Non-negative Least Squares Research Articles

Massive Machine-Type Communication Pilot-Hopping Sequence Detection Architectures Based on Non-Negative Least Squares for Grant-Free Random Access

User activity detection in grant-free random access massive machine type communication (mMTC) using pilot-hopping sequences can be formulated as solving a non-negative least squares (NNLS) problem. In this work, two architectures using different algorithms to solve the NNLS problem is proposed. The algorithms are implemented using a fully parallel approach and fixed-point arithmetic, leading to high detection rates and low power consumption. The first algorithm, fast projected gradients, converges faster to the optimal value. The second algorithm, multiplicative updates, is partially implemented in the logarithmic domain, and provides a smaller chip area and lower power consumption. For a detection rate of about one million detections per second, the chip area for the fast algorithm is about 0.7 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> compared to about 0.5 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for the multiplicative algorithm when implemented in a 28 nm FD-SOI standard cell process at 1 V power supply voltage. The energy consumption is about 300 nJ/detection for the fast projected gradient algorithm using 256 iterations, leading to a convergence close to the theoretical. With 128 iterations, about 250 nJ/detection is required, with a detection performance on par with 192 iterations of the multiplicative algorithm for which about 100 nJ/detection is required.

Evaluation of Synergy-Based Hand Gesture Recognition Method Against Force Variation for Robust Myoelectric Control.

The non-stationary characteristics of surface electromyography (sEMG) and possible adverse variations in real-world conditions make it still an open challenge to realize robust myoelectric control (MEC) for multifunctional prostheses. Variable muscle contraction level is one of the handicaps that may degrade the performance of MEC. In this study, we proposed a force-invariant intent recognition method based on muscle synergy analysis (MSA) in the setting of three self-defined force levels (low, medium, and high). Specifically, a fast matrix factorization algorithm based on alternating non-negativity constrained least squares (NMF/ANLS) was chosen to extract task-specific synergies associated with each of six hand gestures in the training stage; while for the testing samples, we used the non-negative least square (NNLS) method to estimate neural commands for movement classification. The performance of proposed method was compared with conventional pattern recognition (PR) method consisting of LDA (linear discrimination analysis) classifier and representative features in three offline evaluation scenarios. Statistical tests on ten able-bodied subjects revealed no significant difference in intra-force-level (p = 0.353) and multi-force-level (p = 0.695) accuracy; But the synergy-based method performed significantly better than conventional PR-based method under inter-force-level conditions (p < 0.05). Similar results were observed for nine amputee subjects though there was a drop in the classification accuracy. This study was the first to concurrently demonstrate the robustness and predictive power of task-specific synergies under variant force levels and explore their potential for reliable intent recognition against force variation. Although the online performance is yet to be demonstrated, the proposed method is characterized by simple training procedure and acceptable computational efficiency, which would potentially provide an alternative approach for the development of clinically viable prostheses and rehabilitation robots driven by sEMG.

A Blind Spectral Unmixing in Wavelet Domain

In this article, a wavelet-based energy minimization framework is developed for joint estimation of endmembers and abundances without assuming pure pixels while considering noisy scenario. Spectrally dense and overlapped hyperspectral data are represented using biorthogonal wavelet bases that yield a compact linear mixing model in the wavelet domain. It acts as the data term and helps to reduce solution space of the unmixed components. Three prior terms are incorporated to better handle the ill-posedness, i.e., the logarithm of determinant volume regularizer enforces minimum endmember simplex, smoothness (spatial) prior to individual abundance maps, and spectral constraint through learning dictionary of abundances. Alternating nonnegative least-squares is employed to optimize the regularized and constrained nonnegative matrix factorization functional in the wavelet domain. We conduct theoretical analysis, discuss convergence and algorithmic details. Experiments are conducted on synthetic and three real benchmark hyperspectral data AVIRIS Cuprite, HYDICE Urban, and AVIRIS Jasper Ridge. The efficacy of the proposed algorithm is evaluated by comparing results with state of the art.

A Build-In Data Inversion Method to Retrieve Aerosol Size Distributions for a Portable Ultrafine Particle Sizer (PUPS)

A build-in data inversion method to retrieve aerosol size distributions based on the principle of particle electrical mobility has been introduced, whose required computational effort is low for a portable ultrafine particle sizer (PUPS). The PUPS is cost-effective for the measurements of the fine and ultrafine particles in polluted environments near-source (e.g., cities with high traffic density, freeways, airports or stationary combustion sources). The particle sizer is mainly composed of a unipolar charger, a plate differential mobility analyzer (PDMA), and a Faraday cup electrometer (FCE). The classification efficiencies of the PDMA are strongly dependent on the charging distribution of the unipolar charger, in which multiple charging is more significant than that for a bipolar charger. To reduce the excessive overlap in the kernel function caused by multiple charging, a guidance method for selecting the classification voltages and operating parameters of the PDMA is proposed with the help of MATLAB. Subsequently, a combination of the nonnegative least squares (NNLS) algorithm and post facto smoothing method has been employed to derive the discretized solution of the Fredholm integral equation of the first kind. In the end, the accuracy and stability of the proposed approach are tested under a range of particle size distribution scenarios. The synthesized data results show that for the unimodal aerosol distribution, almost all of the relative errors are less than 20 %, regardless of nonideal operating conditions. The inversion algorithm can be run on Cortex-M3, an ARM embedded chip for low-cost and low-power consumption applications. When a reasonable error range can be permitted, the inversion algorithm can meet the requirements of the PUPS.

Non-negative Least Squares Approach to Quantification of 1H Nuclear Magnetic Resonance Spectra of Human Urine.

Because of its quantitative character and capability for high-throughput screening, 1H nuclear magnetic resonance (NMR) spectroscopy is used extensively in the profiling of biofluids such as urine and blood plasma. However, the narrow frequency bandwidth of 1H NMR spectroscopy leads to a severe overlap of the spectra of components present in the complex mixtures such as biofluids. Therefore, 1H NMR-based metabolomics analysis is focused on targeted studies related to concentrations of the small number of metabolites. Here, we propose a library-based approach to quantify proportions of overlapping metabolites from 1H NMR mixture spectra. The method boils down to the linear non-negative least squares (NNLS) problem, whereas proportions of the pure components contained in the library stand for the unknowns. The method is validated on an estimation of the proportions of (i) the 78 pure spectra, presumably related to type 2 diabetes mellitus (T2DM), from their synthetic linear mixture; (ii) metabolites present in 62 1H NMR spectra of urine of subjects with T2DM and 62 1H NMR spectra of urine of control subjects. In both cases, the in-house library of 210 pure component 1H NMR spectra represented the design matrix in the related NNLS problem. The proposed method pinpoints 63 metabolites that in a statistically significant way discriminate the T2DM group from the control group and 46 metabolites discriminating control from the T2DM group. For several T2DM-discriminative metabolites, we prove their presence by independent analytical determination or by pointing out the corresponding findings in the published literature.

An efficient and robust method for structural distributed load identification based on mesh superposition approach

Accurate load identification is vital for the structural optimization design and the structural health monitoring in different engineering disciplines. However, the external loads usually are difficult to determine with direct measurements. In the present manuscript, an efficient and robust method is proposed to identify the distributed static or quasi-static loads on linear-elastic structures. The superimposed loading mesh approach is proposed to map the unknown loads, and nodal values of the superimposed loading mesh are taken as inverse variables in the inverse problem. With this strategy, the inverse problem is converted to solving a set of linear equations which maps the relationship between the inverse variables and measured responses. To find the optimal solution, the modified second-order Tikhonov regularization method (TRM) is employed. Furthermore, to ensure the non-negativity of the identified loads, the non-negative least squares (NNLS) is applied. Three numerical tests are employed to verify the feasibility of the proposed method. The results suggest that the distributed loads can be accurately identified, and that the inverse system is well-posed. The proposed method has been found to be robust that reasonable accuracy can be obtained even with significant measurement error.

A fast inversion method of 2D nuclear magnetic resonance based on the novel hybrid algorithm

To make up for the limitations and improve the accuracy of 1D nuclear-magnetic-resonance (NMR) logging in the evaluation of formation fluid properties, 2D NMR logging has become the focus of research. Increasing the sequence and inversion parameters of the 2D NMR can effectively improve the antinoise properties and resolution of the inversion, but at the same time, the reduced inversion speed and increased memory occupied will put forward higher requirements on the computer configuration and add to the cost of calculation, which poses challenges to the application of the traditional 2D NMR inversion algorithms. In view of the above defects, we have developed a new fast 2D NMR inversion LSQR-RSVD hybrid algorithm, and we have used the nonnegative least-squares (LSQR) calculation result as the initial value of the RSVD inversion. Taking oil-water and gas-water models as examples, the 2D NMR inversion effects of ( T2, D), ( T1, T2) are analyzed in detail, and ( T1, D) is also discussed by several groups of echo trains with variable echo interval ( TE) and waiting time ( TW). Compared to the inversion algorithm commonly used, the new hybrid algorithm can improve the inversion speed and significantly reduce the memory occupancy. Its remarkable advantages can further promote the application of 2D and even multidimensional NMR logging in practice.

Exact Complexity Certification of a Nonnegative Least-Squares Method for Quadratic Programming

In this letter we propose a method to exactly certify the complexity of an active-set method which is based on reformulating strictly convex quadratic programs to nonnegative least-squares problems. The exact complexity of the method is determined by proving the correspondence between the method and a standard primal active-set method for quadratic programming applied to the dual of the quadratic program to be solved. Once this correspondence has been established, a complexity certification method which has already been established for the primal active-set method is used to also certify the complexity of the nonnegative least-squares method. The usefulness of the proposed method is illustrated on a multi-parametric quadratic program originating from model predictive control of an inverted pendulum.

3D shape clustering with Nonnegative Least Squares coding and fusion on multilayer graphs

The well-known method of spectral clustering for 3D shape datasets is revisited. The graph construction by NNLS (Nonnegative Least Squares) coding technique is at the core of our method. Using graph-based encoding techniques and well-known shape descriptors, a framework is presented here which is applied to 3D shape clustering. Provided a shape database, a graph is first constructed. Weights in the graph are calculated so as to approximate each shape as a sparse linear combination of the remaining dataset objects. This framework is further enhanced by using the multilayer graphs process combining NNLS with L2graph. The L2graph is a sparse similarity graph, which conveys complementary information to NNLS coding. A criterion for the complementary action of the two graphs in terms of graph distance is also presented. Experimental results conducted on SHREC10, SHREC11 and SCHREC15 datasets validate the excellent performance of our clustering framework.

DCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS

We provide a numerical package for the computation of a d-variate near G-optimal polynomial regression design of degree m on a finite design space X ⊂ R d , by few iterations of a basic multiplicative algorithm followed by Tchakaloff-like compression of the discrete measure keeping the reached G-efficiency, via an accelerated version of the Lawson-Hanson algorithm for Non-Negative Least Squares (NNLS) problems. This package can solve on a personal computer large-scale problems where c a r d ( X ) × dim ( P 2 m d ) is up to 10 8 – 10 9 , being dim ( P 2 m d ) = 2 m + d d = 2 m + d 2 m . Several numerical tests are presented on complex shapes in d = 3 and on hypercubes in d &gt; 3 .

LED Solar Spectrum Computer Simulation Based on Non-dominated Sorting Genetic Algorithm

The solar computer simulation technology has been extensively applied in the fields of polymer curing test, solar cell detection and calibration, and satellite heat balance test, etc. The non-negative least-squares solution of the overdetermined equations based on the non-dominated sorting genetic algorithm (NSGA) to optimize the monochromatic light-emitting diode (LED) matching light source combination, replace some monochromatic LED with white LED to simulate the solar spectrum, and discuss several LED lights with different peak wavelengths that can be replaced by white LED. The simulation results suggest that in the range of 300 ∼ 1100 nm, as the monochromatic LED types replaced by white LED increase, the total number of LEDs used is reduced, and the spectral match decreases. When LEDs with three different peak wavelengths are replaced, the correlation index in the fitting based on the algorithm is 0.9035, where the number of LEDs can be reduced by 15.6%, and the simulation spectrum is basically consistent with the target one. The proposed method has a small spectral mismatch and can be used to distinguish two absorption valleys of the standard solar spectrum AM1.5 accurately.

Myelin water fraction estimation using small-tip fast recovery MRI.

To demonstrate the feasibility of an optimized set of small-tip fast recovery (STFR) MRI scans for rapidly estimating myelin water fraction (MWF) in the brain. We optimized a set of STFR scans to minimize the Cramér-Rao Lower Bound of MWF estimates. We evaluated the RMSE of MWF estimates from the optimized scans in simulation. We compared STFR-based MWF estimates (both modeling exchange and notmodeling exchange) to multi-echo spin echo (MESE)-based estimates. We used the optimized scans to acquire in vivo data from which a MWF map was estimated. We computed the STFR-based MWF estimates using PERK, a recently developed kernel regression technique, and the MESE-based MWF estimates using both regularized non-negative least squares (NNLS) and PERK. In simulation, the optimized STFR scans led to estimates of MWF with low RMSE across a range of tissue parameters and across white matter and gray matter. The STFR-based MWF estimates that modeled exchange compared well to MESE-based MWF estimates in simulation. When the optimized scans were tested in vivo, the MWF map that was estimated using a 3-compartment model with exchange was closer to the MESE-based MWF map. The optimized STFR scans appear to be well suited for estimating MWF in simulation and in vivo when we model exchange in training. In this case, the STFR-based MWF estimates are close to the MESE-based estimates.

Neurodegenerative diseases detection using distance metrics and sparse coding: A new perspective on gait symmetric features

Gait rhythm fluctuations are of great importance for automatic neurodegenerative diseases (NDDs) detection. They provide a cost-effective and noninvasive monitoring tool in which their parameters are related to neuromuscular function. This study investigated a new solution based on a set of new symmetric features and sparse non-negative least squares (NNLS) coding classifier. Dynamic gait series warping (DGSW), Euclidean, Manhattan, Minkowski, Chebyshev, Canberra distances, and cosine function were used to quantify the amount of divergence between the left and right stride, swing, and stance intervals. The algorithm was evaluated using the gait signals of 16 healthy control subjects, 13 patients with amyotrophic lateral sclerosis (ALS), 15 patients with Parkinson's disease (PD) and 20 patients with Huntington's disease (HD).The proposed new approach using symmetric features and NNLS technique achieved outstanding accuracies of 98%, 97%, and 95% on the patients with PD, ALS, and HD, respectively. The findings also suggested that the new DGSW, cosine function, and Chebyshev distance, which are designed to dynamically, geometrically, or nonlinearly quantify the similarity between two time series, provide the discriminatory measures to describe how NDDs alter the gait symmetry. In comparison with other studies, combining symmetric features with a sparse NNLS coding classifier can improve the detection accuracy providing an efficient and cost-effective framework for the development of a NDDs detection system.

Improving the resolution of underwater acoustic image measurement by deconvolution

The conventional beamforming (CBF) map of underwater acoustic image measurement can be expressed as a convolution of the source distribution and the response of the beamformer to a point source, defined as the beam pattern or the point spread function (PSF). By deconvolving the CBF beamformer’s map, the distribution of the actual sources with a clean beam map can be obtained to improve the resolution. In this paper, the deconvolved conventional beamforming (dCv) is applied to underwater acoustic image measurement to improve the accuracy of sound source localization. Due to the point spread function of the array in near field is dependent on the focused point, which means that the PSF is shift variant, so it is necessary to use shift-variant deconvolution method. In this paper, an extended Richardson-Lucy (Ex-RL) algorithm is applied to the two-dimensional shift-variant deconvolution acoustic image measurement problem to improve resolution. The method is compared with the original-RL, classical deconvolution approach for the mapping of acoustic sources (DAMAS) and non-negative least squares (NNLS). The simulation and the experiment results verify the effectiveness of the algorithm.

Monitor Ionizing Radiation-Induced Cellular Responses with Raman Spectroscopy, Non-Negative Matrix Factorization, and Non-Negative Least Squares

Radiation therapy (RT) is one of the most commonly prescribed cancer treatments. New tools that can accurately monitor and evaluate individual patient responses would be a major advantage and lend to the implementation of personalized treatment plans. In this study, Raman spectroscopy (RS) was applied to examine radiation-induced cellular responses in H460, MCF7, and LNCaP cancer cell lines across different dose levels and times post-irradiation. Previous Raman data analysis was conducted using principal component analysis (PCA), which showed the ability to extract biological information of glycogen. In the current studies, the use of non-negative matrix factorization (NMF) allowed for the discovery of multiplexed biological information, specifically uncovering glycogen-like and lipid-like component bases. The corresponding scores of glycogen and previously unidentified lipids revealed the content variations of these two chemicals in the cellular data. The NMF decomposed glycogen and lipid-like bases were able to separate the cancer cell lines into radiosensitive and radioresistant groups. A further lipid phenotype investigation was also attempted by applying non-negative least squares (NNLS) to the lipid-like bases decomposed individually from three cell lines. Qualitative differences found in lipid weights for each lipid-like basis suggest the lipid phenotype differences in the three tested cancer cell lines. Collectively, this study demonstrates that the application of NMF and NNLS on RS data analysis to monitor ionizing radiation-induced cellular responses can yield multiplexed biological information on bio-response to RT not revealed by conventional chemometric approaches.

Molecular Dynamics Ensemble Refinement of Intrinsically Disordered Peptides According to Deconvoluted Spectra from Circular Dichroism

We have developed a computational method of atomistically refining the structural ensemble of intrinsically disordered peptides (IDPs) facilitated by experimental measurements using circular dichroism spectroscopy (CD). A major challenge surrounding this approach stems from the deconvolution of experimental CD spectra into secondary structure features of the IDP ensemble. Currently available algorithms for CD deconvolution were designed to analyze the spectra of proteins with stable secondary structures. Herein, our work aims to minimize any bias from the peptide deconvolution analysis by implementing a non-negative linear least-squares fitting algorithm in conjunction with a CD reference data set that contains soluble and denatured proteins (SDP48). The non-negative linear least-squares method yields the best results for deconvolution of proteins with higher disordered content than currently available methods, according to a validation analysis of a set of protein spectra with Protein Data Bank entries. We subsequently used this analysis to deconvolute our experimental CD data to refine our computational model of the peptide secondary structure ensemble produced by all-atom molecular dynamics simulations with implicit solvent. We applied this approach to determine the ensemble structures of a set of short IDPs, that mimic the calmodulin binding domain of calcium/calmodulin-dependent protein kinase II and its 1-amino-acid and 3-amino-acid mutants. Our study offers a, to our knowledge, novel way to solve the ensemble secondary structures of IDPs in solution, which is important to advance the understanding of their roles in regulating signaling pathways through the formation of complexes with multiple partners.

The Spatial Distribution of Water Components with Similar T2 May Provide Insight into Pathways for Large Molecule Transportation in the Brain.

Purpose:Although there is no lymphatic system in the central nervous system (CNS), there seems to be a mechanism to remove macro molecules from the brain. Cerebrospinal fluid (CSF) and interstitial fluid (ISF) are thought to be parts of this pathway, but the details are not known. In this study, MR signal of the extracellular water was decomposed into components with distinct T2’s, to obtain some information about distribution of waste material in the brain.Methods:Images were acquired using a Curr, Purcell, Meiboom, Gill (CPMG) imaging sequence. In order to reduce T1 contamination and the signal oscillation, hard pulses were used as refocusing pulses. The signal was then decomposed into many T2 components using non-negative least squares (NNLS) in pixel-by-pixel basis. Finally, a color map was generated by assigning different color for each T2 component, then adding them together.Results:From the multi-echo images, it was possible to decompose the decaying signal into separate T2 components. By adjusting the color table to create the color map, it is possible to visualize the extracellular water distribution, as well as their T2 values. Several observation points include: (1) CSF inside ventricles has very long T2 (∼2 s), and seems to be relatively homogeneous, (2) subarachnoid CSF also have long T2, but there are short T2 component at the brain surface, at the surface of dura, at the blood vessels in the subarachnoid space, etc., (3) in the brain parenchyma, short T2 components (longer than intracellular component but shorter than CSF) exists along the white matter, in the choroid plexus, etc. These can be considered as distribution of macromolecules (waste materials) in the brain.Conclusion:From T2 component analysis it is possible to obtain some insight into pathways for the transport of large molecules in the CNS, where no lymphatic system is present.

An efficient nonmonotone projected Barzilai–Borwein method for nonnegative matrix factorization with extrapolation

ABSTRACT In this paper, we present an efficient method for nonnegative matrix factorization (NMF) based on the alternating nonnegative least-squares framework. To solve the nonnegativity constrained least-squares problems efficiently, we propose an extrapolated quadratic regularization projected Barzilai–Borwein (EQRPBB) method utilizing the extrapolation technique and a modified nonmonotone line search. The efficiency of the proposed method is demonstrated through experiments on synthetic and image datasets. We observe that our method significantly outperform existing ones in terms of computational speed.

Myelin water imaging data analysis in less than one minute

PurposeBased on a deep learning neural network (NN) algorithm, a super fast and easy to implement data analysis method was proposed for myelin water imaging (MWI) to calculate the myelin water fraction (MWF). MethodsA NN was constructed and trained on MWI data acquired by a 32-echo 3D gradient and spin echo (GRASE) sequence. Ground truth labels were created by regularized non-negative least squares (NNLS) with stimulated echo corrections. Voxel-wise GRASE data from 5 brains (4 healthy, 1 multiple sclerosis (MS)) were used for NN training. The trained NN was tested on 2 healthy brains, 1 MS brain with segmented lesions, 1 healthy spinal cord, and 1 healthy brain acquired from a different scanner. ResultsProduction of whole brain MWF maps in approximately 33 ​s can be achieved by a trained NN without graphics card acceleration. For all testing regions, no visual differences between NN and NNLS MWF maps were observed, and no obvious regional biases were found. Quantitatively, all voxels exhibited excellent agreement between NN and NNLS (all R2>0.98, p ​< ​0.001, mean absolute error <0.01). ConclusionThe time for accurate MWF calculation can be dramatically reduced to less than 1 ​min by the proposed NN, addressing one of the barriers facing future clinical feasibility of MWI.

On the identification of the blood vessel confounding effect in intravoxel incoherent motion (IVIM) Diffusion-Weighted (DW)-MRI in liver: An efficient sparsity based algorithm.

IntraVoxel Incoherent Motion (IVIM) Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) is of great interest for evaluating tissue diffusion and perfusion and producing parametric maps in clinical applications for liver pathologies. However, the presence of macroscopic blood vessels (not capillaries) in a given Region of Interest (ROI) results in a confounding effect that bias the quantification of tissue perfusion. Therefore, it is necessary to identify those voxels affected by blood vessels. In this paper, an efficient algorithm for an automatic identification of blood vessels in a given ROI is proposed. It relies on the sparsity of the spatial distribution of blood vessels. This sparsity prior can be easily incorporated using the all-voxel IVIM-MRI model introduced in this paper. In addition to the identification of blood vessels, the proposed algorithm provides a quantification of blood vessels, tissue diffusion and tissue perfusion of all voxels in a given ROI, in one single step. Besides, two strategies are proposed in this paper to deal with the nonnegativity of the model parameters. The efficiency of the proposed algorithm compared to the Non-Negative Least Square (NNLS)-based method, recently introduced to deal with the confounding blood vessel effect in the IVIM-MRI model, is confirmed using both realistic and real DW-MR images.