Optimal distribution of piezoelectric patches for active vibration reduction of a thick plate using singular value decomposition approach.
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ABSTRACT:
SUBMITTER: Nadi A
PROVIDER: S-EPMC8253778 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named sparse tensor alternating thresholding for singular value decomposition (STAT-SVD) is proposed. The proposed procedure features a novel double projection & thresholding scheme, which provides a sharp criterion for thresholding in each iteration. Compared with regular tensor SVD model, STAT-SVD permits more robust estimation under weaker assumptions. Both the upper and lower bounds for estimation accuracy are developed. The proposed procedure is shown to be minimax rate-optimal in a general class of situations. Simulation studies show that STAT-SVD performs well under a variety of configurations. We also illustrate the merits of the proposed procedure on a longitudinal tensor dataset on European country mortality rates. Supplementary materials for this article are available online.
| S-EPMC8290930 | biostudies-literature
Project description:MotivationHigh throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data analysis. Existing methods, aimed at signal reconstruction and deconvolution, in general, are either supervised, contain parameters that need to be estimated or present other types of ad hoc features. We here introduce SubMatrix Selection Singular Value Decomposition (SMSSVD), a parameter-free unsupervised signal decomposition and dimension reduction method, designed to reduce noise, adaptively for each low-rank-signal in a given data matrix, and represent the signals in the data in a way that enable unbiased exploratory analysis and reconstruction of multiple overlaid signals, including identifying groups of variables that drive different signals.ResultsThe SMSSVD method produces a denoised signal decomposition from a given data matrix. It also guarantees orthogonality between signal components in a straightforward manner and it is designed to make automation possible. We illustrate SMSSVD by applying it to several real and synthetic datasets and compare its performance to golden standard methods like PCA (Principal Component Analysis) and SPC (Sparse Principal Components, using Lasso constraints). The SMSSVD is computationally efficient and despite being a parameter-free method, in general, outperforms existing statistical learning methods.Availability and implementationA Julia implementation of SMSSVD is openly available on GitHub (https://github.com/rasmushenningsson/SubMatrixSelectionSVD.jl).Supplementary informationSupplementary data are available at Bioinformatics online.
| S-EPMC6361234 | biostudies-literature
Project description:In microarray data there are a number of biological samples, each assessed for the level of gene expression for a typically large number of genes. There is a need to examine these data with statistical techniques to help discern possible patterns in the data. Our technique applies a combination of mathematical and statistical methods to progressively take the data set apart so that different aspects can be examined for both general patterns and very specific effects. Unfortunately, these data tables are often corrupted with extreme values (outliers), missing values, and non-normal distributions that preclude standard analysis. We develop a robust analysis method to address these problems. The benefits of this robust analysis will be both the understanding of large-scale shifts in gene effects and the isolation of particular sample-by-gene effects that might be either unusual interactions or the result of experimental flaws. Our method requires a single pass and does not resort to complex "cleaning" or imputation of the data table before analysis. We illustrate the method with a commercial data set.
| S-EPMC263735 | biostudies-literature
Project description:BackgroundBoth microarrays and quantitative real-time PCR are convenient tools for studying the transcriptional levels of genes. The former is preferable for large scale studies while the latter is a more targeted technique. Because of platform-dependent systematic effects, simple comparisons or merging of datasets obtained by these technologies are difficult, even though they may often be desirable. These difficulties are exacerbated if there is only partial overlap between the experimental conditions and genes probed in the two datasets.ResultsWe show here that the generalized singular value decomposition provides a practical tool for merging a small, targeted dataset obtained by quantitative real-time PCR of specific genes with a much larger microarray dataset. The technique permits, for the first time, the identification of genes present in only one dataset co-expressed with a target gene present exclusively in the other dataset, even when experimental conditions for the two datasets are not identical. With the rapidly increasing number of publically available large scale microarray datasets the latter is frequently the case. The method enables us to discover putative candidate genes involved in the biosynthesis of the (1,3;1,4)-beta-D-glucan polysaccharide found in plant cell walls.ConclusionWe show that the generalized singular value decomposition provides a viable tool for a combined analysis of two gene expression datasets with only partial overlap of both gene sets and experimental conditions. We illustrate how the decomposition can be optimized self-consistently by using a judicious choice of genes to define it. The ability of the technique to seamlessly define a concept of "co-expression" across both datasets provides an avenue for meaningful data integration. We believe that it will prove to be particularly useful for exploiting large, publicly available, microarray datasets for species with unsequenced genomes by complementing them with more limited in-house expression measurements.
| S-EPMC2562393 | biostudies-literature
Project description:High-dimensional data, such as those obtained from a gene expression microarray or second generation sequencing experiment, consist of a large number of dependent features measured on a small number of samples. One of the key problems in genomics is the identification and estimation of factors that associate with many features simultaneously. Identifying the number of factors is also important for unsupervised statistical analyses such as hierarchical clustering. A conditional factor model is the most common model for many types of genomic data, ranging from gene expression, to single nucleotide polymorphisms, to methylation. Here we show that under a conditional factor model for genomic data with a fixed sample size, the right singular vectors are asymptotically consistent for the unobserved latent factors as the number of features diverges. We also propose a consistent estimator of the dimension of the underlying conditional factor model for a finite fixed sample size and an infinite number of features based on a scaled eigen-decomposition. We propose a practical approach for selection of the number of factors in real data sets, and we illustrate the utility of these results for capturing batch and other unmodeled effects in a microarray experiment using the dependence kernel approach of Leek and Storey (2008, Proceedings of the National Academy of Sciences of the United States of America 105, 18718-18723).
| S-EPMC3165001 | biostudies-literature
Project description:Ultrasound contrast agents (UCAs) are designed to be used below 10 MHz, but interest is growing in studying the response of agents to high-frequency ultrasound. In this study, the subharmonic response of polymer-shelled UCAs with a mean diameter of 1.1 mum excited with 40-MHz tone-bursts of 1-20 cycles was analyzed. UCAs were diluted in water and streamed through a flow phantom that permitted single-bubble backscatter events to be acquired at peak-negative pressures from 0.75 to 5.0 MPa. At each exposure condition, 1000 single-bubble-backscatter events were digitized. Subharmonic content at 20 MHz was screened using a conventional and a singular-value-decomposition (SVD) method. The conventional method evaluated each event spectrum individually while the SVD method treated the 1000-event data set at one time. A subharmonic score (SHS) indicative of how much subharmonic content a 1000-event data set contained was computed for both methods. Empirical-simulation results indicated that SHSs obtained from the two methods were linearly related. Also, experimental data with both methods indicated that subharmonic likelihood increased with pulse duration and peaked near 2 MPa. The SVD method also yielded quantitative information about subharmonic events not available with the conventional method.
| S-EPMC2719484 | biostudies-other
Project description:We describe the use of singular value decomposition in transforming genome-wide expression data from genes x arrays space to reduced diagonalized "eigengenes" x "eigenarrays" space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.
| S-EPMC27718 | biostudies-literature
Project description:BackgroundNumerous studies on discovering the roles of long non-coding RNAs (lncRNAs) in the occurrence, development and prognosis progresses of various human diseases have drawn substantial attentions. Since only a tiny portion of lncRNA-disease associations have been properly annotated, an increasing number of computational methods have been proposed for predicting potential lncRNA-disease associations. However, traditional predicting models lack the ability to precisely extract features of biomolecules, it is urgent to find a model which can identify potential lncRNA-disease associations with both efficiency and accuracy.ResultsIn this study, we proposed a novel model, SVDNVLDA, which gained the linear and non-linear features of lncRNAs and diseases with Singular Value Decomposition (SVD) and node2vec methods respectively. The integrated features were constructed from connecting the linear and non-linear features of each entity, which could effectively enhance the semantics contained in ultimate representations. And an XGBoost classifier was employed for identifying potential lncRNA-disease associations eventually.ConclusionsWe propose a novel model to predict lncRNA-disease associations. This model is expected to identify potential relationships between lncRNAs and diseases and further explore the disease mechanisms at the lncRNA molecular level.
| S-EPMC8561941 | biostudies-literature
Project description:We propose a new sparsification method for the singular value decomposition-called the constrained singular value decomposition (CSVD)-that can incorporate multiple constraints such as sparsification and orthogonality for the left and right singular vectors. The CSVD can combine different constraints because it implements each constraint as a projection onto a convex set, and because it integrates these constraints as projections onto the intersection of multiple convex sets. We show that, with appropriate sparsification constants, the algorithm is guaranteed to converge to a stable point. We also propose and analyze the convergence of an efficient algorithm for the specific case of the projection onto the balls defined by the norms L1 and L2. We illustrate the CSVD and compare it to the standard singular value decomposition and to a non-orthogonal related sparsification method with: 1) a simulated example, 2) a small set of face images (corresponding to a configuration with a number of variables much larger than the number of observations), and 3) a psychometric application with a large number of observations and a small number of variables. The companion R-package, csvd, that implements the algorithms described in this paper, along with reproducible examples, are available for download from https://github.com/vguillemot/csvd.
| S-EPMC6415851 | biostudies-literature
Project description:BackgroundAccurate classification of patients with a complex disease into subtypes has important implications for medicine and healthcare. Using more homogeneous disease subtypes in genetic association analysis will facilitate the detection of new genetic variants that are not detectible using the non-differentiated disease phenotype. Subtype differentiation can also improve diagnostic classification, which can in turn inform clinical decision making and treatment matching. Currently, the most sophisticated methods for disease subtyping perform cluster analysis using patients' clinical features. Without guidance from genetic information, the resultant subtypes are likely to be suboptimal and efforts at genetic association may fail.ResultsWe propose a multi-view matrix decomposition approach that integrates clinical features with genetic markers to detect confirmatory evidence for a disease subtype. This approach groups patients into clusters that are consistent between the clinical and genetic dimensions of data; it simultaneously identifies the clinical features that define the subtype and the genotypes associated with the subtype. A simulation study validated the proposed approach, showing that it identified hypothesized subtypes and associated features. In comparison to the latest biclustering and multi-view data analytics using real-life disease data, the proposed approach identified clinical subtypes of a disease that differed from each other more significantly in the genetic markers, thus demonstrating the superior performance of the proposed approach.ConclusionsThe proposed algorithm is an effective and superior alternative to the disease subtyping methods employed to date. Integration of phenotypic features with genetic markers in the subtyping analysis is a promising approach to identify concurrently disease subtypes and their genetic associations.
| S-EPMC4077642 | biostudies-literature