Nonlinear autoassociation is not equivalent to PCA

A common misperception within the neural network community is that even with nonlinearities in their hidden layer, autoassociators trained with backpropagation are equivalent to linear methods such as principal component analysis (PCA). Our purpose is to demonstrate that nonlinear autoassociators actually behave differently from linear methods and that they can outperform these methods when used for latent extraction, projection, and classification. While linear autoassociators emulate PCA, and thus exhibit a flat or unimodal reconstruction error surface, autoassociators with nonlinearities in their hidden layer learn domains by building error reconstruction surfaces that, depending on the task, contain multiple local valleys. This interpolation bias allows nonlinear autoassociators to represent appropriate classifications of nonlinear multimodal domains, in contrast to linear autoassociators, which are inappropriate for such tasks. In fact, autoassociators with hidden unit nonlinearities can be shown to perform nonlinear classification and nonlinear recognition.     

Learning Linear and Nonlinear PCA with Linear Programming

An SVM-like framework provides a novel way to learn linear principal component analysis (PCA). Actually it is a weighted PCA and leads to a semi-definite optimization problem (SDP). In this paper, we learn linear and nonlinear PCA with linear programming problems, which are easy to be solved and can obtain the unique global solution. Moreover, two algorithms for learning linear and nonlinear PCA are constructed, and all principal components can be obtained. To verify the performance of the proposed method, a series of experiments on artificial datasets and UCI benchmark datasets are accomplished. Simulation results demonstrate that the proposed method can compete with or outperform the standard PCA and kernel PCA (KPCA) in generalization ability but with much less memory and time consuming.     

基于神经网络的非线性PCA方法

由于普通的主元分析（PCA）方法无法提取数据中的非线性相关特性,本文提出了一种基于神经网络的非线性PCA（NIPCA）方法,不仅提取了高维原始数据的线性信息还能提取非线性信息。在此基础上进一步提出了样本中显著误差及劣点的检测方法,从而支持对其进行合理剔除或是修正,仿真试验表明它能有效地减小误差点对网络训练精度的影响,大大增强了算法的鲁棒性。     

Kernel PCA for Feature Extraction and De-Noising in Nonlinear Regression

In this paper, we propose the application of the Kernel Principal Component Analysis (PCA) technique for feature selection in a high-dimensional feature space, where input variables are mapped by a Gaussian kernel. The extracted features are employed in the regression problems of chaotic Mackey–Glass time-series prediction in a noisy environment and estimating human signal detection performance from brain event-related potentials elicited by task relevant signals. We compared results obtained using either Kernel PCA or linear PCA as data preprocessing steps. On the human signal detection task, we report the superiority of Kernel PCA feature extraction over linear PCA. Similar to linear PCA, we demonstrate de-noising of the original data by the appropriate selection of various nonlinear principal components. The theoretical relation and experimental comparison of Kernel Principal Components Regression, Kernel Ridge Regression and ε-insensitive Support Vector Regression is also provided.     

基于非线性PCA准则的两个盲信号分离算法

该文首先基于Oja定义的非线性PCA准则J1(W),利用矩阵广义逆递推得到一种盲信号分离算法,然后对Karhunen给出的非线性PCA加权误差平方和准则J2(W),采用梯度下降算法和线性寻优而得到另一种自适应盲信号分离算法。对这两个分离算法进行了计算机仿真,仿真结果表明它们的有效性。     

LS-SVM的非线性特征提取新方法及与PCA的关系研究

提出一种基于最小二乘支持向量机(LS-SVM)的非线性特征提取新方法.先将线性特征提取公式表达成与LS-SVM回归算法中相同的形式;再根据SVM思想,将数据集由输入空间映射到高维特征空间,进而通过核技巧实现非线性特征提取.在理论上证明了所提特征提取方法的结果与PCA方法具有一致性,是传统PCA的一种对偶形式,更适合高维特征数据集的提取.最后,通过近红外光谱数据集特征提取实例验证了在上述条件下该方法的优越性.     

基于神经网络的非线性PCA方法

该文采用基于正交最小二乘方法(OLS)的径向基函数(RBF)神经网络进行非线性主元分析(NLPCA)算法的训练，提高了训练速度，且不存在局部最优问题。将其应用到聚丙烯生产的高维非线性数据相关特性的提取中，仿真试验显示这种NLPCA方法提高了熔融指数(MI)的预报精度，具有实际应用价值。     

A novel approach to polarimetric SAR data processing based on Nonlinear PCA

In remotely sensed Synthetic Aperture Radar (SAR) images, scattering from a target is often the result of a mixture of different mechanisms. For this reason, detection of targets and classification of SAR images may be very difficult and very different from other sensor imagery. Fully polarimetric data offer the possibility to separate the different mechanisms, interpret them and consequently identify the geometry of the targets. To achieve this task, several target decomposition techniques have been proposed in the literature to improve the interpretation of this kind of data. Among these, the physical based techniques are the most considered.     

Nonlinear Control of an Electrostatic Micromirror Beyond Pull-In With Experimental Validation

This paper is aimed at demonstrating the potential benefits of applying nonlinear control techniques to a type of microelectromechanical system, namely, electrostatic micromirrors, in order to extend their stable operation range, enhance the system's performance, and allow controller tuning and system operation to be performed in a systematic manner. A nonlinear tracking control based on feedback linearization and trajectory planning has been developed. Aspects essential to the implementation, such as the prevention of devices from destruction due to contact, modeling and sensing schemes, the influence of the dynamics of the driving circuit on performance, and the device characterization, have been thoroughly addressed, and practical solutions have been proposed. The experimentation is performed on a setup built with low-cost commercial off-the-shelf instruments and components in a laboratory environment. The experimental results show that the developed control system can achieve stable operation beyond the pull-in position for both set-point and scanning controls.$hfill$ [2008-0268]      

SVM和基于PCA、PLS的SVM在非线性辨识中的比较研究*

对于同一个非线性系统,比较单纯ε不灵敏支持向量机方法和基于主元提取、基于偏最小二乘提取的ε不灵敏支持向量机方法在输入相关和不相关两种情况下的拟合性能和抗干扰性能。仿真结果表明：当输入变量之间存在相关性时,基于特征提取的方法优于直接采用ε不灵敏支持向量机的方法。     

Local PCA algorithms

Within the last years various principal component analysis (PCA) algorithms have been proposed. In this paper we use a general framework to describe those PCA algorithms which are based on Hebbian learning. For an important subset of these algorithms, the local algorithms, we fully describe their equilibria, where all lateral connections are set to zero and their local stability. We show how the parameters in the PCA algorithms have to be chosen in order to get an algorithm which converges to a stable equilibrium which provides principal component extraction.     

PCA versus LDA

In the context of the appearance-based paradigm for object recognition, it is generally believed that algorithms based on LDA (linear discriminant analysis) are superior to those based on PCA (principal components analysis). In this communication, we show that this is not always the case. We present our case first by using intuitively plausible arguments and, then, by showing actual results on a face database. Our overall conclusion is that when the training data set is small, PCA can outperform LDA and, also, that PCA is less sensitive to different training data sets     

Nonlinear Observer-based Control Design and Experimental Validation for Gasoline Engines with Exhaust Gas Recirculation

This paper presents a nonlinear observer-based control design approach for gasoline engines equipped with exhaust gas recirculation (EGR) system. A mean value engine model is designed for control which includes both the intake manifold and exhaust manifold dynamic focused on gas mass flows. Then, the nonlinear feedback controller based on the developed model is designed for the state tracking control, and the stability of the close loop system is guaranteed by a constructed Lyapunov function. Since the exhaust manifold pressure is usually unmeasurable in the production engines, a nonlinear observer-based feedback controller is proposed by using standard sensors equipped on the engine, and the asymptotic stability of the both observer dynamic system and control dynamic system are guaranteed with Lyapunov design assisted by the detail analysis of the model. The experimental validations show that the observer-based nonlinear feedback controller is able to regulate the intake pressure and exhaust pressure state to the desired values during both the steady-state and transient conditions quickly by only using the standard sensors.     

Variational Bayesian functional PCA

A Bayesian approach to analyze the modes of variation in a set of curves is suggested. It is based on a generative model thus allowing for noisy and sparse observations of curves. A Demmler-Reinsch(-type) basis is used to enforce smoothness of the latent (‘eigen’)functions. Inference, including estimation, error assessment and model choice, particularly the choice of the number of eigenfunctions and their degree of smoothness, is derived from a variational approximation of the posterior distribution. The proposed analysis is illustrated with simulated and real data.     

Probabilistic PCA Self-Organizing Maps

In this paper, we present a probabilistic neural model, which extends Kohonen's self-organizing map (SOM) by performing a probabilistic principal component analysis (PPCA) at each neuron. Several SOMs have been proposed in the literature to capture the local principal subspaces, but our approach offers a probabilistic model while it has a low complexity on the dimensionality of the input space. This allows to process very high-dimensional data to obtain reliable estimations of the probability densities which are based on the PPCA framework. Experimental results are presented, which show the map formation capabilities of the proposal with high-dimensional data, and its potential in image and video compression applications.     

一种自适应权值的PCA算法

针对传统PCA方法对离群点鲁棒性差的问题,提出了一种具有更高鲁棒性且自适应权值的PCA方法。在PCA方法的基础上建立了一个加权的重建误差和最小模型,通过引入信息熵来调节重建误差的权值;通过交替优化算法迭代求解模型。在Yale人脸库和UCI数据集上的实验表明该方法具有很好的鲁棒性和识别率。     

Variational Bayesian functional PCA

A Bayesian approach to analyze the modes of variation in a set of curves is suggested. It is based on a generative model thus allowing for noisy and sparse observations of curves. A Demmler–Reinsch(-type) basis is used to enforce smoothness of the latent (‘eigen’)functions. Inference, including estimation, error assessment and model choice, particularly the choice of the number of eigenfunctions and their degree of smoothness, is derived from a variational approximation of the posterior distribution. The proposed analysis is illustrated with simulated and real data.     

PCA在语音检测中的应用研究

提出主元分析PCA(Principal Component Analysis)用于语音检测的方法研究.用主元分析法在多维空间中建立坐标轴,将待处理信号投影到该坐标轴中,通过分析投影结果判断是否为语音信号.通过将语音和非语音分别建立子空间,来区分语音和非语音信号.该方法不同于常规的语音时域、频域处理方法,而是在多维空间中对信号进行分析.实验结果表明,该方法准确率高、简单、容易实现,而且能区分多种非语音信号.