Optimization on the orthogonal group for independent component analysis

This paper derives a new algorithm that performs independent component analysis (ICA) by optimizing the contrast function of the RADICAL algorithm. The core idea of the proposed optimization method is to combine the global search of a good initial condition with a gradient-descent algorithm. This new ICA algorithm performs faster than the RADICAL algorithm (based on Jacobi rotations) while still preserving, and even enhancing, the strong robustness properties that result from its contrast. © Springer-Verlag Berlin Heidelberg 2007.

Geometric optimization methods for independent component analysis applied on gene expression data

DNA microarrays provide a huge amount of data and require therefore dimensionality reduction methods to extract meaningful biological information. Independent Component Analysis (ICA) was proposed by several authors as an interesting means. Unfortunately, experimental data are usually of poor quality- because of noise, outliers and lack of samples. Robustness to these hurdles will thus be a key feature for an ICA algorithm. This paper identifies a robust contrast function and proposes a new ICA algorithm. © 2007 IEEE.

Broadband terahertz time-domain spectroscopy of drugs-of-abuse and the use of principal component analysis

EPSRC, the European Community IST FP6 Integrated, etc

Principle and analysis of the moving-optical-wedge interferometer

A new type of interferometer, the moving-optical-wedge interferometer, is presented, and its principle and properties are studied. The novel interferometer consists of one beam splitter, two flat fixed mirrors, two fixed compensating plates, one fixed optical wedge, and one moving optical wedge. The optical path difference (OPD) as a function of the displacement of the moving optical wedge from the zero path difference position is accomplished by the straight reciprocating motion of the moving optical wedge. A large physical shift of the moving optical wedge corresponds to a very short OPD value of the new interferometer if the values of the wedge angle and the refractive index of the two optical wedges are given properly. The new interferometer is not so sensitive to the velocity variation of the moving optical wedge and the mechanical disturbances compared with the Michelson interferometer, and it is very applicable to low-spectral-resolution application for any wavenumber region from the far infrared down to the ultraviolet. (C) 2008 Optical Society of America.

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．

On Combining Morphological Component Analysis and Concentric Morphology Model for Mammographic Mass Detection

Mammographic mass detection is an important task for the early diagnosis of breast cancer. However, it is difficult to distinguish masses from normal regions because of their abundant morphological characteristics and ambiguous margins. To improve the mass detection performance, it is essential to effectively preprocess mammogram to preserve both the intensity distribution and morphological characteristics of regions. In this paper, morphological component analysis is first introduced to decompose a mammogram into a piecewise-smooth component and a texture component. The former is utilized in our detection scheme as it effectively suppresses both structural noises and effects of blood vessels. Then, we propose two novel concentric layer criteria to detect different types of suspicious regions in a mammogram. The combination is evaluated based on the Digital Database for Screening Mammography, where 100 malignant cases and 50 benign cases are utilized. The sensitivity of the proposed scheme is 99% in malignant, 88% in benign, and 95.3% in all types of cases. The results show that the proposed detection scheme achieves satisfactory detection performance and preferable compromises between sensitivity and false positive rates.

基于独立分量分析的地震属性分析方法研究

Conventional seismic attribute analysis is not only time consuming, but also has several possible results. Therefore, seismic attribute optimization and multi-attribute analysis are needed. In this paper, Fuyu oil layer in Daqing oil field is our main studying object. And there is much difference between seismic attributes and well logs. So under this condition, Independent Component Analysis (ICA) and Kohonen neural net are introduced to seismic attribute optimization and multi-attribute analysis. The main contents are as follows: (1) Now the method of seismic attribute compression is mainly principal component analysis (PCA). In this article, independent component analysis (ICA), which is superficially related to PCA, but much more powerful, is used to seismic reservoir characterizeation. The fundamental, algorithms and applications of ICA are surveyed. And comparation of ICA with PCA is stydied. On basis of the ne-entropy measurement of independence, the FastICA algorithm is implemented. (2) Two parts of ICA application are included in this article: First, ICA is used directly to identify sedimentary characters. Combined with geology and well data, ICA results can be used to predict sedimentary characters. Second, ICA treats many attributes as multi-dimension random vectors. Through ICA transform, a few good new attributes can be got from a lot of seismic attributes. Attributes got from ICA optimization are independent. (3) In this paper, Kohonen self-organizing neural network is studied. First, the characteristics of neural network’s structure and algorithm is analyzed in detail, and the traditional algorithm is achieved which has been used in seism. From experimental results, we know that the Kohonen self-organizing neural network converges fast and classifies accurately. Second, the self-organizing feature map algorithm needs to be improved because the result of classification is not very exact, the boundary is not quite clear and the velocity is not fast enough, and so on. Here frequency sensitive principle is introduced. Combine it with the self-organizing feature map algorithm, then get frequency sensitive self-organizing feature map algorithm. Experimental results show that it is really better. (4) Kohonen self-organizing neural network is used to classify seismic attributes. And it can be avoided drawing confusing conclusions because the algorithm’s characteristics integrate many kinds of seismic features. The result can be used in the division of sand group’s seismic faces, and so on. And when attributes are extracted from seismic data, some useful information is lost because of difference and deriveative. But multiattributes can make this lost information compensated in a certain degree.

Structural Analysis of Network Traffic Flows

Network traffic arises from the superposition of Origin-Destination (OD) flows. Hence, a thorough understanding of OD flows is essential for modeling network traffic, and for addressing a wide variety of problems including traffic engineering, traffic matrix estimation, capacity planning, forecasting and anomaly detection. However, to date, OD flows have not been closely studied, and there is very little known about their properties. We present the first analysis of complete sets of OD flow timeseries, taken from two different backbone networks (Abilene and Sprint-Europe). Using Principal Component Analysis (PCA), we find that the set of OD flows has small intrinsic dimension. In fact, even in a network with over a hundred OD flows, these flows can be accurately modeled in time using a small number (10 or less) of independent components or dimensions. We also show how to use PCA to systematically decompose the structure of OD flow timeseries into three main constituents: common periodic trends, short-lived bursts, and noise. We provide insight into how the various constituents contribute to the overall structure of OD flows and explore the extent to which this decomposition varies over time.

Improved Process Monitoring Using Nonlinear Principal Component Models

This paper presents two new approaches for use in complete process monitoring. The firstconcerns the identification of nonlinear principal component models. This involves the application of linear
principal component analysis (PCA), prior to the identification of a modified autoassociative neural network (AAN) as the required nonlinear PCA (NLPCA) model. The benefits are that (i) the number of the reduced set of linear principal components (PCs) is smaller than the number of recorded process variables, and (ii) the set of PCs is better conditioned as redundant information is removed. The result is a new set of input data for a modified neural representation, referred to as a T2T network. The T2T NLPCA model is then used for complete process monitoring, involving fault detection, identification and isolation. The second approach introduces a new variable reconstruction algorithm, developed from the T2T NLPCA model. Variable reconstruction can enhance the findings of the contribution charts still widely used in industry by reconstructing the outputs from faulty sensors to produce more accurate fault isolation. These ideas are illustrated using recorded industrial data relating to developing cracks in an industrial glass melter process. A comparison of linear and nonlinear models, together with the combined use of contribution charts and variable reconstruction, is presented.

Application of Nonlinear PCA for Fault Detection in Polymer Extrusion Processes

This paper describes the application of an improved nonlinear principal component analysis (PCA) to the detection of faults in polymer extrusion processes. Since the processes are complex in nature and nonlinear relationships exist between the recorded variables, an improved nonlinear PCA, which incorporates the radial basis function (RBF) networks and principal curves, is proposed. This algorithm comprises two stages. The first stage involves the use of the serial principal curve to obtain the nonlinear scores and approximated data. The second stage is to construct two RBF networks using a fast recursive algorithm to solve the topology problem in traditional nonlinear PCA. The benefits of this improvement are demonstrated in the practical application to a polymer extrusion process.

Improved Nonlinear PCA for Process Monitoring Using Support Vector Data Description

Nonlinear principal component analysis (PCA) based on neural networks has drawn significant attention as a monitoring tool for complex nonlinear processes, but there remains a difficulty with determining the optimal network topology. This paper exploits the advantages of the Fast Recursive Algorithm, where the number of nodes, the location of centres, and the weights between the hidden layer and the output layer can be identified simultaneously for the radial basis function (RBF) networks. The topology problem for the nonlinear PCA based on neural networks can thus be solved. Another problem with nonlinear PCA is that the derived nonlinear scores may not be statistically independent or follow a simple parametric distribution. This hinders its applications in process monitoring since the simplicity of applying predetermined probability distribution functions is lost. This paper proposes the use of a support vector data description and shows that transforming the nonlinear principal components into a feature space allows a simple statistical inference. Results from both simulated and industrial data confirm the efficacy of the proposed method for solving nonlinear principal component problems, compared with linear PCA and kernel PCA.