Uncovering Community Structures with Initialized Bayesian Nonnegative Matrix Factorization

Uncovering community structures is important for understanding networks. Currently, several nonnegative matrix factorization algorithms have been proposed for discovering community structure in complex networks. However, these algorithms exhibit some drawbacks, such as unstable results and inefficient running times. In view of the problems, a novel approach that utilizes an initialized Bayesian nonnegative matrix factorization model for determining community membership is proposed. First, based on singular value decomposition, we obtain simple initialized matrix factorizations from approximate decompositions of the complex network’s adjacency matrix. Then, within a few iterations, the final matrix factorizations are achieved by the Bayesian nonnegative matrix factorization method with the initialized matrix factorizations. Thus, the network’s community structure can be determined by judging the classification of nodes with a final matrix factor. Experimental results show that the proposed method is highly accurate and offers competitive performance to that of the state-of-the-art methods even though it is not designed for the purpose of modularity maximization.     

Limited-Memory Fast Gradient Descent Method for Graph Regularized Nonnegative Matrix Factorization

Graph regularized nonnegative matrix factorization (GNMF) decomposes a nonnegative data matrix to the product of two lower-rank nonnegative factor matrices, i.e., and () and aims to preserve the local geometric structure of the dataset by minimizing squared Euclidean distance or Kullback-Leibler (KL) divergence between X and WH. The multiplicative update rule (MUR) is usually applied to optimize GNMF, but it suffers from the drawback of slow-convergence because it intrinsically advances one step along the rescaled negative gradient direction with a non-optimal step size. Recently, a multiple step-sizes fast gradient descent (MFGD) method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton''s method. However, the computational cost of MFGD is high because 1) the high-dimensional Hessian matrix is dense and costs too much memory; and 2) the Hessian inverse operator and its multiplication with gradient cost too much time. To overcome these deficiencies of MFGD, we propose an efficient limited-memory FGD (L-FGD) method for optimizing GNMF. In particular, we apply the limited-memory BFGS (L-BFGS) method to directly approximate the multiplication of the inverse Hessian and the gradient for searching the optimal step size in MFGD. The preliminary results on real-world datasets show that L-FGD is more efficient than both MFGD and MUR. To evaluate the effectiveness of L-FGD, we validate its clustering performance for optimizing KL-divergence based GNMF on two popular face image datasets including ORL and PIE and two text corpora including Reuters and TDT2. The experimental results confirm the effectiveness of L-FGD by comparing it with the representative GNMF solvers.     

CloudNMF: A MapReduce Implementation of Nonnegative Matrix Factorization for Large-scale Biological Datasets

In the past decades,advances in high-throughput technologies have led to the generation of huge amounts of biological data that require analysis and interpretation.Recently,nonnegative matrix factorization(NMF) has been introduced as an efficient way to reduce the complexity of data as well as to interpret them,and has been applied to various fields of biological research.In this paper,we present CloudNMF,a distributed open-source implementation of NMF on a MapReduce framework.Experimental evaluation demonstrated that CloudNMF is scalable and can be used to deal with huge amounts of data,which may enable various kinds of a high-throughput biological data analysis in the cloud.CloudNMF is freely accessible at http://admis.fudan.edu.cn/projects/CloudNMF.html.     

Efficient Blind Spectral Unmixing of Fluorescently Labeled Samples Using Multi-Layer Non-Negative Matrix Factorization

The ample variety of labeling dyes and staining methods available in fluorescence microscopy has enabled biologists to advance in the understanding of living organisms at cellular and molecular level. When two or more fluorescent dyes are used in the same preparation, or one dye is used in the presence of autofluorescence, the separation of the fluorescent emissions can become problematic. Various approaches have been recently proposed to solve this problem. Among them, blind non-negative matrix factorization is gaining interest since it requires little assumptions about the spectra and concentration of the fluorochromes. In this paper, we propose a novel algorithm for blind spectral separation that addresses some of the shortcomings of existing solutions: namely, their dependency on the initialization and their slow convergence. We apply this new algorithm to two relevant problems in fluorescence microscopy: autofluorescence elimination and spectral unmixing of multi-labeled samples. Our results show that our new algorithm performs well when compared with the state-of-the-art approaches for a much faster implementation.     

Using Dynamic Multi-Task Non-Negative Matrix Factorization to Detect the Evolution of User Preferences in Collaborative Filtering

Predicting what items will be selected by a target user in the future is an important function for recommendation systems. Matrix factorization techniques have been shown to achieve good performance on temporal rating-type data, but little is known about temporal item selection data. In this paper, we developed a unified model that combines Multi-task Non-negative Matrix Factorization and Linear Dynamical Systems to capture the evolution of user preferences. Specifically, user and item features are projected into latent factor space by factoring co-occurrence matrices into a common basis item-factor matrix and multiple factor-user matrices. Moreover, we represented both within and between relationships of multiple factor-user matrices using a state transition matrix to capture the changes in user preferences over time. The experiments show that our proposed algorithm outperforms the other algorithms on two real datasets, which were extracted from Netflix movies and Last.fm music. Furthermore, our model provides a novel dynamic topic model for tracking the evolution of the behavior of a user over time.     

A Model with Three Compartments and Nonnegative Transfers

We consider a periodic model with three compartments, which can be considered as a simplified model for the dynamics of follicles. We give necessary and sufficient conditions for the solvability in nonnegative inputs, transfers and outputs, and we determine the minimal solution. If the problem is not solvable according to measurement errors of the given data, we recover suitable values by the method of least-squares, solving a quadratic optimization problem.     

Multi-Scale Analysis of the European Airspace Using Network Community Detection

We show that the European airspace can be represented as a multi-scale traffic network whose nodes are airports, sectors, or navigation points and links are defined and weighted according to the traffic of flights between the nodes. By using a unique database of the air traffic in the European airspace, we investigate the architecture of these networks with a special emphasis on their community structure. We propose that unsupervised network community detection algorithms can be used to monitor the current use of the airspace and improve it by guiding the design of new ones. Specifically, we compare the performance of several community detection algorithms, both with fixed and variable resolution, and also by using a null model which takes into account the spatial distance between nodes, and we discuss their ability to find communities that could be used to define new control units of the airspace.     

Unified Saliency Detection Model Using Color and Texture Features

Saliency detection attracted attention of many researchers and had become a very active area of research. Recently, many saliency detection models have been proposed and achieved excellent performance in various fields. However, most of these models only consider low-level features. This paper proposes a novel saliency detection model using both color and texture features and incorporating higher-level priors. The SLIC superpixel algorithm is applied to form an over-segmentation of the image. Color saliency map and texture saliency map are calculated based on the region contrast method and adaptive weight. Higher-level priors including location prior and color prior are incorporated into the model to achieve a better performance and full resolution saliency map is obtained by using the up-sampling method. Experimental results on three datasets demonstrate that the proposed saliency detection model outperforms the state-of-the-art models.     

A Novel GBM Saliency Detection Model Using Multi-Channel MRI

The automatic computerized detection of regions of interest (ROI) is an important step in the process of medical image processing and analysis. The reasons are many, and include an increasing amount of available medical imaging data, existence of inter-observer and inter-scanner variability, and to improve the accuracy in automatic detection in order to assist doctors in diagnosing faster and on time. A novel algorithm, based on visual saliency, is developed here for the identification of tumor regions from MR images of the brain. The GBM saliency detection model is designed by taking cue from the concept of visual saliency in natural scenes. A visually salient region is typically rare in an image, and contains highly discriminating information, with attention getting immediately focused upon it. Although color is typically considered as the most important feature in a bottom-up saliency detection model, we circumvent this issue in the inherently gray scale MR framework. We develop a novel pseudo-coloring scheme, based on the three MRI sequences, viz. FLAIR, T2 and T1C (contrast enhanced with Gadolinium). A bottom-up strategy, based on a new pseudo-color distance and spatial distance between image patches, is defined for highlighting the salient regions in the image. This multi-channel representation of the image and saliency detection model help in automatically and quickly isolating the tumor region, for subsequent delineation, as is necessary in medical diagnosis. The effectiveness of the proposed model is evaluated on MRI of 80 subjects from the BRATS database in terms of the saliency map values. Using ground truth of the tumor regions for both high- and low- grade gliomas, the results are compared with four highly referred saliency detection models from literature. In all cases the AUC scores from the ROC analysis are found to be more than 0.999 ± 0.001 over different tumor grades, sizes and positions.     

Matrix approach to land carbon cycle modeling: A case study with the Community Land Model

The terrestrial carbon (C) cycle has been commonly represented by a series of C balance equations to track C influxes into and effluxes out of individual pools in earth system models (ESMs). This representation matches our understanding of C cycle processes well but makes it difficult to track model behaviors. It is also computationally expensive, limiting the ability to conduct comprehensive parametric sensitivity analyses. To overcome these challenges, we have developed a matrix approach, which reorganizes the C balance equations in the original ESM into one matrix equation without changing any modeled C cycle processes and mechanisms. We applied the matrix approach to the Community Land Model (CLM4.5) with vertically‐resolved biogeochemistry. The matrix equation exactly reproduces litter and soil organic carbon (SOC) dynamics of the standard CLM4.5 across different spatial‐temporal scales. The matrix approach enables effective diagnosis of system properties such as C residence time and attribution of global change impacts to relevant processes. We illustrated, for example, the impacts of CO₂ fertilization on litter and SOC dynamics can be easily decomposed into the relative contributions from C input, allocation of external C into different C pools, nitrogen regulation, altered soil environmental conditions, and vertical mixing along the soil profile. In addition, the matrix tool can accelerate model spin‐up, permit thorough parametric sensitivity tests, enable pool‐based data assimilation, and facilitate tracking and benchmarking of model behaviors. Overall, the matrix approach can make a broad range of future modeling activities more efficient and effective.     

Rapid Detection and Quantification of Members of the Archaeal Community by Quantitative PCR Using Fluorogenic Probes

We describe a rapid, reproducible, and sensitive method for detection and quantification of archaea in naturally occurring microbial communities. A domain-specific PCR primer set and a domain-specific fluorogenic probe having strong and weak selectivity, respectively, for archaeal rRNA genes (rDNAs) were designed. A universal PCR primer set and a universal fluorogenic probe for both bacterial and archaeal rDNAs were also designed. Using these primers and probes, we demonstrated that detection and quantification of archaeal rDNAs in controlled microbial rDNA assemblages can be successfully achieved. The system which we designed was also able to detect and quantify archaeal rDNAs in DNA samples obtained not only from environments in which thermophilic archaea are abundant but also from environments in which methanogenic archaea are abundant. Our findings indicate that this method is applicable to culture-independent molecular analysis of microbial communities in various environments.     

蜡梅群落生态学研究与展望

本文从群落分布与群落环境,区系组成、外貌和结构,种群结构及生理生态学等方面综述了蜡梅群落生态学研究的最新进展,指出了现今研究中存在的一些问题,提出了今后研究的若干重点领域和方向。     

Generative FDG-PET and MRI Model of Aging and Disease Progression in Alzheimer's Disease

The failure of current strategies to provide an explanation for controversial findings on the pattern of pathophysiological changes in Alzheimer''s Disease (AD) motivates the necessity to develop new integrative approaches based on multi-modal neuroimaging data that captures various aspects of disease pathology. Previous studies using [18F]fluorodeoxyglucose positron emission tomography (FDG-PET) and structural magnetic resonance imaging (sMRI) report controversial results about time-line, spatial extent and magnitude of glucose hypometabolism and atrophy in AD that depend on clinical and demographic characteristics of the studied populations. Here, we provide and validate at a group level a generative anatomical model of glucose hypo-metabolism and atrophy progression in AD based on FDG-PET and sMRI data of 80 patients and 79 healthy controls to describe expected age and symptom severity related changes in AD relative to a baseline provided by healthy aging. We demonstrate a high level of anatomical accuracy for both modalities yielding strongly age- and symptom-severity- dependant glucose hypometabolism in temporal, parietal and precuneal regions and a more extensive network of atrophy in hippocampal, temporal, parietal, occipital and posterior caudate regions. The model suggests greater and more consistent changes in FDG-PET compared to sMRI at earlier and the inversion of this pattern at more advanced AD stages. Our model describes, integrates and predicts characteristic patterns of AD related pathology, uncontaminated by normal age effects, derived from multi-modal data. It further provides an integrative explanation for findings suggesting a dissociation between early- and late-onset AD. The generative model offers a basis for further development of individualized biomarkers allowing accurate early diagnosis and treatment evaluation.     

Detecting the Community Structure and Activity Patterns of Temporal Networks: A Non-Negative Tensor Factorization Approach

The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule.     

Source Apportionment of Trace Element Pollution in Surface Sediments Using Positive Matrix Factorization Combined Support Vector Machines: Application to the Jinjiang River, China

In this study, a method of positive matrix factorization (PMF) combined support vector machines (SVMs) was adopted to identify possible sources and apportion contributions for trace element pollution in surface sediments from the Jinjiang River, Southeastern China. Utilizing diagnostics tools, four significant factors were extracted from sediment samplers, which were collected in December 2010 at 15 different sites. By treating source identification as a pattern recognition problem, the factor loadings derived from PMF were classified by SVM classifiers which have been trained and validated with fingerprints of eight potential source categories. Using SVM, industrial wastewater from lead ore mining and metal handcraft manufacture, atmospheric deposition, and natural background were identified as main sources of trace element pollution in surface sediments from the Jinjiang River, which were affirmed by visually comparing compound patterns and the differences between the predicted and actual fractional compositions. Apportionment results showed that source of lead ore mining made the largest contribution (33.62 %), followed by atmospheric deposition (30.99 %), metal handcraft manufacture (30.09 %), and natural background (5.29 %).     

Dynamic Social Community Detection and Its Applications

Community structure is one of the most commonly observed features of Online Social Networks (OSNs) in reality. The knowledge of this feature is of great advantage: it not only provides helpful insights into developing more efficient social-aware solutions but also promises a wide range of applications enabled by social and mobile networking, such as routing strategies in Mobile Ad Hoc Networks (MANETs) and worm containment in OSNs. Unfortunately, understanding this structure is very challenging, especially in dynamic social networks where social interactions are evolving rapidly. Our work focuses on the following questions: How can we efficiently identify communities in dynamic social networks? How can we adaptively update the network community structure based on its history instead of recomputing from scratch? To this end, we present Quick Community Adaptation (QCA), an adaptive modularity-based framework for not only discovering but also tracing the evolution of network communities in dynamic OSNs. QCA is very fast and efficient in the sense that it adaptively updates and discovers the new community structure based on its history together with the network changes only. This flexible approach makes QCA an ideal framework applicable for analyzing large-scale dynamic social networks due to its lightweight computing-resource requirement. To illustrate the effectiveness of our framework, we extensively test QCA on both synthesized and real-world social networks including Enron, arXiv e-print citation, and Facebook networks. Finally, we demonstrate the applicability of QCA in real applications: (1) A social-aware message forwarding strategy in MANETs, and (2) worm propagation containment in OSNs. Competitive results in comparison with other methods reveal that social-based techniques employing QCA as a community detection core outperform current available methods.     

Soil Functional Operating Range Linked to Microbial Biodiversity and Community Composition Using Denitrifiers as Model Guild

Soil microorganisms are key players in biogeochemical cycles. Yet, there is no consistent view on the significance of microbial biodiversity for soil ecosystem functioning. According to the insurance hypothesis, declines in ecosystem functioning due to reduced biodiversity are more likely to occur under fluctuating, extreme or rapidly changing environmental conditions. Here, we compare the functional operating range, a new concept defined as the complete range of environmental conditions under which soil microbial communities are able to maintain their functions, between four naturally assembled soil communities from a long-term fertilization experiment. A functional trait approach was adopted with denitrifiers involved in nitrogen cycling as our model soil community. Using short-term temperature and salt gradients, we show that the functional operating range was broader and process rates were higher when the soil community was phylogenetically more diverse. However, key bacterial genotypes played an important role for maintaining denitrification as an ecosystem functioning under certain conditions.