrained fixed-point algorithm.     

基于独立分量分析——最小二乘支持向量机的公路建设项目投资估算新模型

为快速、准确地进行公路建设项目投资估算,提出了一种新型的公路建设项目投资估算模型.该模型首先基于独立分量分析技术,根据最小互信息原理,有效分离出公路建设项目投资估算的独立影响因素源.然后,将这些独立影响因素源用于最小二乘支持向量机的训练,从而建立了基于独立分量分析技术—最小二乘支持向量机的公路建设项目投资估算模型.该模型将独立分量分析技术的盲信号分离能力与最小二乘支持向量机处理有限样本条件下非线性回归问题的优势有机结合,提高了模型预测的准确性.     

基于智能化信息处理的建筑工程造价短期预测

提出了一种新的基于智能化信息处理的建筑工程造价短期预测模型.该模型首次利用数据的高阶统计信息,提出了改进独立分量分析技术.通过构建适用于建筑工程造价的属性重构空间,挖掘出表征能力更强的造价独立属性,用于神经网络的学习和训练,从而建立了全新的建筑工程造价短期预测智能模型.该模型通过发挥独立分量分析强大的信号分离能力,增强了神经网络的学习效率,提高了预测精度.实例数据验证了文中所建模型的有效性.     

Riemannian Newton-type methods for joint diagonalization on the Stiefel manifold with application to independent component analysis

The joint approximate diagonalization of non-commuting symmetric matrices is an important process in independent component analysis. This problem can be formulated as an optimization problem on the Stiefel manifold that can be solved using Riemannian optimization techniques. Among the available optimization techniques, this study utilizes the Riemannian Newton’s method for the joint diagonalization problem on the Stiefel manifold, which has quadratic convergence. In particular, the resultant Newton’s equation can be effectively solved by means of the Kronecker product and the vec and veck operators, which reduce the dimension of the equation to that of the Stiefel manifold. Numerical experiments are performed to show that the proposed method improves the accuracy of the approximate solution to this problem. The proposed method is also applied to independent component analysis for the image separation problem. The proposed Newton method further leads to a novel and fast Riemannian trust-region Newton method for the joint diagonalization problem.     

Efficiency measurement using independent component analysis and data envelopment analysis

Efficiency measurement is an important issue for any firm or organization. Efficiency measurement allows organizations to compare their performance with their competitors’ and then develop corresponding plans to improve performance. Various efficiency measurement tools, such as conventional statistical methods and non-parametric methods, have been successfully developed in the literature. Among these tools, the data envelopment analysis (DEA) approach is one of the most widely discussed. However, problems of discrimination between efficient and inefficient decision-making units also exist in the DEA context (Adler and Yazhemsky, 2010). In this paper, a two-stage approach of integrating independent component analysis (ICA) and data envelopment analysis (DEA) is proposed to overcome this issue. We suggest using ICA first to extract the input variables for generating independent components, then selecting the ICs representing the independent sources of input variables, and finally, inputting the selected ICs as new variables in the DEA model. A simulated dataset and a hospital dataset provided by the Office of Statistics in Taiwan’s Department of Health are used to demonstrate the validity of the proposed two-stage approach. The results show that the proposed method can not only separate performance differences between the DMUs but also improve the discriminatory capability of the DEA’s efficiency measurement.     

Hybrid linear and nonlinear complexity pursuit for blind source separation

Blind source separation (BSS) is an increasingly popular data analysis technique with many applications. Several methods for BSS using the statistical properties of original sources have been proposed; for a famous case, non-Gaussianity, this leads to independent component analysis (ICA). In this paper, we propose a hybrid BSS method based on linear and nonlinear complexity pursuit, which combines three statistical properties of source signals: non-Gaussianity, linear predictability and nonlinear predictability. A gradient learning algorithm is presented by minimizing a loss function. Simulations verify the efficient implementation of the proposed method.     

NMF versus ICA for blind source separation

Blind source separation (BSS) is a problem of recovering source signals from signal mixtures without or very limited information about the sources and the mixing process. From literatures, nonnegative matrix factorization (NMF) and independent component analysis (ICA) seem to be the mainstream techniques for solving the BSS problems. Even though the using of NMF and ICA for BSS is well studied, there is still a lack of works that compare the performances of these techniques. Moreover, the nonuniqueness property of NMF is rarely mentioned even though this property actually can make the reconstructed signals vary significantly, and thus introduces the difficulty on how to choose the representative reconstructions from several possible outcomes. In this paper, we compare the performances of NMF and ICA as BSS methods using some standard NMF and ICA algorithms, and point out the difficulty in choosing the representative reconstructions originated from the nonuniqueness property of NMF.