The Joint Inference of Topic Diffusion and Evolution in Social Communities

In this paper, we propose a new estimation procedure for discovering the structure of Gaussian Markov random fields (MRFs) with false discovery rate (FDR) control, making use of the sorted l1-norm (SL1) regularization. A Gaussian MRF is an acyclic graph representing a multivariate Gaussian distribution, where nodes are random variables and edges represent the conditional dependence between the connected nodes. Since it is possible to learn the edge structure of Gaussian MRFs directly from data, Gaussian MRFs provide an excellent way to understand complex data by revealing the dependence structure among many inputs features, such as genes, sensors, users, documents, etc. In learning the graphical structure of Gaussian MRFs, it is desired to discover the actual edges of the underlying but unknown probabilistic graphical model-it becomes more complicated when the number of random variables (features) p increases, compared to the number of data points n. In particular, when p >> n, it is statistically unavoidable for any estimation procedure to include false edges. Therefore, there have been many trials to reduce the false detection of edges, in particular, using different types of regularization on the learning parameters. Our method makes use of the SL1 regularization, introduced recently for model selection in linear regression. We focus on the benefit of SL1 regularization that it can be used to control the FDR of detecting important random variables. Adapting SL1 for probabilistic graphical models, we show that SL1 can be used for the structure learning of Gaussian MRFs using our suggested procedure nsSLOPE (neighborhood selection Sorted L-One Penalized Estimation), controlling the FDR of detecting edges.

Abstract. We present a method to infer spatially and spatio-temporally correlated emissions of greenhouse gases from atmospheric measurements and a chemical transport model. The method allows fast computation of spatial emissions using a hierarchical Bayesian framework as an alternative to Markov chain Monte Carlo algorithms. The spatial emissions follow a Gaussian process with a Matérn correlation structure which can be represented by a Gaussian Markov random field through a stochastic partial differential equation approach. The inference is based on an integrated nested Laplacian approximation (INLA) for hierarchical models with Gaussian latent fields. Combining an autoregressive temporal correlation and the Matérn field provides a full spatio-temporal correlation structure. We first demonstrate the method on a synthetic data example and follow this using a well-studied test case of inferring UK methane emissions from tall tower measurements of atmospheric mole fraction. Results from these two test cases show that this method can accurately estimate regional greenhouse gas emissions, accounting for spatio-temporal uncertainties that have traditionally been neglected in atmospheric inverse modelling.

Abstract. Digital Elevation Models (DEMs) are considered as one of the most relevant geospatial data to carry out land-cover and land-use classification. This work deals with the application of a mathematical framework based on a Gaussian Markov Random Field (GMRF) to interpolate grid DEMs from scattered elevation data. The performance of the GMRF interpolation model was tested on a set of LiDAR data (0.87 points/m2) provided by the Spanish Government (PNOA Programme) over a complex working area mainly covered by greenhouses in Almería, Spain. The original LiDAR data was decimated by randomly removing different fractions of the original points (from 10% to up to 99% of points removed). In every case, the remaining points (scattered observed points) were used to obtain a 1 m grid spacing GMRF-interpolated Digital Surface Model (DSM) whose accuracy was assessed by means of the set of previously extracted checkpoints. The GMRF accuracy results were compared with those provided by the widely known Triangulation with Linear Interpolation (TLI). Finally, the GMRF method was applied to a real-world case consisting of filling the LiDAR-derived DSM gaps after manually filtering out non-ground points to obtain a Digital Terrain Model (DTM). Regarding accuracy, both GMRF and TLI produced visually pleasing and similar results in terms of vertical accuracy. As an added bonus, the GMRF mathematical framework makes possible to both retrieve the estimated uncertainty for every interpolated elevation point (the DEM uncertainty) and include break lines or terrain discontinuities between adjacent cells to produce higher quality DTMs.

Applications of Noncausal Gauss–Markov Random Field Models in Image and Video Processing

Infrared (IR) images are essential to improve the visibility of dark or camouflaged objects. Object recognition and segmentation based on a neural network using IR images provide more accuracy and insight than color visible images. But the bottleneck is the amount of relevant IR images for training. It is difficult to collect real-world IR images for special purposes, including space exploration, military and fire-fighting applications. To solve this problem, we created color visible and IR images using a Unity-based 3D game editor. These synthetically generated color visible and IR images were used to train cycle consistent adversarial networks (CycleGAN) to convert visible images to IR images. CycleGAN has the advantage that it does not require precisely matching visible and IR pairs for transformation training. In this study, we discovered that additional synthetic data can help improve CycleGAN performance. Neural network training using real data (N = 20) performed more accurate transformations than training using real (N = 10) and synthetic (N = 10) data combinations. The result indicates that the synthetic data cannot exceed the quality of the real data. Neural network training using real (N = 10) and synthetic (N = 100) data combinations showed almost the same performance as training using real data (N = 20). At least 10 times more synthetic data than real data is required to achieve the same performance. In summary, CycleGAN is used with synthetic data to improve the IR image conversion performance of visible images.

This paper proposes a GMRF (Gaussian Markov random field)-model based restoration method of missing areas in still images. The GMRF model used in the proposed method is realized by a new assumption that reasonably holds for an image source. This model can express important image features such as edges because of the use of the new assumption. Therefore, the proposed method restores the missing areas using the modified GMRF model and can correctly reconstruct the missing edges. Consequently, the proposed method achieves more accurate restoration than those of the traditional methods on both objective and subjective measures. Extensive experimental results demonstrate the improvement of the proposed method over previous methods.

Gibbs sampling on large lattice with GMRF

Extracting efiective features to describe texture is always a key problem in writer identiflcation. This paper proposes a novel method for texture feature extraction by integrating Gabor fllter and Gauss Markov Random Field (GMRF). That is to say, the handwriting images are flrstly flltered by a bank of Gabor fllters in which global features such as directional information can be detected; then GMRF models are developed for every flltered image that is ∞exible enough to capture the local spatial structure and the model parameters of all GMRFs are concatenated as texture features for writer identiflcation, and flnally, Support Vector Machine (SVM) is applied to evaluate the performance of calligraphic artist identiflcation. The experimental results show that this method can achieve a classiflcation rate of 98%, which has outperformed the traditional Gabor fllter method.

This chapter introduces several fundamental models and algorithms for probabilistic clustering, including mixture models, Expectation-Maximization (EM) algorithm, and probabilistic topic models. It focuses on general framework of modeling, the probabilistic explanation, the standard algorithms to learn the model, and its applications. Mixture models are probabilistic models which are increasingly used to find the clusters for univariate and multivariate data. The chapter begins the discussion of mixture models, in which the values of the discrete latent variables can be interpreted as the assignments of data points to specific components of the mixture. It uses the Gaussian mixture model to motivate the EM algorithm in an informal way, and then gives a more general view of the EM algorithm, which is a standard learning algorithm for many probabilistic models. The chapter presents two popular probabilistic topic models, i.e., probabilistic latent semantic analysis (PLSA) and latent Dirichlet allocation (LDA), for document clustering and analysis.

Research problem: In the current information age, people are increasingly accustomed to sharing their special interests online and are influenced by the relationships developed from that sharing. The purpose of this study was to better measure peer influence in these online communities. Research questions: 1. How can peer influence in online communities be measured in a way that comprehensively incorporates peer-based characteristics, the homophily effect, and the structural position of a user in the network? 2. Is the method proposed in this study superior to other existing methods? Literature review: Previous literature on measuring online user influence can be classified into two streams: 1. Those that focus on the intrinsic characteristics of social media players to measure peer influence; 2. Those that address social network structure. Relevant computing algorithms include Topic-Based PageRank, Quality-Structure index, and so on. Although the first stream considers afocal peer's intrinsic characteristics, it overlooks the interpeer attraction in terms of similarity and discrepant knowledge among peers. The second stream mostly stresses the structures of social networks to measure network-wide peer influence but underestimates the effect of interpeer attraction that may leverage every diffusion step of peer influence through the network. To fill this research gap, this study proposes a new method of measuring network user influence that incorporates peers' intrinsic factors, interpeer influence factors as homophily effect, and network structure. Homophily refers to the degree to which pairs of individuals who interact are similar with respect to certain attributes. Methodology: From the communication sender-receiver perspective, we developed a computable method that incorporates peer-based characteristics, the homophily effect, and the structural position of a user in the network to measure the social network user influence. Two empirical studies were subsequently conducted in a social network service-based online community and an online professional logistics community to verify the effectiveness of the proposed method. Results and conclusions: The empirical results show that our proposed method provides higher prediction accuracy of user influence rank in an online community than the other existing methods. These findings lay a foundation for future theoretical exploration and provide a useful tool for targeting influential users in online communities such as blogs, bulletin board systems, and forums.

Understanding the evolution of research topics is crucial to detect emerging trends in science. This paper proposes a new approach and a framework to discover the evolution of topics based on dynamic co-word networks and communities within them. The NEViewer software was developed according to this approach and framework, as compared to the existing studies and science mapping software tools, our work is innovative in three aspects: (a) the design of a longitudinal framework based on the dynamics of co-word communities; (b) it proposes a community labelling algorithm and community evolution verification algorithms; (c) and visualizes the evolution of topics at the macro and micro level respectively using alluvial diagrams and coloring networks. A case study in computer science and a careful assessment was implemented and demonstrating that the new method and the software NEViewer is feasible and effective.

The discrimination ability of texture features derived from Gaussian Markov random fields (GMRFs) and grey level co-occurrence probabilities (GLCPs) are compared and contrasted. More specifically, the role of window size in feature consistency and separability as well as the role of multiple textures within a window are investigated. GLCPs are demonstrated to have improved discrimination ability relative to MRFs with decreasing window size, an important concept when performing image segmentation. On the other hand, GLCPs are more sensitive to texture boundary confusion than GMRFs.

Accurately modelled computer-generated data can be used in place of real-world signals for the design, test and validation of signal processing techniques in situations where real data is difficult to obtain. Bio-signal processing researchers interested in working with fNIRS data are restricted due to the lack of freely available fNIRS data and by the prohibitively expensive cost of fNIRS systems. We present a simplified mathematical description and associated MATLAB implementation of model-based synthetic fNIRS data which could be used by researchers to develop fNIRS signal processing techniques. The software, which is freely available, allows users to generate fNIRS data with control over a wide range of parameters and allows for fine-tuning of the synthetic data. We demonstrate how the model can be used to generate raw fNIRS data similar to recorded fNIRS signals. Signal processing steps were then applied to both the real and synthetic data. Visual comparisons between the temporal and spectral properties of the real and synthetic data show similarity. This paper demonstrates that our model for generating synthetic fNIRS data can replicate real fNIRS recordings.

In location-based social networks (LBSNs), users implicitly interact with each other by visiting places, issuing comments and/or uploading photos. These heterogeneous interactions convey the latent information for identifying meaningful user groups, namely social communities, which exhibit unique location-oriented characteristics. In this work, we aim to detect and profile social communities in LBSNs by representing the heterogeneous interactions with a multimodality nonuniform hypergraph. Here, the vertices of the hypergraph are users, venues, textual comments or photos and the hyperedges characterize the k -partite heterogeneous interactions such as posting certain comments or uploading certain photos while visiting certain places. We then view each detected social community as a dense subgraph within the heterogeneous hypergraph, where the user community is constructed by the vertices and edges in the dense subgraph and the profile of the community is characterized by the vertices related with venues, comments and photos and their inter-relations. We present an efficient algorithm to detect the overlapped dense subgraphs, where the profile of each social community is guaranteed to be available by constraining the minimal number of vertices in each modality. Extensive experiments on Foursquare data well validated the effectiveness of the proposed framework in terms of detecting meaningful social communities and uncovering their underlying profiles in LBSNs.

Exospheric tomography is a computational 3-D imaging technique that provides the estimates of the neutral density distributions of the terrestrial exosphere from space-based ultraviolet (UV) measurements. Variability of neutral densities during geomagnetically active conditions has been previously reported, motivating the development of time-dependent tomographic techniques that can characterize both the spatial and temporal scales of densities during these events. However, solving the dynamic exospheric tomography problem can be challenging owing to its ill-posedness. In this letter, we introduce a novel algorithm for 4-D exospheric tomography based on optimal interpolation (OI) and Gaussian Markov random field (GMRF) theory. The OI analysis enables iterative reconstructions of the exosphere when a statistical background field is provided. Its mean is selected from previous knowledge of the exosphere, and its covariance matrix is estimated using GMRF. To validate the performance, we apply our proposed methodology to six days of UV data acquired by National Aeronautics and Space Administration (NASA) two-wide angle imaging neutral-atom spectrometer (TWINS) mission during the geomagnetic storm that occurred on June 15, 2008.