Markov Random Field Research Articles

Sensitivity analysis of prior distributions in Bayesian graphical modeling: Guiding informed prior choices for conditional independence testing

Bayesian analysis methods provide a significant advancement in network psychometrics, allowing researchers to use the edge inclusion Bayes factor for testing conditional independence between pairs of variables in the network. Using this methodology requires setting prior distributions on the network parameters and on the network’s structure. However, the impact of both prior distributions on the inclusion Bayes factor is underexplored. In this paper, we focus on a specific class of Markov Random Field models for ordinal and binary data. We first discuss the different choices of prior distributions for the network parameters and the network structure, and then perform an extensive simulation study to assess the sensitivity of the inclusion Bayes factor to these distributions. We pay particular attention to the effect of the scale of the prior on the inclusion Bayes factor. To improve the accessibility of the results, we also provide an interactive Shiny app. Finally, we present the R package simBgms, which provides researchers with a user-friendly tool to perform their own simulation studies for Bayesian Markov Random Field models. All of this should help researchers make more informed, evidence-based decisions when preparing to analyze empirical data using network psychometric models.

Credit strategy research based on Markov random field and enterprise association knowledge graph

This paper investigates banks' credit strategies concerning micro, small and medium enterprises (MSMEs) by taking into consideration the intrinsic characteristics of individual enterprises and external correlations among them when assessing credit risk. We analysed transaction data between enterprises and utilised the Bean Search algorithm and Markov random field to construct enterprise network topology diagrams, quantifying inter-enterprise correlations. We also applied the combined weight method to balance their creditworthiness and strength indices and developed a comprehensive and scientifically grounded credit strategy model for MSMEs by employing genetic algorithms to solve nonlinear programming problems. Overall, our proposed model aims to maximise loan revenues while simultaneously minimising the risk of customer default.

Bayesian inference for long memory term structure models

In this study, we propose a novel adaptation of the Dynamic Nelson–Siegel term structure model, incorporating long memory properties to enhance its forecasting accuracy. Our approach involves modelling the evolution of latent factors using fractional Gaussian noise processes, approximated by a weighted sum of independent first-order autoregressive components. The resulting formulation allows for a Gaussian Markov Random Field representation, facilitating the application of computationally efficient Bayesian techniques through Integrated Nested Laplace Approximations. Extensive simulation and empirical analysis demonstrate that integrating long memory significantly improves the model's forecasting performance, particularly for longer time horizons. By shedding light on the potential benefits of incorporating long memory concepts into traditional term structure models, our research highlights its utility in capturing intricate temporal dependencies and enhancing prediction precision.

Attention-enabled adaptive Markov graph convolution

Attention-enabled adaptive Markov graph convolution

A graph theory based similarity metric enables comparison of subpopulation psychometric networks.

Network psychometrics leverages pairwise Markov random fields to depict conditional dependencies among a set of psychological variables as undirected edge-weighted graphs. Researchers often intend to compare such psychometric networks across subpopulations, and recent methodological advances provide invariance tests of differences in subpopulation networks. What remains missing, though, is an analogue to an effect size measure that quantifies differences in psychometric networks. We address this gap by complementing recent advances for investigating whether psychometric networks differ with an intuitive similarity measure quantifying the extent to which networks differ. To this end, we build on graph-theoretic approaches and propose a similarity measure based on the Frobenius norm of differences in psychometric networks' weighted adjacency matrices. To assess this measure's utility for quantifying differences between psychometric networks, we study how it captures differences in subpopulation network models implied by both latent variable models and Gaussian graphical models. We show that a wide array of network differences translates intuitively into the proposed measure, while the same does not hold true for customary correlation-based comparisons. In a simulation study on finite-sample behavior, we show that the proposed measure yields trustworthy results when population networks differ and sample sizes are sufficiently large, but fails to identify exact similarity when population networks are the same. From these results, we derive a strong recommendation to only use the measure as a complement to a significant test for network similarity. We illustrate potential insights from quantifying psychometric network similarities through cross-country comparisons of human values networks. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

An automated method for tendon image segmentation on ultrasound using grey-level co-occurrence matrix features and hidden Gaussian Markov random fields

Background:Despite knowledge of qualitative changes that occur on ultrasound in tendinopathy, there is currently no objective and reliable means to quantify the severity or prognosis of tendinopathy on ultrasound. Objective:The primary objective of this study is to produce a quantitative and automated means of inferring potential structural changes in tendinopathy by developing and implementing an algorithm which performs a texture based segmentation of tendon ultrasound (US) images. Method:A model-based segmentation approach is used which combines Gaussian mixture models, Markov random field theory and grey-level co-occurrence (GLCM) features. The algorithm is trained and tested on 49 longitudinal B-mode ultrasound images of the Achilles tendons which are labelled as tendinopathic (24) or healthy (25). Hyperparameters are tuned, using a training set of 25 images, to optimise a decision tree based classification of the images from texture class proportions. We segment and classify the remaining test images using the decision tree. Results:Our approach successfully detects a difference in the texture profiles of tendinopathic and healthy tendons, with 22/24 of the test images accurately classified based on a simple texture proportion cut-off threshold. Results for the tendinopathic images are also collated to gain insight into the topology of structural changes that occur with tendinopathy. It is evident that distinct textures, which are predominantly present in tendinopathic tendons, appear most commonly near the transverse boundary of the tendon, though there was a large variability among diseased tendons. Conclusion:The GLCM based segmentation of tendons under ultrasound resulted in distinct segmentations between healthy and tendinopathic tendons and provides a potential tool to objectively quantify damage in tendinopathy.

Using Markov Random Field and Analytic Hierarchy Process to Account for Interdependent Criteria

The Analytic Hierarchy Process (AHP) has been a widely used multi-criteria decision-making (MCDM) method since the 1980s because of its simplicity and rationality. However, the conventional AHP assumes criteria independence, which is not always accurate in realistic scenarios where interdependencies between criteria exist. Several methods have been proposed to relax the postulation of the independent criteria in the AHP, e.g., the Analytic Network Process (ANP). However, these methods usually need a number of pairwise comparison matrices (PCMs) and make it hard to apply to a complicated and large-scale problem. This paper presents a groundbreaking approach to address this issue by incorporating discrete Markov Random Fields (MRFs) into the AHP framework. Our method enhances decision making by effectively and sensibly capturing interdependencies among criteria, reflecting actual weights. Moreover, we showcase a numerical example to illustrate the proposed method and compare the results with the conventional AHP and Fuzzy Cognitive Map (FCM). The findings highlight our method’s ability to influence global priority values and the ranking of alternatives when considering interdependencies between criteria. These results suggest that the introduced method provides a flexible and adaptable framework for modeling interdependencies between criteria, ultimately leading to more accurate and reliable decision-making outcomes.

Satellite imagery retrieval based on adaptive Gaussian–Markov random field model with Bayes deep convolutional neural network

Satellite imagery retrieval based on adaptive Gaussian–Markov random field model with Bayes deep convolutional neural network

Understanding financial distress by using Markov random fields on linked administrative data

Household financial distress is a complicated problem. Several social problems have been identified as potential risk factors. Conversely, financial distress has also been identified as a risk factor for some of those social problems. Graphical models can be used to better understand the co-dependencies between these problems. In this approach, problem variables are network nodes and the relations between them are represented by weighted edges. Linked administrative data on social service usage by 6,848 households from neighbourhoods with a high proportion of social housing were used to estimate a pairwise Markov random field with binary variables. The main challenges in graph estimation from data are (a) determining which nodes are directly connected by edges and (b) assigning weights to those edges. The eLasso method used in psychological networks addresses both these challenges. In the resulting graph financial distress occupies a central position that connects to both youth related problems as well as adult social problems. The graph approach contributes to a better theoretical understanding of financial distress and it offers valuable insights to social policy makers.

Uncertainty based regional-decision fusion of multispectral and nDSM for ultra-high resolution UAV imagery

ABSTRACT The recent advancement in the pattern recognition technique has demonstrated the superiority of remote sensing technology. Deep neural networks use spatial feature representations such as convolution neural networks (CNN) to provide better generalisation capability. Our aim is two-fold: firstly, increase the reliability feature by performing the Dual-scale fusion via a modified Markov random field known as DuCNN-MMRF. Secondly, an integration framework was introduced to combine the multispectral image classification produced by DuCNN-MMRF and Normalised-Digital Surface Model (nDSM) information, using a novel approach known as constraint-based Dempster Shafer theory (C-DST). C-DST targeted DuCNN-MMRF’s uncertain information (ambiguous information) and rectified it with complementary information.

Modeling multivariate extreme value distributions via Markov trees

AbstractMultivariate extreme value distributions are a common choice for modeling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max‐stable distributions into a Markov random field with respect to a tree. Although in general not max‐stable itself, this Markov tree is attracted by a multivariate max‐stable distribution. The latter serves as a tree‐based approximation to an unknown max‐stable distribution with the given bivariate distributions as margins. Given data, we learn an appropriate tree structure by Prim's algorithm with estimated pairwise upper tail dependence coefficients as edge weights. The distributions of pairs of connected variables can be fitted in various ways. The resulting tree‐structured max‐stable distribution allows for inference on rare event probabilities, as illustrated on river discharge data from the upper Danube basin.

Accurate and robust registration of low overlapping point clouds

Point cloud registration has various applications within the computer-aided design (CAD) community, such as model reconstruction, retrieving, and analysis. Previous approaches mainly deal with the registration with a high overlapping hypothesis, while few existing methods explore the registration between low overlapping point clouds. However, the latter registration task is both challenging and essential, since the weak correspondence in point clouds usually leads to an inappropriate initialization, making the algorithm get stuck in a local minimum. To improve the performance against low overlapping scenarios, in this work, we develop a novel algorithm for accurate and robust registration of low overlapping point clouds using optimal transformation. The core of our method is the effective integration of geometric features with the probabilistic model hidden Markov random field. First, we determine and remove the outliers of the point clouds by modeling a hidden Markov random field based on a high dimensional feature distribution. Then, we derive a necessary and sufficient condition when the symmetric function is minimized and present a new curvature-aware symmetric function to make the point correspondence more discriminative. Finally, we integrate our curvature-aware symmetric function into a geometrically stable sampling framework, which effectively constrains unstable transformations. We verify the accuracy and robustness of our method on a wide variety of datasets, particularly on low overlapping range scanned point clouds. Results demonstrate that our proposed method attains better performance with higher accuracy and robustness compared to representative state-of-the-art approaches.

Real Aperture Radar Super-Resolution Imaging for Sea Surface Monitoring Based on a Hybrid Model

In recent years, super-resolution imaging techniques have been intensely introduced to enhance the azimuth resolution of real aperture scanning radar (RASR). However, there is a paucity of research on the subject of sea surface imaging with small incident angles for complex scenarios. This research endeavors to explore super-resolution imaging for sea surface monitoring, with a specific emphasis on grounded or shipborne platforms. To tackle the inescapable interference of sea clutter, it was segregated from the imaging objects and was modeled alongside I/Q channel noise within the maximum likelihood framework, thus mitigating clutter’s impact. Simultaneously, for characterizing the non-stationary regions of the monitoring scene, we harnessed the Markov random field (MRF) model for its two-dimensional (2D) spatial representational capacity, augmented by a quadratic term to bolster outlier resilience. Subsequently, the maximum a posteriori (MAP) criterion was employed to unite the ML function with the statistical model regarding imaging scene. This hybrid model forms the core of our super-resolution methodology. Finally, a fast iterative threshold shrinkage method was applied to solve this objective function, yielding stable estimates of the monitored scene. Through the validation of simulation and real data experiments, the superiority of the proposed approach in recovering the monitoring scenes and clutter suppression has been verified.

Markov-Driven Graph Convolutional Networks for Social Spammer Detection

With the growing popularity of social media, spammers unfairly overpower legitimate users with unwanted content to achieve their illegal purposes, which encourages research on spammer detection. The existing spammer detection methods can be characterized into feature-based and propagation-based detection. However, feature-based methods (e.g., GCN) cannot capture the user's following relations, while propagation-based methods cannot utilize the rich text features. To this end, we consider combining these two methods and propose an Adaptive Reward Markov Random Field(ARMRF) layer. ARMRF layer models three intuitions on user label relations and assign them different learnable rewards. Besides, we learn the reward weights by stacking the ARMRF layer on top of GCN for end-to-end training, and we call the stacked model ARMGCN. To further improve ARMGCNs expressive ability, we propose the Markov-Driven Graph Convolutional Network(MDGCN), which integrates conditional random fields(CRF) and ARMGCN. CRF establishes the label joint probability distribution conditioned features for learning user dependencies, and the distribution can be optimized by a variational EM algorithm. We extensively evaluate the proposed method on two real-world Twitter datasets, and the experimental results demonstrate that MDGCN outperforms the state-of-the-art baselines. In addition, the ARMRF layer can be integrated with existing detection methods to improve performance further.

Graph Decoupling Attention Markov Networks for Semisupervised Graph Node Classification.

Graph neural networks (GNNs) have been ubiquitous in graph node classification tasks. Most GNN methods update the node embedding iteratively by aggregating its neighbors' information. However, they often suffer from negative disturbances, due to edges connecting nodes with different labels. One approach to alleviate this negative disturbance is to use attention to learn the weights of aggregation, but current attention-based GNNs only consider feature similarity and suffer from the lack of supervision. In this article, we consider label dependency of graph nodes and propose a decoupling attention mechanism to learn both hard and soft attention. The hard attention is learned on labels for a refined graph structure with fewer interclass edges so that the aggregation's negative disturbance can be reduced. The soft attention aims to learn the aggregation weights based on features over the refined graph structure to enhance information gains during message passing. Particularly, we formulate our model under the expectation-maximization (EM) framework, and the learned attention is used to guide label propagation in the M-step and feature propagation in the E-step, respectively. Extensive experiments are performed on six well-known benchmark graph datasets to verify the effectiveness of the proposed method.

Combining Color and Spatial Image Features for Unsupervised Image Segmentation with Mixture Modelling and Spectral Clustering

The demand for accurate and reliable unsupervised image segmentation methods is high. Regardless of whether we are faced with a problem for which we do not have a usable training dataset, or whether it is not possible to obtain one, we still need to be able to extract the desired information from images. In such cases, we are usually gently pushed towards the best possible clustering method, as it is often more robust than simple traditional image processing methods. We investigate the usefulness of combining two clustering methods for unsupervised image segmentation. We use the mixture models to extract the color and spatial image features based on the obtained output segments. Then we construct a similarity matrix (adjacency matrix) based on these features to perform spectral clustering. In between, we propose a label noise correction using Markov random fields. We investigate the usefulness of our method on many hand-crafted images of different objects with different shapes, colorization, and noise. Compared to other clustering methods, our proposal performs better, with 10% higher accuracy. Compared to state-of-the-art supervised image segmentation methods based on deep convolutional neural networks, our proposal proves to be competitive.

Single image dehazing via decomposition and enhancement

AbstractHazy images suffer from two problems. The low contrast can be enhanced by estimating a transmission layer, and the colour cast can be restored by estimating an airlight. These two variables, together with the albedo layer, are the constitutive elements of a hazy image. The resulting quality of dehazed images is inextricably linked to the accurate estimation of these components. However, it is ill‐posed to decompose these variables from a single image. As such, this paper presents an innovative algorithm intended to facilitate the optimal decomposition of a hazy image. Using the Markov random field model, an optimal framework is established that allows the simultaneous estimation of the three components across the three‐colour channels. To improve the visual quality, three improvements are proposed in the variational solution for the optimal components. The dehazed result is recomposed from the components with the transmission enhanced to circumvent any potential artefacts or information loss. Extensive experiments on natural images corroborate that the proposed algorithm outperforms state‐of‐the‐art dehazing methods, both qualitatively and quantitatively.

Polarimetric Synthetic Aperture Radar Image Classification Based on Double-Channel Convolution Network and Edge-Preserving Markov Random Field

Deep learning methods have gained significant popularity in the field of polarimetric synthetic aperture radar (PolSAR) image classification. These methods aim to extract high-level semantic features from the original PolSAR data to learn the polarimetric information. However, using only original data, these methods cannot learn multiple scattering features and complex structures for extremely heterogeneous terrain objects. In addition, deep learning methods always cause edge confusion due to the high-level features. To overcome these limitations, we propose a novel approach that combines a new double-channel convolutional neural network (CNN) with an edge-preserving Markov random field (MRF) model for PolSAR image classification, abbreviated to “DCCNN-MRF”. Firstly, a double-channel convolution network (DCCNN) is developed to combine complex matrix data and multiple scattering features. The DCCNN consists of two subnetworks: a Wishart-based complex matrix network and a multi-feature network. The Wishart-based complex matrix network focuses on learning the statistical characteristics and channel correlation, and the multi-feature network is designed to learn high-level semantic features well. Then, a unified network framework is designed to fuse two kinds of weighted features in order to enhance advantageous features and reduce redundant ones. Finally, an edge-preserving MRF model is integrated with the DCCNN network. In the MRF model, a sketch map-based edge energy function is designed by defining an adaptive weighted neighborhood for edge pixels. Experiments were conducted on four real PolSAR datasets with different sensors and bands. The experimental results demonstrate the effectiveness of the proposed DCCNN-MRF method.

Multivariate Bayesian structured variable selection for pharmacogenomic studies

Abstract Cancer drug sensitivity screens combined with multi-omics characterisation of the cancer cells have become an important tool to determine the optimal treatment for each patient. We propose a multivariate Bayesian structured variable selection model for sparse identification of multi-omics features associated with multiple correlated drug responses. Our model uses known structure between drugs and their targeted genes via a Markov random field (MRF) prior in sparse seemingly unrelated regression. The use of MRF prior can improve the model performance compared to other common priors. The proposed model is applied to the Genomics of Drug Sensitivity in Cancer data.

A fully automatic framework for sub-pixel mapping of thermokarst lakes using Sentinel-2 images

Mapping and monitoring thermokarst lakes are crucial to understanding the impact of climate change on permafrost regions and quantifying permafrost-related carbon emissions. Several automatic methods based on remote sensing images have been developed for thermokarst lake mapping. However, mixed pixels containing both land and water characteristics in the lakeshore zones pose a significant challenge to the accuracy of these methods. Furthermore, few approaches were able to fully automate the identification of thermokarst lakes without the manual training sample selection or parameter tuning. In this study, we present a fully automatic framework for thermokarst lake mapping using moderate-resolution Sentinel-2 images. The proposed method combines multidimensional hierarchical clustering and sub-pixel mapping (SPM) based on the radial basis function (RBF) interpolation and Markov random field (MRF) (referred to as RBF-then-MRF SPM), so as to achieve thermokarst lake mapping at a spatial resolution of 3.3 m. We apply the proposed method to two representative thermokarst lake distribution regions in the Northern Hemisphere and achieve a mean Kappa coefficient of 0.89 and 0.99, and a mean Quality of 89.86% and 96.60% on the central Tibetan Plateau and the northern Seward Peninsula, respectively. The results demonstrate that the proposed method significantly improves the accuracy of mixed pixel extraction, and the automatic thermokarst lake mapping is applicable to diverse permafrost regions.