Nonnegative Component Research Articles

Analyzing the Influence of Telematics-Based Pricing Strategies on Traditional Rating Factors in Auto Insurance Rate Regulation

This study examines how telematics variables such as annual percentage driven, total miles driven, and driving patterns influence the distributional behaviour of conventional rating factors when incorporated into predictive models for capturing auto insurance risk in rate regulation. To effectively manage the complexity inherent in telematics data, we advocate for the adoption of non-negative sparse principal component analysis (NSPCA) as a structured approach for data dimensionality reduction. By emphasizing sparsity and non-negativity constraints, NSPCA enhances the interpretability and predictive power of models concerning both loss severity and claim counts. This methodological innovation aims to advance statistical analyses within insurance pricing frameworks, ensuring the robustness of predictive models and providing insights crucial for rate regulation strategies specific to the auto insurance sector. Results show that, to enhance auto insurance risk pricing models, it is essential to address data dimension reduction challenges when integrating telematics data variables. Our findings underscore that integrating telematics variables into predictive models maintains the integrity of risk relativity estimates associated with traditional policy variables.

Non-negative least-squares variance and covariance component estimation using the positive-valued function for errors-in-variables models

Abstract Although (co)variance component estimation has been widely applied in the errors-in-variables (EIV) model, the occurrence of negative variance components is still a major issue in the estimated variance components. This problem may be due to the following unfavorable factors: 1) unreasonable selection of initial variance values; 2) low redundancy in the EIV functional model; 3) improper design in the EIV stochastic model, and 4) other data quality problems. Many attempts have been made to prevent the appearance of negative variance components. In this contribution, a novel and efficient non-negative least-squares variance component estimation using the PVF (PVF-NLS-VCE) is introduced, which can simultaneously estimate the unknown (co)variance components in the EIV stochastic model and the parameters in the EIV functional model. Its principle is to implicitly impose a non-negative constraint by replacing the variance component with the positive-valued function (PVF) whose range is the set of positive real numbers. Two numerical examples using real and simulated data are presented. The numerical results of linear regression are identical to those obtained based on least-squares variance component estimation (LS-VCE) with positive initial values of variance components. The numerical results of two-dimensional affine transformation are shown to prevent negative variance components and precede those obtained by LS-VCE with a negative initial value of variance component. Both numerical examples verify the effectiveness of the PVF-NLS-VCE method whether the initial values of variance components are positive or negative. The proposed PVF-NLS-VCE is a simple, convenient and flexible method to achieve the non-negative estimates of variance components, which can reduce sensitivity to initial value selection and automatically guarantee a non-negative definite covariance matrix.

Quadratic Programming Approach in the Non-Negatif Matrix Factorization

Non-negative Matrix Factorization is an iteration optimization algorithm. ie to decipher one matrix into several non-negative component matrices. Non-negative Matrix Factorization (FMN) serves to obtain a picture of non-negative data. There is a problem in the Non-negative Matrix Factorization that is optimization at the constraint boundary, where in the optimization solution on the constraint boundary it is necessary to do long iteration and of course very difficult and conquers a long time. Quadratic Programing is an approach to solving linear optimization problems where the constraint is linear function and its purpose function is the square of the decision variable or multiplication of the two decision variables. This method is considered to be an effective method to overcome the optimization in the Non-negative Matrix Factorization.

Riemannian optimization on unit sphere with p-norm and its applications

This study deals with Riemannian optimization on the unit sphere in terms of p-norm with general $$p> 1$$ . As a Riemannian submanifold of the Euclidean space, the geometry of the sphere with p-norm is investigated, and several geometric tools used for Riemannian optimization, such as retractions and vector transports, are proposed and analyzed. Applications to Riemannian optimization on the sphere with nonnegative constraints and $$\textit{L}_{\textit{p}}$$ -regularization-related optimization are also discussed. As practical examples, the former includes nonnegative principal component analysis, and the latter is closely related to the Lasso regression and box-constrained problems. Numerical experiments verify that Riemannian optimization on the sphere with p-norm has substantial potential for such applications, and the proposed framework provides a theoretical basis for such optimization.

Multi-target reconstruction strategy based on blind source separation of surface measurement signals in FMT.

Fluorescence molecular tomography (FMT) is a promising molecular imaging technique for tumor detection in the early stage. High-precision multi-target reconstructions are necessary for quantitative analysis in practical FMT applications. The existing reconstruction methods perform well in retrieving a single fluorescent target but may fail in reconstructing a multi-target, which remains an obstacle to the wider application of FMT. In this paper, a novel multi-target reconstruction strategy based on blind source separation (BSS) of surface measurement signals was proposed, which transformed the multi-target reconstruction problem into multiple single-target reconstruction problems. Firstly, by multiple points excitation, multiple groups of superimposed measurement signals conforming to the conditions of BSS were constructed. Secondly, an efficient nonnegative least-correlated component analysis with iterative volume maximization (nLCA-IVM) algorithm was applied to construct the separation matrix, and the superimposed measurement signals were separated into the measurements of each target. Thirdly, the least squares fitting method was combined with BSS to determine the number of fluorophores indirectly. Lastly, each target was reconstructed based on the extracted surface measurement signals. Numerical simulations and in vivo experiments proved that it has the ability of multi-target resolution for FMT. The encouraging results demonstrate the significant effectiveness and potential of our method for practical FMT applications.

Non-negative sparse component decomposition based modeling and robust unmixing for hyperspectral images

Non-negative sparse component decomposition based modeling and robust unmixing for hyperspectral images

Machine Learning Approach to Enable Spectral Imaging Analysis for Particularly Complex Nanomaterial Systems.

Scanning transmission electron microscopy-based electron energy loss spectroscopy spectral imaging (STEM-EELS-SI) has been widely used in material research to capture a wealth of information, including elemental, electron density, and bonding state distributions. However, its exploitation still faces many challenges due to the difficulty of extracting information from noisy and overlapping edges in the convoluted spatial and spectroscopic data set. A traditional EELS spectral imaging analysis lacks the capability to isolate noise and deconvolute such overlapping edges, which either limits the resolution or the signal-to-noise ratio of the maps generated by EELS-SI. Existing machine learning (ML) algorithms can achieve denoising and deconvolution to a certain extent, but the extracted spectra lack physical meaning. To address these challenges, we have developed a ML method tailored to a spectral imaging analysis system and based on a non-negative robust principal component analysis. This approach offers an effective way to analyze EELS spectral images with improved space-time resolution, signal-to-noise ratio, and the capability to separate subtle differences in the spectrum. We apply this algorithm to 13 nanomaterial systems to show that ML can greatly improve image quality compared to a traditional approach, especially for more challenging systems. This will expand the type of nanomaterial systems that can be characterized by EELS-SI, and aid the analysis of structural, chemical, and electronic properties that are otherwise difficult to obtain.

Spectroscopic signature of ZnO NP-induced cell death modalities assessed by non-negative PCA

Selective cytotoxicity of ZnO nanoparticles among different cell types and cancer and non-cancerous cells has been demonstrated earlier. In the view of anticancer potential of ZnO nanoparticles and their presence in numerous industrial products, it is of great importance to carefully evaluate their effects and mechanisms of action in both cancerous and healthy cells. In this paper, the effects of ZnO nanoparticles on cancerous HeLa and non-cancerous MRC-5 cells are investigated by studying the changes in the vibrational properties of the cells using Raman spectroscopy. Both types of cells were incubated with ZnO nanoparticles of average size 40 nm in the doses from the range 10–40 µg/ml for the period of 48 h, after which Raman spectra were collected. Raman modes’ intensity ratios I1659/I1444, I2855/I2933 and I1337/I1305 were determined as spectral markers of the cytotoxic effect of ZnO in both cell types. Non-negative principal component analysis was used instead of standard one for analysis and detection of spectral features characteristic for nanoparticle-treated cells. The first several non-negative loading vectors obtained in this analysis coincided remarkably well with the Raman spectra of particular biomolecules, showing increase of lipid and decrease of nucleic acids and protein content. Our study pointed out that Raman spectral markers of lipid unsaturation, especially I1270/I1300, are relevant for tracing the cytotoxic effect of ZnO nanoparticles on both cancerous and non-cancerous cells. The change of these spectral markers is correlated to the dose of applied nanoparticles and to the degree of cellular damage. Furthermore, great similarity of spectral features of increasing lipids to spectral features of phosphatidylserine, one of the main apoptotic markers, was recognized in treated cells. Finally, the results strongly indicated that the degree of lipid saturation, presented in the cells, plays an important role in the interaction of cells with nanoparticles.

Biologically plausible single-layer networks for nonnegative independent component analysis.

An important problem in neuroscience is to understand how brains extract relevant signals from mixtures of unknown sources, i.e., perform blind source separation. To model how the brain performs this task, we seek a biologically plausible single-layer neural network implementation of a blind source separation algorithm. For biological plausibility, we require the network to satisfy the following three basic properties of neuronal circuits: (i) the network operates in the online setting; (ii) synaptic learning rules are local; and (iii) neuronal outputs are nonnegative. Closest is the work by Pehlevan et al.(Neural Comput 29:2925-2954, 2017), which considers nonnegative independent component analysis (NICA), a special case of blind source separation that assumes the mixture is a linear combination of uncorrelated, nonnegative sources. They derive an algorithm with a biologically plausible 2-layer network implementation. In this work, we improve upon their result by deriving 2 algorithms for NICA, each with a biologically plausible single-layer network implementation. The first algorithm maps onto a network with indirect lateral connections mediated by interneurons. The second algorithm maps onto a network with direct lateral connections and multi-compartmental output neurons.

Dual-channel event-triggered control for positive nonlinear systems

This paper focuses on the problem of dual-channel event-triggered control for positive nonlinear systems. A dual-channel event-triggered transmission scheme is proposed to determine whether the data packets should be released or not. Two 1-norm-based event-trigger conditions are designed for the sensor-controller channel and controller-actuator channel, respectively. The condition of the system remaining positivity with the designed event-trigger conditions and feedback control law is provided. By using the Lyapunov method and matrix decomposition technique, a sufficient criterion ensuring the closed loop system to be asymptotically stable is proposed. For the linearisation purpose, the control gain is delicately decomposed into a nonnegative component and a non-positive component. Zeno behaviour of the designed event-triggered transmission of sampled data packets is further rigorously proved to be excluded. An example of water pollution control system is provided to show the effectiveness of the obtained results.

Nonnegative principal component analysis in thin layer fingerprint screening: A case of Gentiana extracts from in vitro cultures

Twenty-one species of Gentiana L. were successfully grown in vitro in the same conditions and 72 samples of various cultures of these species (root, shoots, cotyledon callus, hypocotyl callus, and root callus) were obtained. The investigated species were as follows: G. affinis, G. andrewsii, G. bhutanica, G. burseri, G. cachemirica, G. capitata, G. crassicaulis, G. dahurica, G. decumbens, G. freyniana, G. frigida, G. gelida, G. grossheimii, G. kurroo, G. macrophylla, G. paradoxa, G. robusta, G. scabra, G. septemfida, G. siphonantha, and G. tianschanica. The obtained samples were extracted with methanol–acetone–water (3:1:1) mixture, evaporated to dryness, and subjected to TLC on silica gel with mobile phase ethyl acetate–methanol–water (8:2:2) in sandwich mode. Data fusion of two densitometric modes: extinction at 254 nm and fluorescence at 312 nm (emission above 370 nm) were used as a fingerprint of each sample. Densitograms were denoised, subjected to baseline removal, warped, and analyzed with principal component analysis (PCA), hierarchical cluster analysis and—the novel proposal—nonnegative PCA. This allowed to split negatively intercorrelated fingerprint features to subsequent principal components (PCs), which increases the number of PCs required to see the same information, but these PCs are much more informative.

Interpretable, Scalable, and Transferrable Functional Projection of Large-Scale Transcriptome Data Using Constrained Matrix Decomposition.

Large-scale transcriptome data, such as single-cell RNA-sequencing data, have provided unprecedented resources for studying biological processes at the systems level. Numerous dimensionality reduction methods have been developed to visualize and analyze these transcriptome data. In addition, several existing methods allow inference of functional variations among samples using gene sets with known biological functions. However, it remains challenging to analyze transcriptomes with reduced dimensions that are interpretable in terms of dimensions’ directionalities, transferrable to new data, and directly expose the contribution or association of individual genes. In this study, we used gene set non-negative principal component analysis (gsPCA) and non-negative matrix factorization (gsNMF) to analyze large-scale transcriptome datasets. We found that these methods provide low-dimensional information about the progression of biological processes in a quantitative manner, and their performances are comparable to existing functional variation analysis methods in terms of distinguishing multiple cell states and samples from multiple conditions. Remarkably, upon training with a subset of data, these methods allow predictions of locations in the functional space using data from experimental conditions that are not exposed to the models. Specifically, our models predicted the extent of progression and reversion for cells in the epithelial-mesenchymal transition (EMT) continuum. These methods revealed conserved EMT program among multiple types of single cells and tumor samples. Finally, we demonstrate this approach is broadly applicable to data and gene sets beyond EMT and provide several recommendations on the choice between the two linear methods and the optimal algorithmic parameters. Our methods show that simple constrained matrix decomposition can produce to low-dimensional information in functionally interpretable and transferrable space, and can be widely useful for analyzing large-scale transcriptome data.

Non-Negative Sparse PCA: An Intelligible Exact Approach

An iterative method for the computation of a non-negative sparse principal component basis is presented. The iterative nature of the proposed method enables online learning, useful for time-evolving data, such as stock price time series. This way, the computation of the covariance matrix is avoided whenever new data become available. Due to the non-negative constraints explicitly enforced, the extracted eigenvectors turn to be sparse without employing any sparsity controlling parameter. Accordingly, only one parameter has to be tuned, i.e., the learning rate. Also, the complexity of the method under study is approximately linear under plausible assumptions. To assess the method’s performance, comprehensive experimental evaluation is conducted on both image and financial data. The proposed method is thoroughly compared to state-of-the-art and yields promising experimental findings.

Tensor-Decomposition-Based Unsupervised Feature Extraction Applied to Prostate Cancer Multiomics Data

The large p small n problem is a challenge without a de facto standard method available to it. In this study, we propose a tensor-decomposition (TD)-based unsupervised feature extraction (FE) formalism applied to multiomics datasets, in which the number of features is more than 100,000 whereas the number of samples is as small as about 100, hence constituting a typical large p small n problem. The proposed TD-based unsupervised FE outperformed other conventional supervised feature selection methods, random forest, categorical regression (also known as analysis of variance, or ANOVA), penalized linear discriminant analysis, and two unsupervised methods, multiple non-negative matrix factorization and principal component analysis (PCA) based unsupervised FE when applied to synthetic datasets and four methods other than PCA based unsupervised FE when applied to multiomics datasets. The genes selected by TD-based unsupervised FE were enriched in genes known to be related to tissues and transcription factors measured. TD-based unsupervised FE was demonstrated to be not only the superior feature selection method but also the method that can select biologically reliable genes. To our knowledge, this is the first study in which TD-based unsupervised FE has been successfully applied to the integration of this variety of multiomics measurements.

Nonnegative variance component estimation for mixed-effects models

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley’s synthesis is used as a method for finding the coefficients of variance components.

Construction of Multiplex Muscle Network for Precision Pinch Force Control.

Muscle synergy is a fundamental mechanism of motor control. Despite a number of studies focusing on muscle synergy during power grip and pinch at high-level force, relatively less is known about the functional interactions between muscles within low-level force production during precision pinch. Traditional analytical tools such as nonnegative matrix factorization or principal component analysis have limitations in processing nonlinear dynamic electromyographic signals and have confined sensitivity particularly for the low-level force production. In this study, we developed a novel method - multiplex muscle networks, to investigate the dynamical coordination of muscle activities at low-level force production during precision pinch. The multiplex muscle network was constructed based on multiplex limited penetrable horizontal visibility graph (MLPHVG). Seven forearm and hand muscles, including brachioradialis (BR), flexor carpi ulnaris (FCU), flexor carpi radialis (FCR), flexor digitorum superficialis (FDS), extensor digitorum communis (EDC), abductor pollicis brevis (APB) and first dorsal interosseous (FDI), were examined using surface electromyography (sEMG). Eight healthy subjects were instructed to perform a visuomotor force tracking task by producing higher (10% MVC) and lower (1% MVC) precision pinch. Interlayer mutual information I, average edge overlap ω weighted clustering coefficient CW, weighted characteristic path length LW were selected as network metrics. We assessed the undirected weighted network generated from multiplex muscle network after taking the I between paired muscle network layers as edge. There are significant differences between higher and lower force level with higher I, ω, CW and lower LW at higher force level. Advanced efficiency of information processing in the regional and global perspective indicated dynamical alterations when human faces the higher force tracking task. It suggested that ω may be an important characteristic to classify different force control states with the average classification accuracy of 82.21%. These findings reveal related alterations of functional interactions between muscles involved in precision pinch. The novel method for constructing multiplex muscle network may provide insights into muscle synergies during precision pinch force control.

The Self-Motion Information Response Model in Brain-Inspired Navigation

Grid cells are important neurons related to spatial cognition and navigation in the animal brain and can respond to both external information and self-motion information. The existing models simulated these two types of responses separately, but how to simultaneously develop the two types of connection to respond to the different information has not been simulated. In this paper, first, we develop the connections from place cells to grid cells through improved nonnegative principal component analysis. Then, we construct a continuous attractor network model and an autoencoder network model of grid cell module and convert the parameter learning in the continuous attractor network into weight learning in the autoencoder network. Through parameter learning, the continuous attractor network model can spontaneously generate a hexagonal firing pattern. Ultimately, the grid cell firing fields driven by place cell inputs and self-motion information have the same spacing and direction, which means that the grid cell module can respond the same to these two types of information. This model can provide a reference for the construction of an unmanned agent brain-inspired navigation system.

Non-negative variance component estimation for the partial EIV model by the expectation maximization algorithm

A difficulty in variance component estimation (VCE) is that the estimates may become negative, which is not acceptable in practice. This article presents two new methods for non-negative VCE that utilize the expectation maximization algorithm for the partial errors-in-variables model. The former searches for the desired solutions with unconstrained estimation criterion and concludes statistically that the variance components have indeed moved to the edge of the parameter space when negative estimates appear implemented by the other existing VCE methods. We concentrate on the formulation and provide non-negative analysis of this estimator. In particularly, the latter approach, which has greater computational efficiency, would be a practical alternative to the existing VCE-type algorithms. Additionally, this approach is easy to implement, the non-negative variance components are automatically supported by introducing non-negativity constraints. Both algorithms are free from a complex matrix inversion and reduce computational complexity. The results show that our algorithms retrieve well to achieve identical estimates over the other VCE methods, the latter approach can quickly estimate parameters and has practical aspects for the large volume and multisource data processing.

Combining F0 and non-negative constraint robust principal component analysis for singing voice separation

Separating singing voice from a musical mixture remains an important task in the field of music information retrieval. Recent studies on singing voice separation have shown that robust principal component analysis (RPCA) with rank-1 constraint approach can improve separation quality. However, the performance of separation is limited because the vocal part can not be described well by the separated matrix. Therefore, prior information such as fundamental frequency (F0) should be considered. F0 can significantly improve separation performance by removing the spectral components of non-repeating instruments (e.g., bass and guitar). In this paper, we propose a novel singing voice separation algorithm by combining prior information and non-negative constraint RPCA, which incorporates F0 and non-negative rank-1 constraint minimization of singular values in RPCA instead of minimizing the nuclear norm. In addition, we use the original phase recovery in estimating the spectral components of the separated singing voice. Experimental results on the iKala and MIR-1K datasets show higher efficiency of the proposed algorithm compared with state-of-the-art methods in terms of separation accuracy.

Unmixing multi-spectral photoacoustic sources in human carotid plaques using non-negative independent component analysis

Multi-spectral photoacoustic imaging (MSPAI) is promising for morphology assessment of carotid plaques; however, obtaining unique spectral characteristics of chromophores is cumbersome. We used MSPAI and non-negative independent component analysis (ICA) to unmix distinct signal sources in human carotid plaques blindly. The feasibility of the method was demonstrated on a plaque phantom with hemorrhage and cholesterol inclusions, and plaque endarterectomy samples ex vivo. Furthermore, the results were verified with histology using Masson's trichrome staining. Results showed that ICA could separate recent hemorrhages from old hemorrhages. Additionally, the signatures of cholesterol inclusion were also captured for the phantom experiment. Artifacts were successfully removed from signal sources. Histologic examinations showed high resemblance with the unmixed components and confirmed the morphologic distinction between recent and mature hemorrhages. In future pre-clinical studies, unmixing could be used for morphology assessment of intact human plaque samples.