Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Dimensionality Reduction”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7Linked to original sources
PubMed2025

Mechanisms of enhanced or impaired DNA target selectivity driven by protein dimerization.

Successful DNA transcription demands coordination between proteins that bind DNA while simultaneously binding to one another to form dimers or higher-order complexes. For proteins with numerous DNA targets throughout the genome, measurements that report on their dwell time or occupancy thus represent a convolution over a population interacting with specific DNA, nonspecific DNA, or protein partners on DNA. Dimerization is known to add contacts that can help a single protein to stably bind DNA. However, we show here that dimerization can also impair measured dwell times and occupancy on target sequences because the population redistributes across DNA. We combine mass-action kinetic models of pairwise reversible reactions between proteins and DNA with theory and spatial stochastic simulations to isolate the role of dimerization on observed DNA dwell times, occupancy, and spatial distribution of proteins on DNA. Three key themes emerge: (i) Protein-protein interactions, in addition to protein-DNA interactions, can localize a protein to DNA, and relative binding rates can thus widely tune dwell times. (ii) Dimensional reduction achieved through nonspecific binding and subsequent 1D diffusion controls the order-of-magnitude of enhancements despite nucleosome barriers. (iii) Dimerization enhances selectivity for locally clustered targets and often impairs binding to widely-spaced targets by sequestration. Compared with ChIP-seq data, our model explains how the distribution of the essential GAF protein throughout the genome is highly selective for clustered targets due to protein interactions. This model framework predicts when even weak dimerization can redistribute and stabilize proteins on DNA as a necessary part of transcription.

DNA binding↗
PubMed2001

The Whitney reduction network: a method for computing autoassociative graphs.

This article introduces a new architecture and associated algorithms ideal for implementing the dimensionality reduction of an m-dimensional manifold initially residing in an n-dimensional Euclidean space where n >> m. Motivated by Whitney's embedding theorem, the network is capable of training the identity mapping employing the idea of the graph of a function. In theory, a reduction to a dimension d that retains the differential structure of the original data may be achieved for some d < or = 2m + 1. To implement this network, we propose the idea of a good-projection, which enhances the generalization capabilities of the network, and an adaptive secant basis algorithm to achieve it. The effect of noise on this procedure is also considered. The approach is illustrated with several examples.

Journal Article↗
PubMed2005

Accounting for probe-level noise in principal component analysis of microarray data.

MOTIVATION: Principal Component Analysis (PCA) is one of the most popular dimensionality reduction techniques for the analysis of high-dimensional datasets. However, in its standard form, it does not take into account any error measures associated with the data points beyond a standard spherical noise. This indiscriminate nature provides one of its main weaknesses when applied to biological data with inherently large variability, such as expression levels measured with microarrays. Methods now exist for extracting credibility intervals from the probe-level analysis of cDNA and oligonucleotide microarray experiments. These credibility intervals are gene and experiment specific, and can be propagated through an appropriate probabilistic downstream analysis. RESULTS: We propose a new model-based approach to PCA that takes into account the variances associated with each gene in each experiment. We develop an efficient EM-algorithm to estimate the parameters of our new model. The model provides significantly better results than standard PCA, while remaining computationally reasonable. We show how the model can be used to 'denoise' a microarray dataset leading to improved expression profiles and tighter clustering across profiles. The probabilistic nature of the model means that the correct number of principal components is automatically obtained.

Algorithms↗
PubMed2003

Evaluation of stress patterns generated by reduction forceps within a photoelastic mandibular model.

INTRODUCTION: Little attention has been paid to the mechanical effects of fracture reduction forceps. AIM: This study aims to evaluate the stress patterns within the fractured mandible generated by reduction forceps. MATERIAL AND METHODS: Thirty-six mandibular models were fabricated using a photoelastic resin. Each of the three sets of mandibular models was osteotomized according to one of three different fracture types. After reducing the cut segments, reduction forceps were placed into different engagement holes to compress the segments. Photoelastic stress analysis was used to visualize the stress patterns within the fractured mandibular models as generated by the reduction forceps. RESULTS: In the case of symphyseal or parasymphyseal fractures, an optimum distribution of stresses over the fracture site was achieved when placing the reduction forceps more than 12mm away from either side of the fracture line, between the midway level of the mandibular height (bisecting the mandible) and 5mm below this level. In the case of body fractures, optimum stress distribution was achieved when the reduction forceps were placed more than 16mm from the fracture line at the midway level. CONCLUSION: Correct use of the reduction forceps helps to provide a precise three-dimensional reduction for mandibular fractures.

Birefringence↗
PubMedDate not supplied

Transferring of speech movements from video to 3D face space.

We present a novel method for transferring speech animation recorded in low quality videos to high resolution 3D face models. The basic idea is to synthesize the animated faces by an interpolation based on a small set of 3D key face shapes which span a 3D face space. The 3D key shapes are extracted by an unsupervised learning process in 2D video space to form a set of 2D visemes which are then mapped to the 3D face space. The learning process consists of two main phases: 1) Isomap-based nonlinear dimensionality reduction to embed the video speech movements into a low-dimensional manifold and 2) K-means clustering in the low-dimensional space to extract 2D key viseme frames. Our main contribution is that we use the Isomap-based learning method to extract intrinsic geometry of the speech video space and thus to make it possible to define the 3D key viseme shapes. To do so, we need only to capture a limited number of 3D key face models by using a general 3D scanner. Moreover, we also develop a skull movement recovery method based on simple anatomical structures to enhance 3D realism in local mouth movements. Experimental results show that our method can achieve realistic 3D animation effects with a small number of 3D key face models.

Algorithms↗
PubMed1987

Reduction, the trace formula, and semiclassical asymptotics.

We state a theorem that relates the theory of dimensional reduction in Hamiltonian mechanics to the spectral properties of elliptic operators with symmetries on compact manifolds. As an application, we show that the spectrum of the Schrödinger operator, -[unk]hDelta + V, as [unk]h --> 0, contains geometric information about the closed trajectories of a classical particle with Hamiltonian p(2) + V(q). More generally, we show that this is true for particles with internal degrees of freedom and subject to an external Yang-Mills field, the classical limit being the Wong-Sternberg-Weinstein system for such particles.

Journal Article↗
PubMed2006

Complexity of free energy landscapes of peptides revealed by nonlinear principal component analysis.

Employing the recently developed hierarchical nonlinear principal component analysis (NLPCA) method of Saegusa et al. (Neurocomputing 2004;61:57-70 and IEICE Trans Inf Syst 2005;E88-D:2242-2248), the complexities of the free energy landscapes of several peptides, including triglycine, hexaalanine, and the C-terminal beta-hairpin of protein G, were studied. First, the performance of this NLPCA method was compared with the standard linear principal component analysis (PCA). In particular, we compared two methods according to (1) the ability of the dimensionality reduction and (2) the efficient representation of peptide conformations in low-dimensional spaces spanned by the first few principal components. The study revealed that NLPCA reduces the dimensionality of the considered systems much better, than did PCA. For example, in order to get the similar error, which is due to representation of the original data of beta-hairpin in low dimensional space, one needs 4 and 21 principal components of NLPCA and PCA, respectively. Second, by representing the free energy landscapes of the considered systems as a function of the first two principal components obtained from PCA, we obtained the relatively well-structured free energy landscapes. In contrast, the free energy landscapes of NLPCA are much more complicated, exhibiting many states which are hidden in the PCA maps, especially in the unfolded regions. Furthermore, the study also showed that many states in the PCA maps are mixed up by several peptide conformations, while those of the NLPCA maps are more pure. This finding suggests that the NLPCA should be used to capture the essential features of the systems.

Computer Simulation↗
PubMed1996

Dynamics of the sit-to-stand movement.

The strategies of the sit-to-stand movement are investigated by describing the movement in terms of the topology of an associated phase diagram. Kinematic constraints are applied to describe movement sequences, thus reducing the dimension of the phase space. This dimensional reduction allows us to apply theorems of topological dynamics for two-dimensional systems to arrive at a classification of six possible movement strategies, distinguished by the topology of their corresponding phase portrait. Since movement is treated in terms of topological structure rather than specific trajectories, individual variations are automatically included, and the approach is by nature model independent. Pathological movement is investigated, and this method clarifies how subtle abnormalities in movement lead to difficulties in achieving a stable stance upon rising from a seated position.

Humans↗
PubMed2005

Transmit and receive transmission line arrays for 7 Tesla parallel imaging.

Transceive array coils, capable of RF transmission and independent signal reception, were developed for parallel, 1H imaging applications in the human head at 7 T (300 MHz). The coils combine the advantages of high-frequency properties of transmission lines with classic MR coil design. Because of the short wavelength at the 1H frequency at 300 MHz, these coils were straightforward to build and decouple. The sensitivity profiles of individual coils were highly asymmetric, as expected at this high frequency; however, the summed images from all coils were relatively uniform over the whole brain. Data were obtained with four- and eight-channel transceive arrays built using a loop configuration and compared to arrays built from straight stripline transmission lines. With both the four- and the eight-channel arrays, parallel imaging with sensitivity encoding with high reduction numbers was feasible at 7 T in the human head. A one-dimensional reduction factor of 4 was robustly achieved with an average g value of 1.25 with the eight-channel transmit/receive coils.

Brain↗
PubMed2004

Evaluation of structural similarity based on reduced dimensionality representations of protein structure.

Protein similarity estimations can be achieved using reduced dimensional representations and we describe a new application for the generation of two-dimensional maps from the three-dimensional structure. The code for the dimensionality reduction is based on the concept of pseudo-random generation of two-dimensional coordinates and Monte Carlo-like acceptance criteria for the generated coordinates. A new method for calculating protein similarity is developed by introducing a distance-dependent similarity field. Similarity of two proteins is derived from similarity field indices between amino acids based on various criteria such as hydrophobicity, residue replacement factors and conformational similarity, each showing a one factor Gaussian dependence. Results on comparisons of misfolded protein models with data sets of correctly folded structures show that discrimination between correctly folded and misfolded structures is possible. Tests were carried out on five different proteins, comparing a misfolded protein structure with members of the same topology, architecture, family and domain according to the CATH classification.

Computational Biology↗
PubMed2003

Computation in a single neuron: Hodgkin and Huxley revisited.

A spiking neuron "computes" by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a nonlinear decision function over the low-dimensional space. Generalizations of the reverse correlation technique with white noise input provide a numerical strategy for extracting the relevant low-dimensional features from experimental data, and information theory can be used to evaluate the quality of the low-dimensional approximation. We apply these methods to analyze the simplest biophysically realistic model neuron, the Hodgkin-Huxley (HH) model, using this system to illustrate the general methodological issues. We focus on the features in the stimulus that trigger a spike, explicitly eliminating the effects of interactions between spikes. One can approximate this triggering "feature space" as a two-dimensional linear subspace in the high-dimensional space of input histories, capturing in this way a substantial fraction of the mutual information between inputs and spike time. We find that an even better approximation, however, is to describe the relevant subspace as two dimensional but curved; in this way, we can capture 90% of the mutual information even at high time resolution. Our analysis provides a new understanding of the computational properties of the HH model. While it is common to approximate neural behavior as "integrate and fire," the HH model is not an integrator nor is it well described by a single threshold.

Action Potentials↗
PubMed2004

Multidimensional support vector machines for visualization of gene expression data.

MOTIVATION: Since DNA microarray experiments provide us with huge amount of gene expression data, they should be analyzed with statistical methods to extract the meanings of experimental results. Some dimensionality reduction methods such as Principal Component Analysis (PCA) are used to roughly visualize the distribution of high dimensional gene expression data. However, in the case of binary classification of gene expression data, PCA does not utilize class information when choosing axes. Thus clearly separable data in the original space may not be so in the reduced space used in PCA. RESULTS: For visualization and class prediction of gene expression data, we have developed a new SVM-based method called multidimensional SVMs, that generate multiple orthogonal axes. This method projects high dimensional data into lower dimensional space to exhibit properties of the data clearly and to visualize a distribution of the data roughly. Furthermore, the multiple axes can be used for class prediction. The basic properties of conventional SVMs are retained in our method: solutions of mathematical programming are sparse, and nonlinear classification is implemented implicitly through the use of kernel functions. The application of our method to the experimentally obtained gene expression datasets for patients' samples indicates that our algorithm is efficient and useful for visualization and class prediction. CONTACT: komura@hal.rcast.u-tokyo.ac.jp.

Algorithms↗
PubMed2005

Sample phenotype clusters in high-density oligonucleotide microarray data sets are revealed using Isomap, a nonlinear algorithm.

BACKGROUND: Life processes are determined by the organism's genetic profile and multiple environmental variables. However the interaction between these factors is inherently non-linear. Microarray data is one representation of the nonlinear interactions among genes and genes and environmental factors. Still most microarray studies use linear methods for the interpretation of nonlinear data. In this study, we apply Isomap, a nonlinear method of dimensionality reduction, to analyze three independent large Affymetrix high-density oligonucleotide microarray data sets. RESULTS: Isomap discovered low-dimensional structures embedded in the Affymetrix microarray data sets. These structures correspond to and help to interpret biological phenomena present in the data. This analysis provides examples of temporal, spatial, and functional processes revealed by the Isomap algorithm. In a spinal cord injury data set, Isomap discovers the three main modalities of the experiment--location and severity of the injury and the time elapsed after the injury. In a multiple tissue data set, Isomap discovers a low-dimensional structure that corresponds to anatomical locations of the source tissues. This model is capable of describing low- and high-resolution differences in the same model, such as kidney-vs.-brain and differences between the nuclei of the amygdala, respectively. In a high-throughput drug screening data set, Isomap discovers the monocytic and granulocytic differentiation of myeloid cells and maps several chemical compounds on the two-dimensional model. CONCLUSION: Visualization of Isomap models provides useful tools for exploratory analysis of microarray data sets. In most instances, Isomap models explain more of the variance present in the microarray data than PCA or MDS. Finally, Isomap is a promising new algorithm for class discovery and class prediction in high-density oligonucleotide data sets.

Algorithms↗
PubMed1992

[Treatment of unstable fractures of thoracolumbar spine with neurologic injury using a reduction fixation spinal pedicle screws system].

Twenty-six patients with unstable burst fractures, chance fractures and fractures dislocations of the lower thoracic and lumbar spine were treated with a spinal pedical screw reduction fixation system (RF system). This system is a new device designed by Chinese scientists. In biomechanical testing, it provided three-dimensional reduction forces. The special design of angle pedicle screw provided accurate angle to restore the normal thoracic lumbar lordosis and to maintain it. The three-column spine in a lordotic position maximized the reduction and indirectly achieved a neurologic decompression in the spinal canal. All patients had an anatomical reduction by RF system except one case operated two weeks after injury, the spinal canal area increased over 30% by CT (P < 0.01). Except four cases with Frankle A out of twenty patients with neurologic deficits, all other patients had at least one grade progress. Of them one improved from A to D, ten from C and D to normal. These twenty patients were followed-up over six months. All of them maintained anatomical reduction by RF system. Bone grafting had successful fusion by follow-up X-ray examinations. There were no important complications after surgery. The system is of simple structure facilitation implantation and enable the patients beginning ambulatory movements early, therefore it gives more satisfactory results over conventional Harrington and other segmental spinal instrumentation systems.

Adolescent↗
PubMed2005

Canards for a reduction of the Hodgkin-Huxley equations.

This paper shows that canards, which are periodic orbits for which the trajectory follows both the attracting and repelling part of a slow manifold, can exist for a two-dimensional reduction of the Hodgkin-Huxley equations. Such canards are associated with a dramatic change in the properties of the periodic orbit within a very narrow interval of a control parameter. By smoothly connecting stable and unstable manifolds in an asymptotic limit, we predict with great accuracy the parameter value at which the canards exist for this system. This illustrates the power of using singular perturbation theory to understand the dynamical properties of realistic biological systems.

Action Potentials↗
PubMed2002

Advances in computers and image processing with applications in nuclear medicine.

The continuing advances in hardware performance had made many previously computationally unattractive methods feasible, an example being iterative reconstruction in tomography, which is now routine. Dynamic SPECT can also be performed. However the aim of image processing is not just to produce pretty pictures, but to extract good clinical information. The methods also need to incorporate clinical knowledge and be defined using clinical constraints. In general data in nuclear medicine are n-D, often 3-D plus time. Data reduction for example by the extraction of physiological information, is important. Such data are in any case hard to visualise without compression, for example some kind of dimensionality reduction, going from n-D to a 2-D "functional" image. Both linear and non-linear operations can be considered. To extract physiological data, we need to fit models. Two classes of method are important: data driven and hypothesis driven. Examples of data driven methods are principal component analysis and factor analysis, where the model is derived form the data. Hypothesis driven methods are all implicitly or explicitly based on model fitting. A preliminary data driven step followed by an hypothesis driven approach could be called constrained statistical image analysis. Examples are shown as used in nuclear medicine and are being extended to MRI. Another important problem considered is that of multi-modality image registration and fusion. Although many methods exist, all based on the minimisation of an appropriate distance functions between 2 image data sets such as mutual information, additional constraints are required when the images are not so similar. Additional constraints can be imposed by means of cluster analysis of the n-dimensional feature space. In the analysis of such data, tests against reference data sets (atlases) are required, normally requiring warping the data sets in space, for example by the use of optic flow, or some kind of diffusion equation. Real time analysis of data during acquisition can lead to optimisation of acquisition procedures. Incorporation of such image analysis into a decision support system is desirable.

Algorithms↗
PubMed1998

Application of Kohonen Neural Networks in classification of biologically active compounds.

Automated data classification is an indispensable tool in Drug Design. It allows to select homogeneous training sets or to distinguish compounds with required biological properties. The Kohonen Neural Networks (KNN) suggest new means for classification of biologically interesting compounds. In this paper, first, capabilities of KNN in data dimensionality reduction are presented as compared with the capabilities of Principal Component Analysis (PCA) and Hierarchical Cluster Analysis (HCA). The advantages of KNN become evident with increasing data dimensionality and size of the training set. Then, new methods are suggested to evaluate the quality of KNN models. Finally, a case study on chemical and biological data is presented. The database studied includes more than 2000 organophosphorous potent pesticides. The Kohonen maps were obtained which allow to distinguish compounds with different biological behavior.

Cluster Analysis↗
PubMed2002

Semi-three-dimensional algorithm for time-resolved diffuse optical tomography by use of the generalized pulse spectrum technique.

Although a foil three-dimensional (3-D) reconstruction with both 3-D forward and inverse models provide, the optimal solution for diffuse optical tomography (DOT), because of the 3-D nature of photon diffusion in tissue, it is computationally costly for both memory requirement and execution time in a conventional computing environment. Thus in practice there is motivation to develop an image reconstruction algorithm with dimensional reduction based on some modeling approximations. Here we have implemented a semi-3-D modified generalized pulse spectrum technique for time-resolved DOT, where a two-dimensional (2-D) distribution of optical properties is approximately assumed, while we retain 3-D distribution of photon migration in tissue. We have validated the proposed algorithm by reconstructing 3-D structural test objects from both numerically simulated and experimental date. We demonstrate our algorithm by comparing it with the calibrated 2-D reconstruction that is in widespread use as a shortcut to 3-D imaging and proving that the semi-3-D algorithm outperforms the calibrated 2-D algorithm.

Algorithms↗