高维数据降维技术及研究进展

降维技术旨在将高维数据映射到更低维的数据空间上以寻求数据紧凑表示,该技术有利于对数据做进一步处理。随着多媒体技术和计算机技术的高速发展,数据维度呈爆炸性增长,使得机器学习、图像处理等研究领域的数据分析变得为越来越困难。为消除上述问题造成的维度灾难,研究学者提出了一系列的解决方法。文中为探索这些降维技术的实用性,介绍了传统的降维技术以及近年推出的降维技术,分析了典型降维技术的性能,指出降维技术仍存在的问题并分析了未来值得关注的研究方向。     

文本数据的非线性降维方法研究

采用了空间解析几何中的球极映射方法,形成高维向量到低维向量的拓扑变换模型,实现了矩阵形武的高维空间文本集合到低维空间文本集合的一一映射,编制了相应的算法,从而有效地解决了文本挖掘中的非线性降维问题,克服了以往研究中的缺陷.     

Analysis and Classification of Frequency-Domain Terahertz Reflection Spectra Using Supervised and Unsupervised Dimensionality Reduction Methods

Journal of Infrared, Millimeter, and Terahertz Waves - The unique properties of terahertz (THz) spectroscopy show a great potential for security and defense applications such as safe screening of...     

A Modified Minimum Classification Error (MCE) Training Algorithm for Dimensionality Reduction

Dimensionality reduction is an important problem in pattern recognition. There is a tendency of using more and more features to improve the performance of classifiers. However, not all the newly added features are helpful to classification. Therefore it is necessary to reduce the dimensionality of feature space for effective and efficient pattern recognition. Two popular methods for dimensionality reduction are Linear Discriminant Analysis (LDA) and Principal Component Analysis (PCA). While these methods are effective, there exists an inconsistency between feature extraction and the classification objective. In this paper we use Minimum Classification Error (MCE) training algorithm for feature dimensionality reduction and classification on Daterding and GLASS databases. The results of MCE training algorithms are compared with those of LDA and PCA.     

Dimensionality Reduction for Hyperspectral Data Based on Sample-Dependent Repulsion Graph Regularized Auto-encoder

To achieve high classification accuracy of hyperspectral data, a dimensionality reduction algorithm called Sample-dependent repulsion graph regularized auto-encoder (SRGAE) is proposed. Based on the sample-dependent graph, by applying the repulsion force to the samples from different classes but nearby, a sampledependent repulsion graph is built to make the samples from the same class will be projected to samples that are close-by and the samples from different classes will be projected to samples that are far away. The sampledependent repulsion graph can avoid the neighborhood parameter selection problem existing in the nearest neighborhood graph. By integrating advantages of deep learning and graph regularization technique, the SRGAE can maintain the learned deep features are consistent with the inherent manifold structure of the original hyperspectral data. Experimental results on two real hyperspectral data show that, when compared with some popular dimensionality reduction algorithms, the proposed SRGAE can yield higher classification accuracy.     

Dimensionality Reduction in Control and Coordination of the Human Hand

The concept of kinematic synergies is proposed to address the dimensionality reduction problem in control and coordination of the human hand. This paper develops a method for extracting kinematic synergies from joint-angular-velocity profiles of hand movements. Decomposition of a limited set of synergies from numerous movements is a complex optimization problem. This paper splits the decomposition process into two stages. The first stage is to extract synergies from rapid movement tasks using singular value decomposition (SVD). A bank of template functions is then created from shifted versions of the extracted synergies. The second stage is to find weights and onset times of the synergies based on $l_1$ -minimization, whose solutions provide sparse representations of hand movements using synergies.      

基于FPGA的高光谱图像奇异值分解降维技术

为了解决高光谱图像维数高、数据量巨大、实时处理技术实现难的问题,提出了高光谱图像实时处理降维技术.采用奇异值分解(SVD)算法对高光谱图像进行降维,又在可编程门阵列(FPGA)芯片中针对这一算法划为自相关模块、特征求解模块、特征提取模块和降维实现模块4个模块进行编程实现、仿真和验证.仿真结果表明,高光谱图像降维后数据量为降维前的1/3,而降维后的分类像素点误差为0.2109%,证明了奇异值分解算法进行高光谱图像降维算法的有效性.     

Unsupervised,Supervised and Semi-supervised Dimensionality Reduction by Low-Rank Regression Analysis

Techniques for dimensionality reduction have attracted much attention in computer vision and pattern recognition.However,for the supervised or unsupervised case,the methods combining regression analysis and spectral graph analysis do not consider the global structure of the subspace;For semi-supervised case,how to use the unlabeled samples more effectively is still an open problem.In this paper,we propose the methods by Low-rank regression analysis (LRRA) to deal with these problems.For supervised or unsupervised dimensionality reduction,combining spectral graph analysis and LRRA can make a global constraint on the subspace.For semi-supervised dimensionality reduction,the proposed method incorporating LRRA can exploit the unlabeled samples more effectively.The experimental results show the effectiveness of our methods.     

Fourier-Based Feature Extraction for Classification of EEG Signals Using EEG Rhythms

In this paper, we propose a method for the analysis and classification of electroencephalogram (EEG) signals using EEG rhythms. The EEG rhythms capture the nonlinear complex dynamic behavior of the brain system and the nonstationary nature of the EEG signals. This method analyzes common frequency components in multichannel EEG recordings, using the filter bank signal processing. The mean frequency (MF) and RMS bandwidth of the signal are estimated by applying Fourier-transform-based filter bank processing on the EEG rhythms, which we refer intrinsic band functions, inherently present in the EEG signals. The MF and RMS bandwidth estimates, for the different classes (e.g., ictal and seizure-free, open eyes and closed eyes, inter-ictal and ictal, healthy volunteers and epileptic patients, inter-ictal epileptogenic and opposite to epileptogenic zone) of EEG recordings, are statistically different and hence used to distinguish and classify the two classes of signals using a least-squares support vector machine classifier. Experimental results, with 100 % classification accuracy, on a real-world EEG signals database analysis illustrate the effectiveness of the proposed method for EEG signal classification.     

压缩深层神经网络隐藏层维度对其分类性能的影响

为了使深层神经网络具有更好的泛化能力、少量训练时间的性能。文中汲取压缩神经网络的思想,通过将深层神经网络的输入层与隐藏层按照不同的比例将隐藏层的维度进行压缩,并在传统压缩深层神经网络的基础上,在其顶层添加一个分类层,使深层神经网络拥有分类的能力。实验将构建的深层神经网络应用于MNIST手写数据集的分类测试,结果表明,经过适当压缩的深层神经网络比未被压缩的深层神经网络具有更好的分类效果,而且节省了大量的训练时间。     

基于遗传算法的射频工艺容差电性能降维建模

针对射频集成工艺中各类工艺容差电性能的多要素耦合模型研究中由多输入带来的"维数灾难"问题,提出了采用遗传算法进行参数优选降维的方法。以纯BP(Back propagation)神经网络为基本多输入模型,根据集成工艺容差的特点,利用遗传算实现了工艺容差主成分的有效提取。在不降低工艺电性能模型精度的情况下,有效降低了建模所需数据量。通过仿真实验表明,遗传算法对工艺容差参数的筛选符合工艺参数对电性能影响的物理规律,可以准确剔除对电性能耦合弱的工艺参数,从而实现降维目的。同时在建模过程中避免了对大数据样本内在复杂物理机理的研究,既保持了建模的合理准确又降低了建模成本。     

基于黎曼流形监督降维的矩阵CFAR增强检测

矩阵CFAR检测是从几何流形角度处理雷达目标检测问题的新技术。为进一步提升其在复杂杂波背景下的检测性能,本文提出一种黎曼流形监督降维的矩阵CFAR增强检测方法。首先,将检测问题视为目标与杂波的分类问题,分别构建黎曼流形上目标单元与杂波单元的类内和类间权重矩阵;其次,为增强目标与杂波的可分性,采用保持类内几何距离最小,类间几何距离最大的准则建立降维目标函数,并基于Grassmann流形求解降维优化问题获得映射矩阵;最后,提出一种矩阵CFAR增强检测方法,实现目标增强检测。采用蒙特卡罗方法对仿真数据和实测海杂波数据进行实验分析,结果表明,所提出的方法能够进一步提升检测性能。      

思维状态的EEG信号分类方法研究

脑电信号(EEG)是一种研究脑活动的重要信息来源,基于脑电信号的人与计算机的通信已成为一种新的人机接口方式.运用时域回归方法对2～5种不同思维脑电信号进行预处理,用AR模型提取信号分段前后特征,最后用BP算法进行分类.并对分段前后的分类结果进行比较,实验表明,该方法达到很好的分类效果.     

Scalp Current Density Mapping: Value and Estimation from Potential Data

Scalp current density (SCD) makes possible the identification of scalp sources and sinks of current. SCD is reference independent and its peaks and troughs are sharper than those of the scalp potential (SP). SCD, by comparison to SP, reflects mainly the activity of cortical generators. SCD mapping appears to be a valuable tool to spatially split smeared SP distribution due to simultaneously active generators. The SCD map may be computed from any sufficiently smooth mathematical SP map. An evaluation of the error of SCD estimation is given for a surface spline method of interpolation of SP. An example of the simultaneous use of SP and SCD in the analysis of somatosensory evoked data is given.     

Single-Mixture Source Separation Using Dimensionality Reduction of Ensemble Empirical Mode Decomposition and Independent Component Analysis

Blind source separation of single-channel mixed recording is a challenging task that has applications in the fields of speech, audio and bio-signal processing. Numerous blind source separation methods are commonly used for blind separation of single input multiple output. However, the priori knowledge of the signal is assumed to be known or the main channels selected from multi-channel output are not self-adaptive and automatic. Presented in this paper is a new method based on dimensionality reduction of ensemble empirical mode decomposition (EEMD), and ICA does not rely on such assumptions. The EEMD represents any time-domain signal as the sum of a finite set of oscillatory components called intrinsic mode functions (IMFs). ICA finds the independent components by maximizing the statistical independence of the dimensionality reduction IMFs. Principal component analysis (PCA) is applied to reduce dimensions of IMFs. The separated performance of EEMD-PCA-ICA algorithm is compared with EEMD-ICA through simulations, and experimental results show EEMD-PCA-ICA algorithm outperforms EEMD-ICA with higher cross-correlation and lower relative root mean squared error (RRMSE).     

Automatic Classification of Spirometric Data

Pattern recognition principles have been applied to 200 sets of spirometric data obtained from pulmonary function laboratory patients. Each patient was classified by a pulmonary specialist as normal, restricted, or mildly, moderately, severely, or very severely obstructed. Each patient was represented by a five-element pattern vector consisting of forced vital capacity (FVC), forced expiratory volume in one second (FEV1), midmaximum flow rate (MMFR), and flow rates with 50 and 25 percent of the vital capacity remaining (V?50 and V?25) normalized by predicted values. By Karhunen-Loeve expansion techniques, this vector was reduced to a two-feature pattern vector with only a 6 percent residual mean square representation error. The more important feature essentially represented the average of the three flow rates, while the second feature depended on FVC and FEV1. Data were divided into training and testing sets, and using the former, a parametric Bayes classifier and one-and two-layer pair-wise Fisher linear classifiers, were designed to assign patterns described by the two derived features to one of the six categories. With the testing set, overall recognition rates were 81 to 82 percent, with most errors representing misclassifications within the four obstructive categories. If the four obstructive classes were considered as a single class, the recognition rate increased to about 94 percent.     

基于相位同步的脑电信号分类算法研究

脑电同步是脑功能区域整合或绑定的表现.文中将相位同步应用于运动意识想象分类,采用希尔伯变换信号处理方法计算脑电信号瞬时相位值.在合适的时间窗下,选取C3、C4电极与中央区电极进行配对并进行锁相值计算,采用支持向量机进行运动意识想象分类.实验结果表明,采用相位同步方法分类准确率达92.5%.     

Entropy-Based Reduction of Traffic Data

This letter proposes an entropy-based methodology to reduce large network traffic data sets obtained by measurements over real networks. The proposed off-line approach, based on the marginal utility concept, reveals interesting results when applied to real data captured over real networks: to show its applicability, results obtained with traffic traces from a popular network game, counter-strike, are presented