Nonnegative Matrix Underapproximation Research Articles

A comparison of non-negative matrix underapproximation methods for the decomposition of magnetic resonance spectroscopy data from human brain tumors.

Magnetic resonance spectroscopy (MRS) is an MR technique that provides information about the biochemistry of tissues in a noninvasive way. MRS has been widely used for the study of brain tumors, both preoperatively and during follow-up. In this study, we investigated the performance of a range of variants of unsupervised matrix factorization methods of the non-negative matrix underapproximation (NMU) family, namely, sparse NMU, global NMU, and recursive NMU, and compared them with convex non-negative matrix factorization (C-NMF), which has previously shown a good performance on brain tumor diagnostic support problems using MRS data. The purpose of the investigation was 2-fold: first, to ascertain the differences among the sources extracted by these methods; and second, to compare the influence of each method in the diagnostic accuracy of the classification of brain tumors, using them as feature extractors. We discovered that, first, NMU variants found meaningful sources in terms of biological interpretability, but representing parts of the spectrum, in contrast to C-NMF; and second, that NMU methods achieved better classification accuracy than C-NMF for the classification tasks when one class was not meningioma.

Challenges of studying the dietary exposure to chemical mixtures: Example of the association with mortality risk in the E3N French prospective cohort

Food is contaminated by many chemicals which interact with each other, resulting in additive, synergistic or antagonistic effects. It is thus necessary to study the health effects of dietary exposure to chemical mixtures rather than single contaminants.We aimed to investigate the association between dietary exposure to chemical mixtures and mortality risk in the E3N French prospective cohort.We included 72,585 women from the E3N cohort who completed a food frequency questionnaire in 1993. From 197 chemicals, and using sparse non-negative matrix under-approximation (SNMU), we identified six main chemical mixtures to which these women were chronically exposed through the diet. We estimated the associations between dietary exposure to these mixtures and all-cause or cause-specific mortality using Cox proportional hazard models.During the follow-up (1993–2014), 6441 deaths occurred. We observed no association between dietary exposure to three mixtures and all-cause mortality, and a non-monotonic inverse association for the three other mixtures.These results could be explained by the fact that, despite the different dietary adjustment strategies tested, we did not fully succeed in excluding the residual confounding from the overall effect of the diet. We also questioned the number of chemicals to include in mixtures' studies, as a balance needs to be reached between including a large number of chemicals and the interpretability of the results. Integrating a priori knowledge, such as toxicological data, could lead to the identification of more parsimonious mixtures, thus to more interpretable results. Moreover, as the SNMU is a non-supervised method, which identifies the mixtures only on the basis of the correlations between the exposure variables, and not in relation to the outcome, it would be interesting to test supervised methods. Finally, further studies are needed to identify the most adequate approach to investigate the health effects of dietary exposure to chemical mixtures in observational studies.

Identification of chemical mixtures to which women are exposed through the diet: Results from the French E3N cohort

Due to the large number of chemical food contaminants, consumers are exposed simultaneously to a wide range of chemicals which can interact and have a negative impact on health. Nevertheless, due to the multitude of possible chemical combinations it is unrealistic to test all combined toxicological effects. It is therefore essential to identify the most relevant mixtures to which the population is exposed through the diet and investigate their impact on heath.The present study aims to identify and describe the main chemical mixtures to which women enrolled in the E3N study, a large French prospective cohort, are chronically exposed through the diet.74522 women who had answered a validated semi-quantitative food frequency questionnaire in 1993, were included in the present study. Dietary exposure to chemical contaminates was estimated based on the food contamination measured in 186 core food in France collected between 2007 and 2009 by the French agency for food, environment and occupational health, and safety (ANSES) in the framework of the second French total diet study (2TDS). The sparse non-negative matrix under-approximation (SNMU) was used to identify mixtures of chemical substances. A k-means clustering classification of the whole study population was then performed to define clusters with similar co-exposure profiles.Overall, 8 mixtures which explained 83% of the total variance, were retained. The first mixture, entitled “Minerals, inorganic contaminants, and furans”, explained the highest proportion of the total variance (38%), and was correlated in particular with the consumption of “Offal” (rho = 0.22), “Vegetables except roots” (rho = 0.20), and “Eggs” (rho = 0.19). The other seven mixtures explained between 17% and 1% of the variance. Finally, 5 clusters were identified based on the adherence to the 8 mixtures.This study, being the largest ever conducted to identify dietary exposure to chemical mixtures, represents a concrete attempt to prioritize mixtures for which it is essential to investigate combined health effects based on exposure.

To which mixtures are French pregnant women mainly exposed? A combination of the second French total diet study with the EDEN and ELFE cohort studies

Pregnant women and their unborn child are exposed to a large number of substances during pregnancy. Some of these substances may cross the placenta, resulting in exposure of the foetus. There is growing evidence that certain substances could interact to produce a mixture effect. It is therefore essential to identify the main mixtures mothers are exposed to.This study aimed to identify the major mixtures French pregnant women included in EDEN and ELFE cohorts were exposed to, on the basis of the 441 substances analysed in the second French total diet study. Exposure systems and the composition of substances were identified from co-exposures using sparse non-negative matrix under-approximation to generate the main mixtures. Individuals were clustered to define clusters with similar co-exposure profiles.Six clusters associated with eight mixtures were identified. For example in ELFE, cluster 2 comprising 10% of the population was characterised by mixtures “Pest-1” mainly contains pesticides and ”TE-F-PAH″ contains trace elements, furans and polycyclic aromatic hydrocarbons. Five other clusters were also described with their associated mixtures. Similar results were observed for EDEN.This study helps to prioritise mixtures for which it is crucial to investigate possible toxicological effects and to recommend epidemiological studies concerning health effects.

A Sparse and Low-Rank Near-Isometric Linear Embedding Method for Feature Extraction in Hyperspectral Imagery Classification

A sparse and low-rank near-isometric linear embedding (SLRNILE) method has been proposed to make dimensionality reduction and extract proper features for hyperspectral imagery (HSI) classification. The SLRNILE stands on the theory of the John-Lindenstrauss lemma, and tries to estimate a sparse and low-rank projection matrix that satisfies the restricted isometric property (RIP) condition on all secants of the HSI data. The RIP condition guarantees that the desired linear mapping near-isometrically preserves nearest neighbor points of all HSI pixels. Seeking the desired mapping is then modeled into minimizing a Lagrange multipliers formulation. The alternating direction method of multipliers framework is utilized to solve the above convex program, and column generation techniques are adopted to alleviate the computation memory burden during the optimization procedure. Five experiments on three widely used HSI data sets are designed to completely test the performance of SLRNILE, and experimental results are compared against those of six state-of-the-art feature extraction methods, including principal component analysis, Laplacian eigenmaps, locality preserving projections, neighborhood preserving embedding, sparse nonnegative matrix underapproximation, and random projections. The results show that SLRNILE performs best among all the seven methods, and its computational time is longest of all but still bearable for regular users. Therefore, the SLRNILE can be a good choice for feature extraction in HSI classification.

Sequential dimensionality reduction for extracting localized features

Linear dimensionality reduction techniques are powerful tools for image analysis as they allow the identification of important features in a data set. In particular, nonnegative matrix factorization (NMF) has become very popular as it is able to extract sparse, localized and easily interpretable features by imposing an additive combination of nonnegative basis elements. Nonnegative matrix underapproximation (NMU) is a closely related technique that has the advantage to identify features sequentially. In this paper, we propose a variant of NMU that is particularly well suited for image analysis as it incorporates the spatial information, that is, it takes into account the fact that neighboring pixels are more likely to be contained in the same features, and favors the extraction of localized features by looking for sparse basis elements. We show that our new approach competes favorably with comparable state-of-the-art techniques on synthetic, facial and hyperspectral image data sets.

Sparse nonnegative matrix underapproximation and its application to hyperspectral image analysis

Dimensionality reduction techniques such as principal component analysis (PCA) are powerful tools for the analysis of high-dimensional data. In hyperspectral image analysis, nonnegativity of the data can be taken into account, leading to an additive linear model called nonnegative matrix factorization (NMF), which improves interpretability of the decomposition. Recently, another technique based on underapproximations (NMU) has been introduced, which allows the extraction of features in a recursive way, such as PCA, but preserving nonnegativity, such as NMF. Moreover, in some situations, NMU is able to detect automatically the materials present in the scene being imaged. However, for difficult hyperspectral datasets, NMU can mix some materials together, and is therefore not able to separate all of them properly. In this paper we introduce sparse NMU by adding a sparsity constraint on the abundance matrix and use it to extract materials individually in a more efficient way than NMU. This is experimentally demonstrated on the HYDICE images of the San Diego airport and the Urban dataset.

Dimensionality reduction, classification, and spectral mixture analysis using non-negative underapproximation

Non-negative matrix factorization (NMF) and its variants have recently been successfully used as dimensionality reduction techniques for identification of the materials present in hyperspectral images. We study a recently introduced variant of NMF called non-negative matrix underapproximation (NMU): it is based on the introduction of underapproximation constraints, which enables one to extract features in a recursive way, such as principal component analysis, but preserving non-negativity. We explain why these additional constraints make NMU particularly well suited to achieve a parts-based and sparse representation of the data, enabling it to recover the constitutive elements in hyperspectral images. Both ℓ2-norm and ℓ1-norm-based minimization of the energy functional are considered. We experimentally show the efficiency of this new strategy on hyperspectral images associated with space object material identification, and on HYDICE and related remote sensing images.