Two Algorithms for Orthogonal Nonnegative Matrix Factorization with Application to Clustering

Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal nonnegative matrix factorization (ONMF), have been recently introduced and shown to work remarkably well for clustering tasks such as document classification. In this paper, we introduce two new methods to solve ONMF. First, we show athematical equivalence between ONMF and a weighted variant of spherical k-means, from which we derive our first method, a simple EM-like algorithm. This also allows us to determine when ONMF should be preferred to k-means and spherical k-means. Our second method is based on an augmented Lagrangian approach. Standard ONMF algorithms typically enforce nonnegativity for their iterates while trying to achieve orthogonality at the limit (e.g., using a proper penalization term or a suitably chosen search direction). Our method works the opposite way: orthogonality is strictly imposed at each step while nonnegativity is asymptotically obtained, using a quadratic penalty. Finally, we show that the two proposed approaches compare favorably with standard ONMF algorithms on synthetic, text and image data sets.Comment: 17 pages, 8 figures. New numerical experiments (document and synthetic data sets

Spatio temporal and climatic analysis of the high Andean wetland of Chalhuanca (Peru) during the period 1986-2016

[ES] Los humedales altoandinos son considerados ecosistemas frágiles que proporcionan servicios ecosistémicos para el mantenimiento de la biodiversidad y economía andina, sin embargo, actualmente la amenaza global del cambio climático los pone en grave riesgo, es por ello que el objetivo de este estudio es determinar la variación espacio temporal y climática del humedal altoandino de Chalhuanca (Perú), durante el periodo 1986-2016. Se obtuvieron escenas Landsat de la temporada seca de los años 1986, 1991, 1996, 2001, 2006, 2011, 2016 y mediante técnicas de teledetección se calculó el área y el índice de vegetación (NDVI) de los humedales. Para la precipitación, temperatura máxima y temperatura mínima, se realizó un análisis de medias móviles, tendencias lineales y se aplicó la prueba estadística no paramétrica de Mann-Kendall, finalmente mediante correlación y regresión se evaluó la interacción entre las variables. Los resultados muestran que el área de humedal se ha incrementado en razón de 12 ha/año. En cuanto al NDVI, se ha detectado un incremento de los valores promedio para el periodo evaluado, siendo 0,26 el umbral (promedio de valores mínimos). El análisis de los datos climáticos muestra que la precipitación, temperatura máxima y mínima se han incrementado en 32  mm/dec, 0,3  °C/dec y 0,6  °C/dec respectivamente, siendo significativos (α<0,05) la temperatura máxima y mínima. Por último, los análisis de correlación y regresión muestran que la relación área de humedal-precipitación, NDVI-precipitación y área de humedal-NDVI son significativas para α<0,01, en cambio, la relación área de humedal-temperatura y NDVI-temperatura fueron significativos para α<0,05.[EN] The high Andean wetlands are considered fragile ecosystems that provide ecosystem services for the maintenance of Andean biodiversity and economy. However, currently the global threat of climate change puts them at serious risk, which is why the objective of this study is to determine the spatial-temporal and climatic variation of the high Andean wetlands of Chalhuanca (Peru), during the period 1986-2016. Landsat scenes were obtained during dry season in the years 1986, 1991, 1996, 2001, 2006, 2011, 2016, and using remote sensing techniques the area and vegetation index (NDVI) of the wetlands were calculated. For precipitation, maximum and minimum temperature, an analysis of moving averages, linear trends and the Mann-Kendall non-parametric statistical test was carried out, and finally the interaction between the variables was evaluated by using correlation and regression. The results show that the wetland area has increased by 12 ha/year. As for the NDVI, an increase of the average values for the evaluated period has been detected, being 0.26 the average of minimum values. Analysis of climate data shows that precipitation, maximum and minimum temperature have increased by 32 mm/dec, 0.3 °C/dec and 0.6 °C/dec respectively, with the maximum and minimum temperature being significant (α<0.05). Finally, correlation and regression analyses show that the wetland area-precipitation, NDVI-precipitation and wetland-NDVI relationships are significant for α<0.01, while the wetland-temperature and NDVI-temperature relationships were significant for α<0.05.Esta investigación fue financiada por la Universidad Nacional de San Agustín de Arequipa (UNSA) por contrato N° 047-2016-UNSA dentro del proyecto: “Servicios ecosistémicos de los humedales altoandinos y su contribución en la mitigación de los efectos del cambio climático: estudio de caso”, según contrato de subvención, también, se agradece al Tambo Chalhuanca (Programa Nacional PAIS – Midis), a los pobladores de la localidad de Chalhuanca y a la jefatura de la Reserva Nacional de Salinas y Aguada Blanca (Res. Jef. 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Maternal Arterial Stiffness in Women Who Subsequently Develop Pre-Eclampsia

BACKGROUND/OBJECTIVES: Pre-eclampsia (PE) is associated with profound changes in the maternal cardiovascular system. The aim of the present study was to assess whether alterations in the maternal arterial stiffness precede the onset of PE in at risk women. METHODOLOGY/PRINCIPAL FINDINGS: This was a cross sectional study involving 70 pregnant women with normal and 70 women with abnormal uterine artery Doppler examination at 22-24 weeks of gestation. All women had their arterial stiffness (augmentation index and pulse wave velocity of the carotid-femoral and carotid-radial parts of the arterial tree) assessed by applanation tonometry in the second trimester of pregnancy, at the time of the uterine artery Doppler imaging. Among the 140 women participating in the study 29 developed PE (PE group) and 111 did not (non-PE group). Compared to the non-PE group, women that developed PE had higher central systolic (94.9 ± 8.6 mmHg vs 104.3 ± 11.1 mmHg; p  =  < 0.01) and diastolic (64.0 ± 6.0 vs 72.4 ± 9.1; p < 0.01) blood pressures. All the arterial stiffness indices were adjusted for possible confounders and expressed as multiples of the median (MoM) of the non-PE group. The adjusted median augmentation index was similar between the two groups (p  =  0.84). The adjusted median pulse wave velocities were higher in the PE group compared to the non-PE group (carotid-femoral: 1.10 ± 0.14 MoMs vs 0.99 ± 0.11 MoMs; p < 0.01 and carotid-radial: 1.08 ± 0.12 MoMs vs 1.0 ± 0.11 MoMs; p < 0.01). CONCLUSIONS/SIGNIFICANCE: Increased maternal arterial stiffness, as assessed by pulse wave velocity, predates the development of PE in at risk women

Comprehensive evaluation of matrix factorization methods for the analysis of DNA microarray gene expression data

<p>Abstract</p> <p>Background</p> <p>Clustering-based methods on gene-expression analysis have been shown to be useful in biomedical applications such as cancer subtype discovery. Among them, Matrix factorization (MF) is advantageous for clustering gene expression patterns from DNA microarray experiments, as it efficiently reduces the dimension of gene expression data. Although several MF methods have been proposed for clustering gene expression patterns, a systematic evaluation has not been reported yet.</p> <p>Results</p> <p>Here we evaluated the clustering performance of orthogonal and non-orthogonal MFs by a total of nine measurements for performance in four gene expression datasets and one well-known dataset for clustering. Specifically, we employed a non-orthogonal MF algorithm, BSNMF (Bi-directional Sparse Non-negative Matrix Factorization), that applies bi-directional sparseness constraints superimposed on non-negative constraints, comprising a few dominantly co-expressed genes and samples together. Non-orthogonal MFs tended to show better clustering-quality and prediction-accuracy indices than orthogonal MFs as well as a traditional method, K-means. Moreover, BSNMF showed improved performance in these measurements. Non-orthogonal MFs including BSNMF showed also good performance in the functional enrichment test using Gene Ontology terms and biological pathways.</p> <p>Conclusions</p> <p>In conclusion, the clustering performance of orthogonal and non-orthogonal MFs was appropriately evaluated for clustering microarray data by comprehensive measurements. This study showed that non-orthogonal MFs have better performance than orthogonal MFs and <it>K</it>-means for clustering microarray data.</p

A new oscillometric method for pulse wave analysis: comparison with a common tonometric method

In the European Society of Cardiology–European Society of Hypertension guidelines of the year 2007, the consequences of arterial stiffness and wave reflection on cardiovascular mortality have a major role. But the investigators claimed the poor availability of devices/methods providing easy and widely suitable measuring of arterial wall stiffness or their surrogates like augmentation index (AIx) or aortic systolic blood pressure (aSBP). The aim of this study was the validation of a novel method determining AIx and aSBP based on an oscillometric method using a common cuff (ARCSolver) against a validated tonometric system (SphygmoCor). aSBP and AIx measured with the SphygmoCor and ARCSolver method were compared for 302 subjects. The mean age was 56 years with an s.d. of 20 years. At least two iterations were performed in each session. This resulted in 749 measurements. For aSBP the mean difference was −0.1 mm Hg with an s.d. of 3.1 mm Hg. The mean difference for AIx was 1.2% with an s.d. of 7.9%. There was no significant difference in reproducibility of AIx for both methods. The variation estimate of inter- and intraobserver measurements was 6.3% for ARCSolver and 7.5% for SphygmoCor. The ARCSolver method is a novel method determining AIx and aSBP based on an oscillometric system with a cuff. The results agree with common accepted tonometric measurements. Its application is easy and for widespread use

Altered Arterial Stiffness and Subendocardial Viability Ratio in Young Healthy Light Smokers after Acute Exercise

Studies showed that long-standing smokers have stiffer arteries at rest. However, the effect of smoking on the ability of the vascular system to respond to increased demands (physical stress) has not been studied. The purpose of this study was to estimate the effect of smoking on arterial stiffness and subendocardial viability ratio, at rest and after acute exercise in young healthy individuals.Healthy light smokers (n = 24, pack-years = 2.9) and non-smokers (n = 53) underwent pulse wave analysis and carotid-femoral pulse wave velocity measurements at rest, and 2, 5, 10, and 15 minutes following an exercise test to exhaustion. Smokers were tested, 1) after 12h abstinence from smoking (chronic condition) and 2) immediately after smoking one cigarette (acute condition). At rest, chronic smokers had higher augmentation index and lower aortic pulse pressure than non-smokers, while subendocardial viability ratio was not significantly different. Acute smoking increased resting augmentation index and decreased subendocardial viability ratio compared with non-smokers, and decreased subendocardial viability ratio compared with the chronic condition. After exercise, subendocardial viability ratio was lower, and augmentation index and aortic pulse pressure were higher in non-smokers than smokers in the chronic and acute conditions. cfPWV rate of recovery of was greater in non-smokers than chronic smokers after exercise. Non-smokers were also able to achieve higher workloads than smokers in both conditions.Chronic and acute smoking appears to diminish the vascular response to physical stress. This can be seen as an impaired 'vascular reserve' or a blunted ability of the blood vessels to accommodate the changes required to achieve higher workloads. These changes were noted before changes in arterial stiffness or subendocardial viability ratio occurred at rest. Even light smoking in young healthy individuals appears to have harmful effects on vascular function, affecting the ability of the vascular bed to respond to increased demands