Reduced Dimension Representation Research Articles

Hybrid Sampling/Spectral Method for Solving Stochastic Coupled Problems

In this paper, we present a hybrid method that combines Monte Carlo sampling and spectral methods for solving stochastic coupled problems. After partitioning the stochastic coupled problem into subsidiary subproblems, the proposed hybrid method entails iterating between these subproblems in a way that enables the use of the Monte Carlo sampling method for subproblems that depend on a very large number of uncertain parameters and the use of spectral methods for subproblems that depend on only a small or moderate number of uncertain parameters. To facilitate communication between the subproblems, the proposed hybrid method shares between the subproblems a reference representation of all the solution random variables in the form of an ensemble of samples; for each subproblem solved by a spectral method, it uses a dimension-reduction technique to transform this reference representation into a subproblem-specific reduced-dimensional representation to facilitate a computationally efficient solution in a reduced...

Spectral signatures for the classification of microbial species using Raman spectra

In general, classification-based methods based on confocal Raman microscopy are focused on targeted studies under which the spectral libraries are collected under controlled instrument parameters, which facilitate analyses via standard multivariate data analysis methods and cross-validation. We develop and compare approaches to transform spectra collected at different spectral ranges and varying levels of resolution into a single lower-dimension spectral signature library. This will result in a more robust analysis method able to accommodate spectra accumulated at different times and conditions. We demonstrate these approaches on a relevant test case; the identification of microbial species from a natural environment. The training data were based on samples prepared for three unique species collected at two time points and the test data consisted of blinded unknowns prepared and analyzed at a later date with different instrument parameters. The results indicate that using reduced dimension representations of the spectral signatures improves classification accuracy over basic alignment protocols. In particular, utilizing the microbial species partial least squares discriminant analysis classifier on the blinded samples based on alignment achieved ~78% accuracy, while both binning and peak selection approaches yielded 100% accuracy.

The Detection Method of Image Regional Forgery Based DWT and 2DIMPCA

Copy-Move is a common forgery in the research field of digital image forensics, this paper proposes a detection approach based on wavelet transform and two-dimensional image principal component analysis. After reducing the image dimension by Discrete Wavelet Transform(DWT)，2DIMPCA is applied to the fixed sized overlapping blocks of a low-frequency image in the wavelet sub-band to yield a reduced dimension representation from the horizontal direction and the vertical direction. The eigenvectors are then lexicographically sorted, the forgery part are localized by detecting for all neighborhood vectors by a certain threshold. The experiments demonstrate that the proposed approach can not only localize the copy forgery regions accurately, but also reduce the amount of computation and improve the detection efficiency.

Reduced representations of vector-valued coupling variables in decomposition-based design optimization

Decomposition-based optimization strategies decouple a system design problem and introduce coupling variables as decision variables that manage communication among subproblems. The computational cost of such approaches is comparable to that of the equivalent, yet usually unsuccessful, attempts to solve the coupled system directly when the coupling variables consist of a small, finite number of scalars. When the coupling variables are infinite-dimensional quantities, such as functional data, implementing decomposition-based optimization strategies may become computationally challenging. Discretization is typically applied, transforming infinite-dimensional variables into finite-dimensional ones represented as vectors. A large number of discretized points is often necessary to ensure a sufficiently accurate representation of the functional data, and so the dimensionality of these vector-valued coupling variables (VVCVs) can become prohibitively large for decomposition-based design optimization. Therefore, it is desirable to approximate the VVCVs with a reduced dimension representation that improves optimization efficiency while preserving sufficient accuracy. We investigate two VVCV representation techniques, radial-basis function artificial neural networks and proper orthogonal decomposition, and implement each in an analytical target cascading problem formulation for electric vehicle powertrain system optimization. Specifically, both techniques are applied to VVCVs associated with motor boundary torque curves and power loss maps and are assessed in terms of dimensionality reduction, computational expense, and accuracy.

Gesture Control of Sound Synthesis: Analysis and Classification of Percussion Gestures

In recent years, the control of virtual instruments or sound-synthesis processes by natural gestures has become an important research field, both for building new audio-visual tools and for exploring gesture-sound relationships. Such multimodal and interactive tools typically present two advantages, on the one hand they provide realistic virtual instruments whose response can be compared to existing musical instruments, and on the other hand they give the possibility to vary characteristics of natural gestures, while ensuring a certain coherence between gesture and sound parameters. In this paper, we present and evaluate a new framework for explicitly expressing the characteristics of natural percussion gestures used for modeling, controlling and finally synthesizing new percussion gestures. A preliminary analysis of pre-recorded gestures leads to the identification and evaluation of significant parameters using a classification approach. This analysis shows that a reduced-dimension representation of captured motion can be used to control a virtual character. Furthermore, the simulated gestures provide dynamical variables that can be used to control sound synthesis through a mapping-interaction process.

Non‐negative Matrix Factorization for the identification of patterns of atmospheric pressure and geopotential for the Northern Hemisphere

AbstractAs the atmospheric system is characterized by highly complex interactions between a large number of physical variables, it is a challenging task for researchers to break up the complicated structures into a few significant modes of variability.An innovative technique, called Non‐negative Matrix Factorization (NMF), developed to provide a reduced‐dimensional representation of large‐scale non‐negative data and to extract underlying features, is introduced as a tool for meteorological applications. The method is used to decompose space‐time meteorological fields into spatial patterns and associated time indices in order to advance our knowledge of dominant atmospheric processes. For the Northern Hemisphere the 500 hPa geopotential field together with sea level pressure (SLP) are analysed using an up‐to‐date NMF algorithm as well as a helpful method of NMF initialization based on Singular Value Decomposition (SVD). Several NMF patterns correspond to the variations identified by traditional EOF analysis, such as the East Atlantic and the Pacific/North American Pattern. For the North Atlantic Oscillation the NMF identifies sub‐patterns: The positive phase is associated with systems of pressure variation over the Pacific Ocean and the Arctic, respectively, the negative phase resembles the EOF pattern.As the NMF patterns not only represent variability, like EOF patterns, but also are fractions of the total observed values, we demonstrate for a location near Nikolski, Alaska, the temporal development of the geopotential as a superposition of NMF‐factors. Copyright © 2009 Royal Meteorological Society

Signal-to-noise ratios for measuring saliency of features extracted by eigenvector methods from ophthalmic arterial Doppler signals

Abstract: Features are used to represent patterns with minimal loss of important information. The feature vector, which is composed of the set of all features used to describe a pattern, is a reduced-dimensional representation of that pattern. Medical diagnostic accuracies can be improved when the pattern is simplified through representation by important features. By identifying a set of salient features, the noise in a classification model can be reduced, resulting in more accurate classification. In this study, a signal-to-noise ratio saliency measure was employed to determine the saliency of input features of recurrent neural networks (RNNs) used in classification of ophthalmic arterial Doppler signals. Eigenvector methods were used to extract features representing the ophthalmic arterial Doppler signals. The RNNs used in the ophthalmic arterial Doppler signal classification were trained for the signal-to-noise ratio screening method. The application results of the signal-to-noise ratio screening method to the ophthalmic arterial Doppler signals demonstrated that classification accuracies of RNNs with salient input features are higher than those of RNNs with salient and non-salient input features.

Measuring Saliency of Features Using Signal-to-noise Ratios for Detection of Electrocardiographic Changes in Partial Epileptic Patients

Medical diagnostic accuracies can be improved when the pattern is simplified through representation by important features. The feature vector, which is comprised of the set of all features used to describe a pattern, is a reduced-dimensional representation of that pattern. By identifying a set of salient features, the noise in a classification model can be reduced, resulting in more accurate classification. In this study, a signal-to-noise ratio (SNR) saliency measure was employed to determine saliency of input features of probabilistic neural networks (PNNs) used in classification of two types of electrocardiogram (ECG) beats (normal and partial epilepsy). In order to extract features representing the ECG signals, discrete wavelet transform was used. The PNNs used in the ECG signals classification were trained for the SNR screening method. The application results of the SNR screening method to the ECG signals demonstrated that classification accuracies of the PNNs with salient input features are higher than that of the PNNs with salient and non-salient input features.

Measuring saliency of features representing EEG signals using signal-to-noise ratios

Various methodologies of automated diagnosis have been adopted, however the entire process can generally be subdivided into a number of disjoint processing modules: pre-processing, feature extraction/selection, and classification. Features are used to represent patterns with minimal loss of important information. The feature vector, which is comprised of the set of all features used to describe a pattern, is a reduced-dimensional representation of that pattern. Medical diagnostic accuracies can be improved when the pattern is simplified through representation by important features. By identifying a set of salient features, the noise in a classification model can be reduced, resulting in more accurate classification. In this study, a signal-to-noise ratio (SNR) saliency measure was employed to determine saliency of input features of probabilistic neural networks (PNNs) used in classification of electroencephalogram (EEG) signals. In order to extract features representing the EEG signals, eigenvector methods were used. The PNNs used in the EEG signals classification were trained for the SNR screening method. The application results of the SNR screening method to the EEG signals demonstrated that classification accuracies of the PNNs with salient input features are higher than that of the PNNs with salient and non-salient input features.

Measuring saliency of features extracted by model-based methods from internal carotid arterial Doppler signals using signal-to-noise ratios

Medical diagnostic accuracies can be improved when the pattern is simplified through representation by important features. The feature vector, which is comprised of the set of all features used to describe a pattern, is a reduced-dimensional representation of that pattern. The noise in a classification model can be reduced by identifying a set of salient features and then more accurate classification can be obtained. In this study, a signal-to-noise ratio (SNR) saliency measure was employed to determine saliency of input features of probabilistic neural networks (PNNs) used in classification of internal carotid arterial Doppler signals (ICADS). In order to extract features representing the ICADS, model-based methods were used. The PNNs used in the ICADS classification were trained for the SNR screening method. The application results of the SNR screening method to the ICADS demonstrated that classification accuracies of the PNNs with salient input features are higher than that of the PNNs with salient and nonsalient input features.

Distributed shape control of homogeneous swarms of autonomous underwater vehicles

In this paper, we study large formations of underwater autonomous vehicles for the purposes of exploration and sampling the ocean surface. The formations or aggregates we consider are composed of up to hundreds of robots with the capability of forming various complex shapes dictated by the shape of the region to be explored, as well as special shapes suitable for migration. The shapes are determined through bathymetric maps and described with reduced-dimensional representation techniques. The approach we propose is that of breaking up the control and coordination strategy into two decoupled problems, i.e., partitioning the aggregate into two non-overlapping sets: its boundary and its interior. The boundary uses general theory of curve evolution to form shapes while the interior passively complies, using attraction-repulsion forces, to form a uniform distribution inside the boundary. This makes the problem much more tractable than previous methods. Decision making by individual robots is entirely based on local information, autonomous underwater vehicles, formation control, swarm control.

Dynamics of Swelling/Contracting Hard Spheres Surmised by an Irreversible Langevin Equation

The diffusion of molecules through uniform homogeneous materials can readily be described by Brownian motion or generalizations thereof. The further generalization of these models to describe molecular diffusion through heterogeneous and nonstationary solvents is much less understood. Phenomenological nonstationary generalizations of the generalized Langevin equation (GLE) have earlier been developed satisfying the fluctuation-dissipation relationship in quasi-equilibrium limits while exhibiting somewhat complex behavior away from equilibrium. This reduced-dimensional representation should be capable of describing the diffusion of a particle through a colloidal suspension whose average particle size is tuned by an external driving force such as pH. A simple particle model of such a process involves the motion of a hard-sphere particle in an explicit environment of swelling hard spheres. The velocity autocorrelation functions observed in a large number of simulations of the particle model under various swelling rates agree precisely with those of a single form of the nonstationary phenomenological model. Though this procedure is not an explicit projection of the mechanical system onto the nonstationary GLE, it does show that the latter correctly describes the dynamics of the projected coordinate--namely, diffusion of the solute--under nonequilibrium conditions. Both nonequilibrium solvent models lead to behavior reminiscent of beta-relaxation processes at packing fractions substantially below that of the glass transition.

Analysis and visualization of category membership distribution in multivariate data

This paper reports on some advances in generic data processing procedures with focus on a specific materials discovery and design task. The task is to predict whether a new ternary materials system would be compound forming or not, with the prediction to be based on knowledge of many other known exemplars. The activities and results of three related efforts are described in condensed form in this paper. In one effort, using a combination of clustering and mapping procedures, an accuracy of more than 99% was attained in predicting the category status (compound forming or not) of new ternary systems. A second effort addressed the question of how to identify redundant or superfluous features. A procedure for identifying the extent of functional dependency amongst features was developed. That procedure can be used to remove redundant features. A third effort addressed the question of how to obtain reduced dimension representations of multivariate data, albeit at the cost of loss of some information. Visualizations of low-dimensional representations can be helpful in building up holistic views of data space for use in exploration and discovery of new materials.

On Updating Problems in Latent Semantic Indexing

We develop new SVD-updating algorithms for three types of updating problems arising from latent semantic indexing (LSI) for information retrieval to deal with rapidly changing text document collections. We also provide theoretical justification for using a reduced-dimension representation of the original document collection in the updating process. Numerical experiments using several standard text document collections show that the new algorithms give higher (interpolated) average precisions than the existing algorithms, and the retrieval accuracy is comparable to that obtained using the complete document collection.

Dimensionality reduction of electropalatographic data using latent variable models

We consider the problem of obtaining a reduced dimension representation of electropalatographic (EPG) data. An unsupervised learning approach based on latent variable modelling is adopted, in which an underlying lower dimension representation is inferred directly from the data. Several latent variable models are investigated, including factor analysis and the generative topographic mapping (GTM). Experiments were carried out using a subset of the EUR-ACCOR database, and the results indicate that these automatic methods capture important, adaptive structure in the EPG data. Nonlinear latent variable modelling clearly outperforms the investigated linear models in terms of log-likelihood and reconstruction error and suggests a substantially smaller intrinsic dimensionality for the EPG data than that claimed by previous studies. A two-dimensional representation is produced with applications to speech therapy, language learning and articulatory dynamics.

Materials discovery via topologically-correct display of reduced-dimension data

Authors describe and demonstrate a `ratio-conserving' mapping procedure for attaining reduced-dimension representations of multidimensional data. This procedure has a theoretical basis for topological correctness in that the ratio of the metrics in the two representations is maintained constant throughout. It is also demonstrated that comparing the reduced-dimension depiction of data with the results of clustering and spanning tree operations in the full-dimension space can validate such reduced-dimension mappings. Demonstrations are carried out using a body of semiconductor data, with five independent variables and one dependent variable.

Determining Mental State from EEG Signals Using Parallel Implementations of Neural Networks

EEG analysis has played a key role in the modeling of the brain's cortical dynamics, but relatively little effort has been devoted to developing EEG as a limited means of communication. If several mental states can be reliably distinguished by recognizing patterns in EEG, then a paralyzed person could communicate to a device such as a wheelchair by composing sequences of these mental states. EEG pattern recognition is a difficult problem and hinges on the success of finding representations of the EEG signals in which the patterns can be distinguished. In this article, we report on a study comparing three EEG representations, the unprocessed signals, a reduced-dimensional representation using the Karhunen – Loève transform, and a frequency-based representation. Classification is performed with a two-layer neural network implemented on a CNAPS server (128 processor, SIMD architecture) by Adaptive Solutions, Inc. Execution time comparisons show over a hundred-fold speed up over a Sun Sparc 10. The best classification accuracy on untrained samples is 73% using the frequency-based representation.