Inferential Clustering Approach for Microarray Experiments with Replicated Measurements

Cluster analysis has proven to be a useful tool for investigating the association structure among genes in a microarray data set. There is a rich literature on cluster analysis and various techniques have been developed. Such analyses heavily depend on an appropriate (dis)similarity measure. In this paper, we introduce a general clustering approach based on the confidence interval inferential methodology, which is applied to gene expression data of microarray experiments. Emphasis is placed on data with low replication (three or five replicates). The proposed method makes more efficient use of the measured data and avoids the subjective choice of a dissimilarity measure. This new methodology, when applied to real data, provides an easy-to-use bioinformatics solution for the cluster analysis of microarray experiments with replicates (see the Appendix). Even though the method is presented under the framework of microarray experiments, it is a general algorithm that can be used to identify clusters in any situation. The method's performance is evaluated using simulated and publicly available data set. Our results also clearly show that our method is not an extension of the conventional clustering method based on correlation or euclidean distance.     

Quantification of the non-planarity of the human carotid bifurcation

The carotid bifurcation has been a region of particular interest due to its predilection for clinically significant atherosclerosis. It has been shown that the vessel geometry is a major determinant of the local haemodynamic properties which are believed to be associated with the location of atherosclerotic lesions. Current knowledge of the geometry of the carotid bifurcation is insufficient and restricted to basic geometric parameters. To provide some means of quantifying the degree of complexity of the 3D shape of the bifurcation, we made an initial attempt by evaluating the non-planarity of an arterial bifurcation based upon the singular value decomposition theorem.In this paper we present our results obtained on the right carotid bifurcations of six normal subjects, each of whom was scanned twice using the 2D time-of-flight MR sequence. The acquired 2D cross sectional images were processed by using our in-house software which comprises 2D segmentation, 3D reconstruction and smoothing. The centroids of each transverse slices were determined and used as input data for the non-planarity analysis. Our results using the singular value decomposition method have demonstrated discernible differences in non-planarity among individuals. Comparisons with the planarity definition proposed by other investigators suggest that the singular value decomposition method offers more information about the linearity and planarity of the bifurcation. However, it is also realised that a single measure of non-planarity can never fully characterise a bifurcation owing to the great variety of geometries.     

On the statistical analysis of the GS-NS0 cell proteome: imputation, clustering and variability testing

We have undertaken two-dimensional gel electrophoresis proteomic profiling on a series of cell lines with different recombinant antibody production rates. Due to the nature of gel-based experiments not all protein spots are detected across all samples in an experiment, and hence datasets are invariably incomplete. New approaches are therefore required for the analysis of such graduated datasets. We approached this problem in two ways. Firstly, we applied a missing value imputation technique to calculate missing data points. Secondly, we combined a singular value decomposition based hierarchical clustering with the expression variability test to identify protein spots whose expression correlates with increased antibody production. The results have shown that while imputation of missing data was a useful method to improve the statistical analysis of such data sets, this was of limited use in differentiating between the samples investigated, and highlighted a small number of candidate proteins for further investigation.     

Blind Image Blur Assessment Using Singular Value Similarity and Blur Comparisons

The increasing number of demanding consumer image applications has led to increased interest in no-reference objective image quality assessment (IQA) algorithms. In this paper, we propose a new blind blur index for still images based on singular value similarity. The algorithm consists of three steps. First, a re-blurred image is produced by applying a Gaussian blur to the test image. Second, a singular value decomposition is performed on the test image and re-blurred image. Finally, an image blur index is constructed based on singular value similarity. The experimental results obtained on four simulated databases to demonstrate that the proposed algorithm has high correlation with human judgment when assessing blur or noise distortion of images.     

Seven-color fluorescence imaging of tissue samples based on Fourier spectroscopy and singular value decomposition.

Seven-color analyses of immunofluorescence-stained tissue samples were accomplished using Fourier spectroscopy-based hyperspectral imaging and singular value decomposition. This system consists of a combination of seven fluorescent dyes, three filtersets, an epifluorescence microscope, a spectral imaging system, a computer for data acquisition, and data analysis software. The spectra of all pixels in a multicolor image were taken simultaneously using a Sagnac type interferometer. The spectra were deconvolved to estimate the contribution of each component dye, and individual dye images were constructed based on the intensities of assigned signals. To obtain mixed spectra, three filter sets, i.e., Bl, Gr, and Rd for Alexa488 and Alexa532, for Alexa546, Alexa568, and Alexa594, and for Cy5 and Cy5.5, respectively, were used for simultaneous excitation of two or three dyes. These fluorophores have considerable spectral overlap which precludes their separation by conventional analysis. We resolved their relative contributions to the fluorescent signal by a method involving linear unmixing based on singular value decomposition of the matrices consisting of dye spectra. Analyses of mouse thymic tissues stained with seven different fluorescent dyes provided clear independent images, and any combination of two or three individual dye images could be used for constructing multicolor images.     

基于奇异值第一主成分的睡眠脑电分期方法研究

目的:脑电信号含多种噪声和伪迹,信噪比较低,特征提取前必须进行复杂的预处理,严重影响睡眠分期的速度。鉴于此,本文提出一种基于奇异值第一主成分的睡眠脑电分期方法,该方法抗噪性能较强,可省去预处理过程,减少计算量,提高睡眠分期的效率。方法:对未经过预处理的睡眠脑电进行奇异系统分析,研究奇异谱曲线,提取奇异值第一主成分,探索其随睡眠状态变化的规律。并通过支持向量机利用奇异值第一主成分对睡眠分期。结果:奇异值第一主成分不仅能表征脑电信号主体,而且可以抑制噪声、降低维数。随着睡眠的深入,奇异值第一主成分的值逐渐增大,但在REM期处于S1期和S2期之间。经MIT-BIH睡眠数据库中5例同导联位置的脑电数据测试(仅1导脑电数据),睡眠脑电分期的准确率达到86.4%。结论:在未对脑电信号进行预处理的情况下,提取的睡眠脑电的奇异值第一主成分能有效表征睡眠状态,是一种有效的睡眠分期依据。本文运用提出的方法仅采用1导脑电数据,就能得到较为满意的睡眠分期结果。该方法有较强的分类性能,且抗噪能力强,不需要对脑电作复杂的预处理,计算量小,方法简单,很大程度上提高了睡眠分期的效率。     

A Bayesian missing value estimation method for gene expression profile data

MOTIVATION: Gene expression profile analyses have been used in numerous studies covering a broad range of areas in biology. When unreliable measurements are excluded, missing values are introduced in gene expression profiles. Although existing multivariate analysis methods have difficulty with the treatment of missing values, this problem has received little attention. There are many options for dealing with missing values, each of which reaches drastically different results. Ignoring missing values is the simplest method and is frequently applied. This approach, however, has its flaws. In this article, we propose an estimation method for missing values, which is based on Bayesian principal component analysis (BPCA). Although the methodology that a probabilistic model and latent variables are estimated simultaneously within the framework of Bayes inference is not new in principle, actual BPCA implementation that makes it possible to estimate arbitrary missing variables is new in terms of statistical methodology. RESULTS: When applied to DNA microarray data from various experimental conditions, the BPCA method exhibited markedly better estimation ability than other recently proposed methods, such as singular value decomposition and K-nearest neighbors. While the estimation performance of existing methods depends on model parameters whose determination is difficult, our BPCA method is free from this difficulty. Accordingly, the BPCA method provides accurate and convenient estimation for missing values. AVAILABILITY: The software is available at http://hawaii.aist-nara.ac.jp/~shige-o/tools/.     

Generalized optimal spatial filtering using a kernel approach with application to EEG classification

Common spatial patterns (CSP) has been widely used for finding the linear spatial filters which are able to extract the discriminative brain activities between two different mental tasks. However, the CSP is difficult to capture the nonlinearly clustered structure from the non-stationary EEG signals. To relax the presumption of strictly linear patterns in the CSP, in this paper, a generalized CSP (GCSP) based on generalized singular value decomposition (GSVD) and kernel method is proposed. Our method is able to find the nonlinear spatial filters which are formulated in the feature space defined by a nonlinear mapping through kernel functions. Furthermore, in order to overcome the overfitting problem, the regularized GCSP is developed by adding the regularized parameters. The experimental results demonstrate that our method is an effective nonlinear spatial filtering method.     

Determining the movements of the skeleton using well-configured markers

The problem of determining skeletal movements in three dimensions by using a number of landmarks is treated. We present a method that determines the motion of a rigid body by using the positions of the landmarks in least-squares sense. The method uses the singular value decomposition of a matrix derived from the positions of thelandmarks. We show how one can use this method to express movement of skeleton segments relative to each other. As many others have pointed out, the movement can be very ill determined if the landmarks are badly configured. We present a condition number for the problem with good geometrical properties. The condition number depends on the configuration of the landmarks and indicates how to distribute the landmarks in a suitable way.     

Fuzzy kernel clustering of RNA secondary structure ensemble using a novel similarity metric

Measuring the (dis)similarity between RNA secondary structures is critical for the study of RNA secondary structures and has implications to RNA functional characterization. Although a number of methods have been developed for comparing RNA structural similarities, their applications have been limited by the complexity of the required computation. In this paper, we present a novel method for comparing the similarity of RNA secondary structures generated from the same RNA sequence, i.e., a secondary structure ensemble, using a matrix representation of the RNA structures. Relevant features of the RNA secondary structures can be easily extracted through singular value decomposition (SVD) of the representing matrices. We have mapped the feature vectors of the singular values to a kernel space, where (dis)similarities among the mapped feature vectors become more evident, making clustering of RNA secondary structures easier to handle. The pair-wise comparison of RNA structures is achieved through computing the distance between the singular value vectors in the kernel space. We have applied a fuzzy kernel clustering method, using this similarity metric, to cluster the RNA secondary structure ensembles. Our application results suggest that our fuzzy kernel clustering method is highly promising for classifications of RNA structure ensembles, because of its low computational complexity and high clustering accuracy.     

Acetylene reduction in the rhizosphere of rice: Methods of assay

Summary A method is described for thein situ assay of acetylene reduction activity in the rhizosphere of rice involving the use of inexpensive, lightweight equipment. The assay is quick to set up and thus many replicates can be run simultaneously. Control of any acetylene-reducing blue-green algae in the assay chamber is achieved with a photosynthetically active herbicide which has no measurable effect on rhizosphere activity. Results using this method are compared with those from an excised root assay of the same plants. Only a very weak correlation between the two methods was found.     

The use of a synthetic DNA-antibody complex as external reference for chromatin immunoprecipitation

Chromatin immunoprecipitation (ChIP) is an analytical method used to investigate the interactions between proteins and DNA in vivo. ChIP is often used as a quantitative tool, and proper quantification relies on the use of adequate references for data normalization. However, many ChIP experiments involve analyses of samples that have been submitted to experimental treatments with unknown effects, and this precludes the choice of suitable internal references. We have developed a normalization method based on the use of a synthetic DNA-antibody complex that can be used as an external reference instead. A fixed amount of this synthetic DNA-antibody complex is spiked into the chromatin extract at the beginning of the ChIP experiment. The DNA-antibody complex is isolated together with the sample of interest, and the amounts of synthetic DNA recovered in each tube are measured at the end of the process. The yield of synthetic DNA recovery in each sample is then used to normalize the results obtained with the antibodies of interest. Using this approach, we could compensate for losses of material, reduce the variability between ChIP replicates, and increase the accuracy and statistical resolution of the data.     

Improving data acquisition parameters of 31P in vivo spectra for signal analysis in the time domain.

To obtain reliable NMR quantitation, experimental cautions concerning data acquisition must be taken when using automatic predictive calculations. For this study, 2000 31P in vitro and in vivo spectra were processed, using the enhancement procedure with linear prediction using singular value decomposition (EPLPSVD) method, and analyzed. The effects of quadrature detection modes (simultaneous or sequential), of the number of time-domain samples used are investigated and experimental conditions such as sample motions and spectral width are discussed.     

Fuzzy Kernel Clustering of RNA Secondary Structure Ensemble Using a Novel Similarity Metric

Abstract

Measuring the (dis)similarity between RNA secondary structures is critical for the study of RNA secondary structures and has implications to RNA functional characterization. Although a number of methods have been developed for comparing RNA structural similarities, their applications have been limited by the complexity of the required computation. In this paper, we present a novel method for comparing the similarity of RNA secondary structures generated from the same RNA sequence, i.e., a secondary structure ensemble, using a matrix representation of the RNA structures. Relevant features of the RNA secondary structures can be easily extracted through singular value decomposition (SVD) of the representing matrices. We have mapped the feature vectors of the singular values to a kernel space, where (dis)similarities among the mapped feature vectors become more evident, making clustering of RNA secondary structures easier to handle. The pair-wise comparison of RNA structures is achieved through computing the distance between the singular value vectors in the kernel space. We have applied a fuzzy kernel clustering method, using this similarity metric, to cluster the RNA secondary structure ensembles. Our application results suggest that our fuzzy kernel clustering method is highly promising for classifications of RNA structure ensembles, because of its low computational complexity and high clustering accuracy.     

How many replicates of arrays are required to detect gene expression changes in microarray experiments? A mixture model approach

Background  

It has been recognized that replicates of arrays (or spots) may be necessary for reliably detecting differentially expressed genes in microarray experiments. However, the often-asked question of how many replicates are required has barely been addressed in the literature. In general, the answer depends on several factors: a given magnitude of expression change, a desired statistical power (that is, probability) to detect it, a specified Type I error rate, and the statistical method being used to detect the change. Here, we discuss how to calculate the number of replicates in the context of applying a nonparametric statistical method, the normal mixture model approach, to detect changes in gene expression.     

基于Fiedler向量的基因表达谱数据分类方法

尝试将一种基于图的Fiedler向量的聚类算法引入到基因表达谱数据的肿瘤分类中来。该方法将分属不同类的所有样本通过高斯权构造Laplace完全图,经SVD分解后获得Fiedler向量,利用各样本所对应的Fiedler向量分量的符号差异来进行基因表达谱数据的分类。通过模拟数据仿真实验和对白血病两个亚型(ALL与AML)及结肠癌真实数据实验,证明了这一方法的有效性。     

Comparison and testing of least-squares time domain inverse solutions in electrocardiography

The use of several mathematical methods for estimating epicardial ECG potentials from arrays of body surface potentials has been reported in the literature; most of these methods are based on least-squares reconstruction principles and operate in the time-space domain. In this paper we introduce a general Bayesian maximum a posteriori (MAP) framework for time domain inverse solutions in the presence of noise. The two most popular previously applied least-squares methods, constrained (regularized) least-squares and low-rank approximation through the singular value decomposition, are placed in this framework, each of them requiring the a priori knowledge of a ‘regularization parameter’, which defines the degree of smoothing to be applied to the inversion. Results of simulations using these two methods are presented; they compare the ability of each method to reconstruct epicardial potentials. We used the geometric configuration of the torso and internal organs of an individual subject as reconstructed from CT scans. The accuracy of each method at each epicardial location was tested as a function of measurement noise, the size and shape of the subarray of torso sensors, and the regularization parameter. We paid particular attention to an assessment of the potential of these methods for clinical use by testing the effect of using compact, small-size subarrays of torso potentials while maintaining a high degree of resolution on the epicardium.     

On-line state estimation and control in glutamic acid production

An automatic computer control system for glutamic acid production has been developed. A method based on empirical reaction subspace and singular value decomposition was presented for on-line estimation of cell concentration, glutamic acid, and total sugar. The only on-line measured state variable was the oxygen uptake rate. The estimated cell concentration was used as an index for the addition of penicillin. The estimated total sugar concentration was used for system identification. Adaptive control was then applied to manipulate the substrate feeding rate. The total sugar concentration was maintained at a given value during the period of fed-batch culture for glutamic acid production.     

Fermentation data analysis and state estimation in the presence of incomplete mass balance

A method is developed for identifying measurement errors and estimating fermentation states in the presence of unidentified reactant or product. Unlike conventional approaches using elemental balances, this method employs an empirically determined basis, which can tolerate unidentified reaction species. The essence of this approach is derived from the concept of reaction subspace and the technique of singular value decomposition. It is shown that the subspace determined via singular value decomposition of multiple experimental data provides an empirical basis for identifying measurement errors. The same approach is applied to fermentation state estimation. Via the formulation of the reaction subspace, the sensitivity of state estimates to measurement errors is quantified in terms of a dimensionless quantity, maximum error gain (MEG). It is shown that using the empirically determined subspace, one can circumvent the problem of unidentified reaction species, meanwhile reducing the sensitivity of the estimates.