Singular Value Decomposition Component Research Articles

A simplified and accelerated implementation of SVD for filtering ultrafast power Doppler images

Background and ObjectiveUltrafast Power Doppler (UPD) is a growing ultrasound modality for imaging and diagnosing microvasculature disease. A key element of UPD is using singular value decomposition (SVD) as a highly selective filter for tissue and electronic noise. However, two significant drawbacks of SVD are its computational burden and the complexity of its algorithms. These limitations hinder the development of fast and specific SVD algorithms for UPD imaging. This study introduces power SVD (pSVD), a simplified and accelerated algorithm for filtering tissue and noise in UPD images. MethodspSVD exploits several mathematical properties of SVD specific to UPD images. In particular, pSVD allows the direct computation of blood-related SVD components from the temporal singular vectors. This feature simplifies the expression of SVD while significantly accelerating its computation. After detailing the theory behind pSVD, we evaluate its performances in several in vitro and in vivo experiments and compare it to SVD and randomized SVD (rSVD). ResultspSVD strongly decreases the running time of SVD (between 5 and 12 times in vivo) without impacting the quality of UPD images. Compared to rSVD, pSVD can be significantly faster (up to 3 times) or slightly slower but gives access to more estimators to isolate tissue subspaces. ConclusionpSVD is highly valuable for implementing UPD imaging in clinical ultrasound and provides a better understanding of SVD for ultrasound imaging in general.

Continuous Encryption Functions for Security Over Networks

This paper presents a study of continuous encryption functions (CEFs) of secret feature vectors for security over networks, which include physical layer encryption for wireless communications and biometric template security for online Internet applications. While CEFs are defined here to include all prior continuous one-way functions, a good CEF is defined to be a continuous function that turns a random feature vector of limited dimension into a long sequence of numbers in such a way that it is hard to invert and hard to substitute, it has no or little amplification of noise, and its output samples have zero or near-zero correlations and have identical or nearly identical distributions. A number of prior CEFs, such as dynamic random projection, index-of-max hashing and higher-order polynomials, are all shown to fail on these criteria. Based on selected components of singular value decomposition (SVD) of randomly modulated matrices of the feature vector, a family of SVD-CEFs is proposed. Such a SVD-CEF is shown to meet all the criteria for a good CEF and outperform the prior CEFs significantly.

Weak Signal Detection Based on Combination of Sparse Representation and Singular Value Decomposition

Due to the inevitable acquisition system noise and strong background noise, it is often difficult to detect the features of weak signals. To solve this problem, sparse representation can effectively extract useful information according to the sparse characteristics of signals. However, sparse representation is less effective against non-Gaussian white noise. Therefore, a novel SRSVD method combining sparse representation and singular value decomposition is proposed to further improve the denoising performance of the algorithm. All the signal components highly matched with the dictionary are extracted by sparse representation, and then each component of singular value decomposition is weighted by the evaluation index, PMI, which can indicate the component with useful information in the signal, so that the signal denoising performance of the algorithm is greatly improved. The performance of the proposed method is verified by the processing of weak signals in the circuit and early fault signals of bearings. The results show that SRSVD can successfully suppress noise interference. Compared with other existing methods, SRSVD has better denoising performance.

CalFitter 2.0: Leveraging the power of singular value decomposition to analyse protein thermostability.

The importance of the quantitative description of protein unfolding and aggregation for the rational design of stability or understanding the molecular basis of protein misfolding diseases is well established. Protein thermostability is typically assessed by calorimetric or spectroscopic techniques that monitor different complementary signals during unfolding. The CalFitter webserver has already proved integral to deriving invaluable energy parameters by global data analysis. Here, we introduce CalFitter 2.0, which newly incorporates singular value decomposition (SVD) of multi-wavelength spectral datasets into the global fitting pipeline. Processed time- or temperature-evolved SVD components can now be fitted together with other experimental data types. Moreover, deconvoluted basis spectra provide spectral fingerprints of relevant macrostates populated during unfolding, which greatly enriches the information gains of the CalFitter output. The SVD analysis is fully automated in a highly interactive module, providing access to the results to users without any prior knowledge of the underlying mathematics. Additionally, a novel data uploading wizard has been implemented to facilitate rapid and easy uploading of multiple datasets. Together, the newly introduced changes significantly improve the user experience, making this software a unique, robust, and interactive platform for the analysis of protein thermal denaturation data. The webserver is freely accessible at https://loschmidt.chemi.muni.cz/calfitter.

Coarse-to-fine SVD-GAN based framework for enhanced frame synthesis

Frame interpolation and synthesis are growing topics in the field of computer vision. Hence, these topics gained more attention recently where several deep-learning architectures were proposed to enhance the quality of the synthesized frames. In this paper, an efficient handcrafted deep approach is proposed for better frame synthesis. The proposed approach takes advantage of singular value decomposition (SVD) framework and Generative Adversarial Networks (GAN). The proposed approach does not require any computationally expensive feature extraction steps such optical flow techniques and block-based motion compensation techniques. Nonetheless, the SVD components still carry the relevant motion information needed to deal with the challenges such as large motion and occlusion. Thus, the frames are temporally upscaled via SVD based construction procedure where new middle frames are interpolated for further enhancement using a GAN based approach that eliminates most of the visual artifacts. The proposed frame synthesis approach is comprehensively evaluated in different scenarios where its performance is assessed and compared with the state-of-the-art. Our framework outperforms the majority of the deep learning approaches in terms quantitative results in addition to qualitative results where our framework can generate smoother frames with less visual artifacts.

Singular Value Decomposition for Removal of Cardiac Interference from Trunk Electromyogram.

A new algorithm based on singular value decomposition (SVD) to remove cardiac contamination from trunk electromyography (EMG) is proposed. Its performance is compared to currently available algorithms at different signal-to-noise ratios (SNRs). The algorithm is applied on individual channels. An experimental calibration curve to adjust the number of SVD components to the SNR (0–20 dB) is proposed. A synthetic dataset is generated by the combination of electrocardiography (ECG) and EMG to establish a ground truth reference for validation. The performance is compared with state-of-the-art algorithms: gating, high-pass filtering, template subtraction (TS), and independent component analysis (ICA). Its applicability on real data is investigated in an illustrative diaphragm EMG of a patient with sleep apnea. The SVD-based algorithm outperforms existing methods in reconstructing trunk EMG. It is superior to the others in the time (relative mean squared error < 15%) and frequency (shift in mean frequency < 1 Hz) domains. Its feasibility is proven on diaphragm EMG, which shows a better agreement with the respiratory cycle (correlation coefficient = 0.81, p-value < 0.01) compared with TS and ICA. Its application on real data is promising to non-obtrusively estimate respiratory effort for sleep-related breathing disorders. The algorithm is not limited to the need for additional reference ECG, increasing its applicability in clinical practice.

Effects of Heat Treatment on Indomethacin-Cimetidine Mixture; Investigation of Drug-Drug Interaction Using Singular Value Decomposition in FTIR Spectroscopy.

This study investigated the effect of phase transformation on indomethacin (IMC), cimetidine (CIM), and their 1:1 eutectic mixture, using FTIR spectra and multivariate analysis. The IMC form γ, CIM form A, and IMC-CIM 1:1 mixture molar ratio samples were heated on a hot plate at 303-453K for 5min and cooled till room temperature. The prepared samples were investigated by powder X-ray diffraction analysis and infrared spectroscopy with KBr powder. The PXRD patterns suggested the bulk IMC form γ, bulk CIM form A, and 1:1 physical mixture samples phase transformed into low-crystallinity IMC form γ, amorphous CIM, and eutectic mixture, respectively. FTIR spectra combined with singular value decomposition (SVD) suggested by absorbance peak shifts of several vibration modes that the polymorphic transformations of the samples affect their molecular interactions. The estimated melting points of heated samples were evaluated by sigmoid fitting based on the SVD results. The principal components of SVD show that the process of phase transformation of IMC-CIM 1:1 mixture samples affect the IR vibration of the CO stretch of IMC and the C-C stretch and C-H bending of CIM. These results suggest that molecular interaction is an important factor in the eutectic condition of IMC-CIM 1:1 mixture. This observation enables to evaluate for in co-amorphous formulations or stability of drug combinations in a poly pill.

Raman Spectroscopy Allows for the Determination of Elephant Ivory Age.

Determination of the age of ivory is important for controlling illegal trafficking and the proper identification of ivory artifacts. Radiocarbon dating is the standard method of determining the age of ivories; however, it requires the destruction of a fragment of the sample. Raman spectroscopy is a nondestructive technique, and therefore can be used on artwork. Moreover, Raman measurements can be done using a portable system, and the data analysis can be performed on the spot once the groundwork is done. Ivories contain two primary components: collagen and bioapatite. Raman spectrum of ivory material is mainly a sum of the vibrational bands of these components. As collagen deteriorates with time, its Raman signal decreases; therefore, the ratio of collagen to bioapatite peaks is smaller in the older samples compared to the younger ones, providing a basis for sample dating. We have compared the results of Raman and radiocarbon measurements applied to a set of elephant ivory fragments and have successfully calibrated the Raman data set using radiocarbon measurements. We found that the Raman collagen to bioapatite peak ratios of the samples can be used as a metric to determine their age, providing a nondestructive technique to assess the age of ivory samples. We have also used singular value decomposition (SVD) to analyze the whole Raman spectra. We have observed clear separation between samples of different ages in the SVD component space. The samples also tended to align along the timeline diagonal in the correct order. The changes in multiple collagen and bioapatite peaks contribute to the differences in Raman spectra of ivory samples of different age.

Adaptive pre-whiten filtering for the free induction decay transversal signal in weak magnetic detection

The free induction decay (FID) transversal signal is always employed by a proton precession magnetometer (PPM) to evaluate the time-domain geomagnetic field. Nevertheless, the signal-to-noise ratio (SNR) is an important factor that severely affects the detection accuracy of the magnetic field due to uncontrollable interference sources, including random noise and power frequency noise. In this study, aiming to boost the SNR of the FID transversal signal, a novel filtering algorithm based on a prewhiten (PW) strategy is proposed and the PW filtering was combined with singular value decomposition (SVD) for further noise reduction. This method aims to generate adaptive PW input data before filtering, further decorrelating the noise to reduce the impact of varying noise levels in the received FID signals. The efficiency of the proposed joint filtering framework, dubbed PW-SVD, was evaluated by comparing with two state-of-the-art methods, i.e., SVD and principal component analysis and decomposition, using the same data. The results demonstrated that the proposed PW-SVD method obtained the smallest root mean square error and the highest signal-to-noise ratio improvement among all the compared methods, especially for the strong-noisy scenario, which enhances the environmental adaptability of a PPM.

Abstract WP382: Using Natural Language Processing Algorithms to Identify Stroke Cases and Stroke Subtypes From Neuroimaging Reports

Background/Objective: The long-term goal of our research is to develop automated, accurate methods for conducting stroke outcome surveillance across large populations. To facilitate this, we developed natural language processing (NLP) based machine learning algorithms to classify stroke cases and sub-type strokes using neuroimaging reports. We report on the performance of our algorithms. Methods: Our population of interest included patients with stroke symptoms presenting to the emergency room of our large academic healthcare system. We randomly sampled 332 probable stroke cases. A trained neurologist validated stroke diagnoses using neuroimaging reports. Data preprocessing included cleaning and normalizing the reports into a standardized format. We trained and tested machine learning algorithms using the formatted reports. The NLP-based algorithms predicted a stroke diagnosis (binary classification) and a stroke type diagnosis (multiclass classification) using n-grams of length 1 (i.e., ‘stroke’, ‘hemorrhage’) through 3 (i.e., ‘no mass effect’), term-frequency weighting, and feature dimensionality reduction via truncated singular value decomposition (SVD). We report algorithm performance using the area under the receiver operating characteristic curve (AUC-ROC). Classification methods we tested included Multinomial Naïve Bayes, Logistic Regression, Random Forest Classifier, and Support Vector Machine (SVM). Results: The highest performing algorithm for both stroke and stroke sub-type classification contained 1 to 2 n-grams, no term-frequency, and 200 SVD components. For the stroke case detection, SVM achieved the best AUC-ROC of 95.6%. For stroke sub-type detection, SVM also yielded the highest AUC-ROC of 93.5% for no stroke, 92.3% for ischemic stroke, 91.9% for intraparenchymal hemorrhage, and 94.8% for subarachnoid hemorrhage. Conclusions: We report very promising results in our pilot study using machine learning algorithms to classify stroke cases from neuroimaging reports. Feature selection on this pilot data revealed a subset of words that are highly effective in categorizing stroke. Future work will focus on algorithm improvement, finer grained stroke sub-type stratification, and multi-label phenotyping.

SVD-based Tensor-Completion Technique for Background Initialization.

Extracting the background from a video in the presence of various moving patterns is the focus of several background-initialization approaches. To model the scene background using rank-one matrices, this paper proposes a background-initialization technique that relies on the singular-value decomposition (SVD) of spatiotemporally extracted slices from the video tensor. The proposed method is referred to as spatiotemporal slice-based SVD (SS-SVD). To determine the SVD components that best model the background, a depth analysis of the computation of the left/right singular vectors and singular values is performed, and the relationship with tensor-tube fibers is determined. The analysis proves that a rank-1 matrix extracted from the first left and right singular vectors and singular value represents an efficient model of the scene background. The performance of the proposed SS-SVD method is evaluated using 93 complex video sequences of different challenges, and the method is compared with state-of-the-art tensor/matrix completion-based methods, statistical-based methods, search-based methods, and labeling-based methods. The results not only show better performance over most of the tested challenges, but also demonstrate the capability of the proposed technique to solve the background-initialization problem in a less computational time and with fewer frames.

The SST–Wind Coupling Pattern in the East China Sea Based on a Regional Coupled Ocean–Atmosphere Model

ABSTRACTTo study the interaction between sea surface temperature (SST) and surface wind in the East China Sea (ECS), the Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) modelling system is used to downscale a global atmospheric reanalysis product over the study area in 2013. A singular value decomposition (SVD) method is applied to SST and surface wind speed to study their coupling relationship in the ECS. The heterogeneous correlation map indicates that the surface wind has a negative correlation with the SST, especially in the Kuroshio Current. From lead-lag correlations between the first principal component of SST and surface wind SVD (filtered using a Lanczos high-pass filter with a 90-day cut-off), a correlation of about 0.1 is found at lag −6, and a negative correlation of about −0.3 is also found around lag 1. The results indicate a negative feedback between SST and wind fluctuations at short time-scales. Air–sea heat fluxes contribute little to the SST variability in the ECS section of the Kuroshio and the analysis of the mixed-layer heat budget shows that the contribution of horizontal advection is dominant in determining the intraseasonal SST signals.

Inverse Mellin Transformation of Continuous Singular Value Decomposition: A Route to Holographic Renormalization

We examine holographic renormalization by the singular value decomposition (SVD) of matrix data generated by the Monte Carlo snapshot of the 2D classical Ising model at criticality. To take the continuous limit of the SVD enables us to find the mathematical form of each SVD component by the inverse Mellin transformation as well as the power-law behavior of the SVD spectrum. We find that each SVD component is characterized by the two-point spin correlator with a finite correlation length. Then, the continuous limit of the decomposition index in the SVD corresponds to the inverse of the correlation length. These features strongly suggest that the SVD contains mathematical structure the same as the holographic renormalization.

Noise Estimation for Images using Eigen Values and Frobenius norm

Performance of image denoising algorithm is critically dependent on the accuracy of noise level estimation. In the estimation process, restricting the influence of image content on the estimation dataset is a major challenge. In this paper, we propose a novel method which involves the application of Frobenius norm as the basis of content energy measurement. It involves the truncation of SVD (Singular Value Decomposition) components thereby effectively restricting the influence of image details. Application of linear regression for determining content parameter enhances the application scope of the proposed method. The experimental results demonstrates the effectiveness of the proposed approach. Keywords—Frobenius norm, noise estimation, singular value decomposition, linear regression, additive white gaussian noise I. INTRODUCTION Application of Image Denoising or Filtering algorithms is desirable for images corrupted with additive white gaussian noise. This step is applied before many processing algorithms such as image segmentation, restoration etc. Many of these filtering or denoising algorithms rely on the information about the incurred level of noise which is assumed to be known apriori. In real-time applications, this information is obtained by estimation techniques. Accuracy and reliability of estimation algorithms thus affects the filtering or denoising processes concomitantly. More often the noise is assumed to be zero mean additive white gaussian in nature (3), whose distribution is characterized by following equation:

Missing value imputation in multi-environment trials: Reconsidering the Krzanowski method

We propose a new methodology for multiple imputation when faced with missing data in multi-environmental trials with genotype-by-environment interaction, based on the imputation system developed by Krzanowski that uses the singular value decomposition (SVD) of a matrix. Several different iterative variants are described; differential weights can also be included in each variant to represent the influence of different components of SVD in the imputation process. The methods are compared through a simulation study based on three real data matrices that have values deleted randomly at different percentages, using as measure of overall accuracy a combination of the variance between imputations and their mean square deviations relative to the deleted values. The best results are shown by two of the iterative schemes that use weights belonging to the interval [0.75, 1]. These schemes provide imputations that have higher quality when compared with other multiple imputation methods based on the Krzanowski method.

Applications of a Novel Clustering Approach Using Non-Negative Matrix Factorization to Environmental Research in Public Health.

Often data can be represented as a matrix, e.g., observations as rows and variables as columns, or as a doubly classified contingency table. Researchers may be interested in clustering the observations, the variables, or both. If the data is non-negative, then Non-negative Matrix Factorization (NMF) can be used to perform the clustering. By its nature, NMF-based clustering is focused on the large values. If the data is normalized by subtracting the row/column means, it becomes of mixed signs and the original NMF cannot be used. Our idea is to split and then concatenate the positive and negative parts of the matrix, after taking the absolute value of the negative elements. NMF applied to the concatenated data, which we call PosNegNMF, offers the advantages of the original NMF approach, while giving equal weight to large and small values. We use two public health datasets to illustrate the new method and compare it with alternative clustering methods, such as K-means and clustering methods based on the Singular Value Decomposition (SVD) or Principal Component Analysis (PCA). With the exception of situations where a reasonably accurate factorization can be achieved using the first SVD component, we recommend that the epidemiologists and environmental scientists use the new method to obtain clusters with improved quality and interpretability.

SPECTRAL ANALYSIS OF STEGANOGRAMS

The data embedding algorithms in transformation domain of digital images are widely used for increasing the robustness of stegoalgorithmsto known steganalysis methods. Applying of standard transformations the digital images by steganograms forming – two-dimensional discretecosine and wavelet transforms – allows minimizing the garbling the hidden messages by image compression. We propose to use the spectral analysis methods – singular spectrum analysis and multifractal analysis – for revealing the fact of message embedding with usage of standard transform of cover image and stegodata. The advantage of such approach in comparison with statistical steganalysis methods is possibility to simultaneously investigation of several components the cover image, which allows localizing the domain of data hiding.Research of effectiveness of the spectral analysis methods was provided for the case of usage the one-stage and multi-stage embeddingmethods. It is shown that stegodata embedding leads to alteration the all components of singular value decomposition of cover images as wellas appearance the peculiar alteration of multifractal features the steganograms – increasing the cardinality of monofractal components the image. Revealed distinctive features of steganograms are stable in wide range of cover image payloads, which is simplifying of task of stegodata revealing, hidden in transformation domain of digital images.

Band Selection for Hyperspectral Images Using Non-Negativity Constraints

This paper presents a new factorization technique for hyperspectral signal processing based on a constrained singular value decomposition (SVD) approach. Hyperpectral images typically have a large number of contiguous bands that are highly correlated. Likewise the field of view typically contains a limited number of materials and the spectra are also correlated. Only a selected number of bands, the extreme bands that include the dominant materials spectral signatures, are needed to express the data. Factorization can provide a means for interpretation and compression of the spectral data. Hyperspectral images are represented as non-negative matrices by graphic concatenation, with the pixels arranged into columns and each row corresponding to a spectral band. SVD and principal component analysis enjoy a broad range of applications, including, rank estimation, noise reduction, classification and compression, with the resulting singular vectors forming orthogonal basis sets for subspace projection techniques. A key property of non-negative matrices is that their columns/rows form non-negative cones, with any non-negative linear combination of the columns/rows belonging to the cone. Data sets of spectral images and time series reside in non-negative orthants and while subspaces spanned by SVD include all orthants, SVD projections can be constrained to the non-negative orthants. In this paper we utilize constraint sets that confine projections of SVD singular vectors to lie within the cones formed by the spectral data. The extreme vectors of the cone are found and these vectors form a basis for the factorization of the data. The approach is illustrated in an application to hyperspectral data of a mining area collected by an airborne sensor.

Brain dynamic functional connectivity in patients with disorders of consciousness

Ever since the proposal that brain activity is organized into networks of coherent activity in the framework of functional connectivity (FC, [1]), a great amount of research has been conducted to characterize these networks, their inter-relations, and their differential participation in sensory-motor and cognitive processes, as well as their alteration in brain states such as pathological diseases, sleep, etc. The main techniques to study FC are functional magnetic resonance imaging (fMRI) and positron emition tomography (PET), but it has also been described using other techniques, such as MEG and EEG [2]. The classic approach to obtain FC networks is to calculate the correlation between the low-pass filtered time series of brain nodes (i.e., voxels, anatomical areas, etc.) along the scanning period. In this way the studies on FC commonly assume a rather static correlation pattern. Although such studies unraveled important features of brain large-scale functioning, FC is in fact highly variable in time and across subjects [3]. Recent work digs deeper into this variability and brings up important caveats to many previous assumptions. For instance, new findings suggest that networks may reorganize in time, weakening their intra-network connectivity strengh and enforcing the inter-network connectivities, and that there may exist discrete states of multistability over time [4]. In the present work the dynamic functional connectivity was analyzed in a group of patients with disorders of consciousness (DOC) as well as in healthy subjects, during a resting state (RS) fMRI paradigm. The correlation matrices (R) between predefined brain areas were obtained in sequential time windows. The temporal variability of different metrics of the R matrices was examined. Furthermore, main components (i.e., hidden states of frequent brain configurations) were identified from DOC or Control groups' R temporal series by employing singular value decomposition (SVD). SVD is a dimensionality reduction technique that allows for obtaining a latent correlation structure model, and has been previously applied by Leonardi et al. [5] to RS fMRI data. In the present work we investigated whether the main SVD components differ between DOC and Control groups and in which temporal manner. Preliminary results show that the main components present dissimilarities between the groups in specific brain areas. Furthermore, the temporal variation of the largest eigenvalue (that is interpreted as the collective motion of all areas) of the R matrices is different in DOC compared to Control group. The results may contribute to the understanding of the process of consciousness in so far as brain dynamic functionality and have potential impact in the understanding of consciousness disorder.

Predict Subcellular Locations of Singleplex and Multiplex Proteins by Semi-Supervised Learning and Dimension-Reducing General Mode of Chou's PseAAC

Predicting protein subcellular location is one of major challenges in Bioinformatics area since such knowledge helps us understand protein functions and enables us to select the targeted proteins during drug discovery process. While many computational techniques have been proposed to improve predictive performance for protein subcellular location, they have several shortcomings. In this work, we propose a method to solve three main issues in such techniques; i) manipulation of multiplex proteins which may exist or move between multiple cellular compartments, ii) handling of high dimensionality in input and output spaces and iii) requirement of sufficient labeled data for model training. Towards these issues, this work presents a new computational method for predicting proteins which have either single or multiple locations. The proposed technique, namely iFLAST-CORE, incorporates the dimensionality reduction in the feature and label spaces with co-training paradigm for semi-supervised multi-label classification. For this purpose, the Singular Value Decomposition (SVD) is applied to transform the high-dimensional feature space and label space into the lower-dimensional spaces. After that, due to limitation of labeled data, the co-training regression makes use of unlabeled data by predicting the target values in the lower-dimensional spaces of unlabeled data. In the last step, the component of SVD is used to project labels in the lower-dimensional space back to those in the original space and an adaptive threshold is used to map a numeric value to a binary value for label determination. A set of experiments on viral proteins and gram-negative bacterial proteins evidence that our proposed method improve the classification performance in terms of various evaluation metrics such as Aiming (or Precision), Coverage (or Recall) and macro F-measure, compared to the traditional method that uses only labeled data.