Non-negative Principal Component Analysis Research Articles

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.

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.

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.

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.

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.

Internal Emotion Classification Using EEG Signal With Sparse Discriminative Ensemble

Among various physiological signal acquisition methods for the study of the human brain, EEG (Electroencephalography) is more effective. EEG provides a convenient, non-intrusive, and accurate way of capturing brain signals in multiple channels at fine temporal resolution. We propose an ensemble learning algorithm for automatically computing the most discriminative subset of EEG channels for internal emotion recognition. Our method describes an EEG channel using kernel-based representations computed from the training EEG recordings. For ensemble learning, we formulate a graph embedding linear discriminant objective function using the kernel representations. The objective function is efficiently solved via sparse non-negative principal component analysis and the final classifier is learned using the sparse projection coefficients. Our algorithm is useful in reducing the amount of data while improving computational efficiency and classification accuracy at the same time. The experiments on publicly available EEG dataset demonstrate the superiority of the proposed algorithm over the compared methods.

Abstract 5661: A multi modal mass spectrometry imaging strategy to profile the metabolic hallmarks of colorectal cancer

Abstract New methods are required to image the metabolic hallmarks of cancerous tissues and correlate this information with patient tumour pathology, cancer phenotype and treatment outcome. Mass spectrometry imaging (MSI) offers a powerful suite of techniques for imaging metabolites, drugs and proteins in cells and tissues. Here we present a multi-modal MSI strategy and use it to profile PDX, GEMM and biopsy samples. Human and murine colon and small intestine samples were sectioned onto glass slides and stored at -80°C until use. MALDI-MSI (Waters and Bruker) was carried out with pixel sizes between 10 and 50 microns, DESI (Waters) at 20-50 microns and SIMS (IONTOF) at approximately 200 nm per pixel. Data were converted from proprietary format to imzML and analysed in MatLab (2015b, MathWorks) via the SpectralAnalysis software package using non-negative matrix factorisation (NMF) and principal component analysis (PCA). Further reduction and segmentation was achieved using stacked autoencoders and t-distributed stochastic neighbour embedding (t-SNE). To assign the peaks detected to molecular identities, peaks picked from mean spectra were matched to the human metabolome database (HMDB) using custom Matlab scripts. Possible adducts were queried against the database masses, and filtered based on comparison of expected and observed mass, and correlation between the images of the monoisotopic mass and 13C isotope image. Preliminary data show the successful preparation and analysis of multiple GEMM and human tissue samples across several sites by MALDI-MSI, DESI-MSI and SIMS imaging. Converting data to imzML and combining into large, single multi-file images enabled multivariate analysis (MVA) to be performed simultaneously within the same comparison. Of these MVA methods, mass spectrometry imaging (MSI) in combination with t-SNE has been shown to differentiate tumour subpopulations linked with patient outcomes. Current t-SNE methods suffer from three main limitations as compared to other MVA methods; poor computational scaling to large datasets, inability to add new data into the embedding, and inability to return to spectral contributions. By combining t-SNE performed on a subset of data and learning the embedding via deep learning, almost limitless size datasets can be analysed by t-SNE, new data can be incorporated into the embedding, and the spectral contributions towards the three dimensional space can be determined. Database matching on the data from these GEMM samples to the HMDB reveals over 1000 possible molecular assignments, primarily structural lipids, within 10 ppm mass accuracy and with isotope image correlations above 0.6. From these methods, comparisons can be made between the unique molecules detected in different tissues, as well as the relative changes in intensity of those detected between different tissues. Citation Format: Josephine Bunch, Rory T. Steven, Adam J. Taylor, Spencer A. Thomas, Alan M. Race, Alex Dexter, Gregory Hamm, Nicole Strittmatter, Rasmus Havelund, Renata F. Soares, Andrew D. Campbell, Owen J. Sansom, Richard J. Goodwin, Zoltan Takats. A multi modal mass spectrometry imaging strategy to profile the metabolic hallmarks of colorectal cancer [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 5661.

Semi-Supervised Speech Enhancement Combining Nonnegative Matrix Factorization and Robust Principal Component Analysis

Semi-Supervised Speech Enhancement Combining Nonnegative Matrix Factorization and Robust Principal Component Analysis

Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis.

Many recent models study the downstream projection from grid cells to place cells, while recent data have pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells. We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights are learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is -1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA.

Non-Negative Principal Component Analysis: Message Passing Algorithms and Sharp Asymptotics

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional data set. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional knowledge on the principal vector? We study the case in which the principal vector is known to lie in the positive orthant. Similar constraints arise in a number of applications, ranging from the analysis of gene expression data to spike sorting in neural signal processing. In the unconstrained case, the estimation performances of PCA have been precisely characterized using the random matrix theory, under a statistical model known as the spiked model. It is known that the estimation error undergoes a phase transition as the signal-to-noise ratio crosses a certain threshold. Unfortunately, tools from the random matrix theory have no bearing on the constrained problem. Despite this challenge, we develop an analogous characterization in the constrained case, within a one-spike model. In particular: 1) we prove that the estimation error undergoes a similar phase transition, albeit at a different thresholds in signal-to-noise ratio that we determine exactly; 2) we prove that-unlike in the unconstrained case-the estimation error depends on the spike vector, and characterize the least favorable vectors; and 3) we show that a non-negative principal component can be approximately computed-under the spiked model-in nearly linear time. This despite the fact that the problem is non-convex and, in general, NP-hard to solve exactly.

A dimensionality reduction approach for many-objective Markov Decision Processes: Application to a water reservoir operation problem

The operation of complex environmental systems usually accounts for multiple, conflicting objectives, whose presence imposes to explicitly consider the preference structure of the parties involved. Multi-objective Markov Decision Processes are a useful mathematical framework for the resolution of such sequential, decision-making problems. However, the computational requirements of the available optimization techniques limit their application to problems involving few objectives. In real-world applications it is therefore common practice to select few, representative objectives with respect to which the problem is solved. This paper proposes a dimensionality reduction approach, based on the Non-negative Principal Component Analysis (NPCA), to aggregate the original objectives into a reduced number of principal components, with respect to which the optimization problem is solved. The approach is evaluated on the daily operation of a multi-purpose water reservoir (Tono Dam, Japan) with 10 operating objectives, and compared against a 5-objectives formulation of the same problem. Results show that the NPCA-based approach provides a better representation of the Pareto front, especially in terms of consistency and solution diversity.

Physician performance assessment using a composite quality index

Assessing physician performance is important for the purposes of measuring and improving quality of service and reducing healthcare delivery costs. In recent years, physician performance scorecards have been used to provide feedback on individual measures; however, one key challenge is how to develop a composite quality index that combines multiple measures for overall physician performance evaluation. A controversy arises over establishing appropriate weights to combine indicators in multiple dimensions, and cannot be easily resolved. In this study, we proposed a generic unsupervised learning approach to develop a single composite index for physician performance assessment by using non-negative principal component analysis. We developed a new algorithm named iterative quadratic programming to solve the numerical issue in the non-negative principal component analysis approach. We conducted real case studies to demonstrate the performance of the proposed method. We provided interpretations from both statistical and clinical perspectives to evaluate the developed composite ranking score in practice. In addition, we implemented the root cause assessment techniques to explain physician performance for improvement purposes.

Face recognition using two-dimensional nonnegative principal component analysis

Although two-dimensional principal component analysis (2DPCA) extracts image features directly from 2D image matrices rather than one dimensional vectors, 2DPCA is only based on the whole images to preserve total variances by maximizing the trace of feature covariance matrix. Thus, 2DPCA cannot extract localized components, which are usually important for face recognition. Inspired by nonnegative matrix factorization (NMF), which is based on localized features, we propose a novel algorithm for face recognition called two-dimensional nonnegative principal component analysis (2DNPCA) to extract localized components and maintain the maximal variance property of 2DPCA. 2DNPCA is a matrix-based algorithm to preserve the local structure of facial images and has the nonnegative constraint to learn localized components. Therefore, 2DNPCA has both advantages of 2DPCA and NMF. Furthermore, 2DNPCA solves the time-consuming problem by removing the restriction of minimizing the cost function and extracting only the base matrix. The nearest neighbor (NN) classifier and linear regression (LR) classifier are used for classification and extensive experimental results show that 2DNPCA plus NN and 2DNPCA plus LR are both very efficient approaches for face recognition.

Non-negative principal component analysis for NMR-based metabolomic data analysis

Proton nuclear magnetic resonance (1H-NMR) spectroscopy is one of the major analytical platforms used in metabolomics. The data acquired from NMR experiments are frequently processed using multivariate statistical methods such as principal component analysis (PCA) and partial least squares (PLS) to extract biologically meaningful information from complex spectra. Conventionally, these methods produce components with both positive and negative loadings, which contradict with the non-negativity of Fourier-transformed NMR spectra. In recent years, there is an increasing interest in incorporating non-negative constraints into multivariate methods. In the current study, a non-negative principal component analysis (NPCA) algorithm was introduced for the analysis of NMR-based metabolomic data. Using a simulated dataset, we showed that NPCA could reveal interesting local features in multivariate dataset, which are hidden in conventional PCA model. Notably, simulated peaks arising from a single compound were extracted by a same component in NPCA model. The current results also highlighted NPCA to be less susceptible to noise as compared to PCA. Furthermore, a supervised version of NPCA (sNPCA) was developed for class discrimination analysis, and it was used to identify urinary metabolites that distinguished hyperthyroid patients from healthy volunteers. Our results demonstrated that both NPCA and sNPCA could produce easily interpretable results and provide additional information to that of conventional projection methods.

Fast model-based multispectral imaging using nonnegative principal component analysis

Estimation of the spectral reflectance of a scene is a critical problem in image processing and computer vision applications. Model-based multispectral imaging, one of the spectral reflectance estimation methods, can effectively reconstruct the full spectrum using a small number of camera shots. However, it is based on iterative optimization and, thus, is computationally too intensive. In this Letter, we modify the iterative optimization problem to a closed-form problem using nonnegative principal component analysis. The proposed method can substantially reduce the computational cost while maintaining the accuracy.

Nonnegative Principal Component Analysis for Cancer Molecular Pattern Discovery

As a well-established feature selection algorithm, principal component analysis (PCA) is often combined with the state-of-the-art classification algorithms to identify cancer molecular patterns in microarray data. However, the algorithm's global feature selection mechanism prevents it from effectively capturing the latent data structures in the high-dimensional data. In this study, we investigate the benefit of adding nonnegative constraints on PCA and develop a nonnegative principal component analysis algorithm (NPCA) to overcome the global nature of PCA. A novel classification algorithm NPCA-SVM is proposed for microarray data pattern discovery. We report strong classification results from the NPCA-SVM algorithm on five benchmark microarray data sets by direct comparison with other related algorithms. We have also proved mathematically and interpreted biologically that microarray data will inevitably encounter overfitting for an SVM/PCA-SVM learning machine under a Gaussian kernel. In addition, we demonstrate that nonnegative principal component analysis can be used to capture meaningful biomarkers effectively.

Nonnegative principal component analysis for mass spectral serum profiles and biomarker discovery

BackgroundAs a novel cancer diagnostic paradigm, mass spectroscopic serum proteomic pattern diagnostics was reported superior to the conventional serologic cancer biomarkers. However, its clinical use is not fully validated yet. An important factor to prevent this young technology to become a mainstream cancer diagnostic paradigm is that robustly identifying cancer molecular patterns from high-dimensional protein expression data is still a challenge in machine learning and oncology research. As a well-established dimension reduction technique, PCA is widely integrated in pattern recognition analysis to discover cancer molecular patterns. However, its global feature selection mechanism prevents it from capturing local features. This may lead to difficulty in achieving high-performance proteomic pattern discovery, because only features interpreting global data behavior are used to train a learning machine.MethodsIn this study, we develop a nonnegative principal component analysis algorithm and present a nonnegative principal component analysis based support vector machine algorithm with sparse coding to conduct a high-performance proteomic pattern classification. Moreover, we also propose a nonnegative principal component analysis based filter-wrapper biomarker capturing algorithm for mass spectral serum profiles.ResultsWe demonstrate the superiority of the proposed algorithm by comparison with six peer algorithms on four benchmark datasets. Moreover, we illustrate that nonnegative principal component analysis can be effectively used to capture meaningful biomarkers.ConclusionOur analysis suggests that nonnegative principal component analysis effectively conduct local feature selection for mass spectral profiles and contribute to improving sensitivities and specificities in the following classification, and meaningful biomarker discovery.

Auditory Sparse Representation for Robust Speaker Recognition Based on Tensor Structure

This paper investigates the problem of speaker recognition in noisy conditions. A new approach called nonnegative tensor principal component analysis (NTPCA) with sparse constraint is proposed for ...