Image segmentation based on hierarchical belief propagation with variable weighting parameters

In this paper, we develop a Belief Propagation (BP) algorithm for similarity computation to improve the recommendation accuracy of the neighborhood method, which is one of the most popular Collaborative Filtering (CF) recommendation algorithms. We formulate a probabilistic inference problem as to compute the marginal posterior distributions of similarity variables from their joint posterior distribution given the observed ratings. However, direct computation is prohibitive in large-scale recommender systems. Therefore, we introduce an appropriate chosen factor graph to express the factorization of the joint distribution function, and utilize the BP algorithm that operates in the factor graph to exploit the factorization for efficient inference. In addition, since the high degree at the factor node incurs an exponential increase in computational complexity, we also propose a complexity-reduction technique. The overall complexity of the proposed BP algorithm on a factor graph is linear in the number of variables, which ensures scalability. Finally, through experiments on the MovieLens dataset, we show the superior prediction accuracy of the proposed BP-based similarity computation algorithm for recommendation.

In this paper, we use the minimum mean square error (MMSE) criterion to design the scaled and offset belief propagation (BP)-based decoding algorithms for short low-density parity-check (LDPC) codes on the fast Rayleigh fading channel. Based on the MMSE criterion, the theoretical formulas and numerical calculations on the optimum factors for these two improved BP-based algorithms are provided. The simulation results for several short (Chen et al., 2005 and Gallager, 1962) regular LDPC codes on the fast Rayleigh fading channel demonstrate that the scaled and offset BP-based algorithms with our proposed factors can achieve the performance better than that of the BP algorithm.

Belief propagation (BP) is an efficient way to solve inference problems in graphical models, such as Bayesian networks and Markov random fields. It has found great success in many application areas due to its simplicity, high accuracy, and distributed nature. This paper is a first attempt to apply BP algorithms in CSMA wireless networks. Compared to prior CSMA optimization algorithms such as ACSMA, which are measurement-based, BP-based algorithms are proactive and computational, without the need for network probing and traffic measurement. Consequently, BP-based algorithms are not affected by the temporal throughput fluctuations and can converge faster. Specifically, this paper explores three applications of BP. 1) We show how BP can be used to compute the throughputs of different links in the network given their access intensities, defined as the mean packet transmission time divided by the mean backoff countdown time. 2) We propose an inverse-BP algorithm to solve the reverse problem of how to set the access intensities of different links to meet their target throughputs. 3) We introduce a BP-adaptive CSMA algorithm to find the link access intensities that can achieve optimal system utility. The first two applications are NP-hard problems, and BP provides good approximations to them. The advantage of BP is that it can converge faster compared to prior algorithms like ACSMA, especially in CSMA networks with temporal throughput fluctuations. Furthermore, this paper goes beyond BP and considers a generalized version of it, GBP, to improve accuracy in networks with a loopy contention graph. The distributed implementation of GBP is nontrivial to construct. A contribution of this paper is to show that a maximal clique method of forming regions in GBP: 1) yields accurate results; and 2) is amenable to distributed implementation in CSMA networks, with messages passed between one-hop neighbors only. We show that both BP and GBP algorithms for all three applications can yield solutions within seconds in real operation.

Severe intersymbol interference (ISI) is one of the main obstacles for reliable signal reception in ATSC DTV systems. Decision feedback equalizers (DFEs) are commonly used to suppress the ISI. However, DFEs may suffer from error propagation due to incorrect symbol decisions from the symbol slicer. This phenomenon deteriorates the performance even more when the post-cursor ISI is strong. In order to reduce error propagation, we present a novel hybrid equalization scheme for ATSC channels. The proposed scheme consists of an adaptive decision feedback sparsening filter (DFSF), and an iterative maximum a posteriori (MAP) equalizer based on the belief propagation (BP) algorithm. In the first stage, instead of removing all the ISI from post cursors, the DFSF employs a modified feedback filter which leaves the strongest post-cursor ISI taps uncorrected. As a result, a long ISI channel is equalized to a sparse channel having only a small number of nonzero taps. In the second stage, a belief propagation algorithm is applied to mitigate the residual ISI. Since the channel is typically time-varying and suffers from Doppler fading, the DFSF is adapted using the least mean square (LMS) algorithm, such that the amplitude and the locations of the nonzero taps of the equalized sparse channel appear to be fixed. As such, the channel appears to be static during the second stage of equalization which consists of the BP detector. Simulation results demonstrate that the proposed scheme outperforms the traditional DFE in symbol error rate, under both static channels and dynamic ATSC channels.

The cache-enabled D2D network supports direct interconnection among users and can help to offload the data traffic through user caching. In this paper, we consider a reasonable caching strategy design in the cache-enabled D2D network to improve its performance. First we formulate an optimization problem aiming to minimize the average file download time of the users. Next we transform the original problem to a max-product form that can be distributed solved. Then we introduce the factor graph and the conventional belief propagation (BP) algorithm. Finally, we show how we design a BP algorithm with Randomized Gaussian Message Passing scheme and Weighting mechanism (BP-RW) to improve its convergence and performance. The distributed BP-RW algorithm can assign almost all computations to each user in the network, which will help to reduce the heavy computational overhead of the central controller. Meanwhile, simulation results show that the BP-RW algorithm performs better than the conventional BP algorithm, and performs very closely to the centralized greedy algorithm with much lower computational complexity.

In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a network of distributed agents can be approximated by a linear fusion of all the local log-likelihood ratios. The proposed approach clarifies how the BP algorithm works, simplifies the statistical analysis of its behavior, and enables us to develop a performance optimization framework for the BP-based distributed inference systems. Next, we propose a blind learning-adaptation scheme to optimize the system performance when there is no information available a priori describing the statistical behavior of the wireless environment concerned. In addition, we propose a blind threshold adaptation method to guarantee a certain performance level in a BP-based distributed detection system. To clarify the points discussed, we design a novel linear-BP-based distributed spectrum sensing scheme for cognitive radio networks and illustrate the performance improvement obtained, over an existing BP-based detection method, via computer simulations.

In this paper, we propose two novel generalized belief propagation (BP) algorithms to improve the convergence behavior of the conventional BP algorithm. By incorporating a dynamic temperature into the free energy formulation, message passing is performed on a dynamic surface of energy cost. The proposed cooling process helps BP converge to a stable fixed point with a lower energy value that leads to better estimations. For decoding turbo-like error correcting codes, we adopt a parametric Gaussian approximation to relax the binary parity check constraints and generalize the conventional binary networks as well. Both the computational complexity and the convergence rate of the proposed annealed BP algorithms are almost the same as those of the conventional BP algorithm. Simulated performance of the proposed algorithms when they are used to decode a low density parity check (LDPC) code and the (23,12) Golay code is presented to validate our proposals.

A BP-based algorithm with 2-dimensional classified normalized correction is developed to reduce the complexity and improve the performance of decoding algorithm for the low density parity check (LDPC) codes. The algorithm first utilizes classification according to the absolute values of incoming messages in check nodes. Then it uses 2-dimensional normalization to correct the minimum and sub-minimum values. The 2-dimensional normalized factors can be calculated respectively by using probability and statistic theory in the initialization step. Simulation results illustrate that the proposed algorithm achieves better performance in bit error ratio (BER) and average iteration number than normalized BP-based algorithm in the high signal noise ratio (SNR) region, i.e., it can achieve 0.4 dB SNR gain and reduce 20% number of iterations at BER= 5 10  , whose complexity is also much less than that of belief propagation (BP) algorithm. It is concluded that the proposed algorithm offers better tradeoff between performance and complexity.  Index Terms—channel coding theory, density evolution, Iterative decoding algorithm

Women have a higher rupture risk of intracranial aneurysms than men. One possible explanation is that aneurysm volume and shape irregularity, both linked to rupture risk, may differ between women and men. We investigated this with 3-dimensional morphological aneurysm parameters. In a random sample of consecutive patients with unruptured intracranial aneurysms diagnosed between 2008 and 2018, we quantified volume and shape parameters describing global (sphericity, elongation, and flatness) and local shape (shape index and curvedness) on CT or MR angiography scans. We compared these parameters between women and men (reference) with univariable and multivariable linear regression analysis (global parameters) and binary logistic regression analysis (local parameters). The multivariable analysis was adjusted for the confounders: age, hypertension, smoking status, aneurysm size, location, and imaging modality. We included 326 patients (239 women [73%], mean age 58 years [SD 12 years]). Women had smaller aneurysm volumes than men in multivariable analysis (β -0.30 SD, 95%CI -0.55 to -0.06). The global shape parameters sphericity, elongation, and flatness were comparable between sexes. Of the local shape parameters, women had higher aneurysm shape index (OR 2.38, 95%CI 1.03 to 5.49) and lower curvedness (OR 0.50, 95%CI 0.29 to 0.88) in multivariable analysis. Women have intracranial aneurysms with smaller volumes and shape characteristics associated with lower rupture risk. Therefore, factors other than aneurysm morphology are likely responsible for the higher risk of aneurysm rupture in women.

The major obstacle to shallow water acoustic communication is the interference of multipath signal results from surface and bottom reflections. Channel coding is indispensable in practical system to accommodate these adverse channel transmission characteristics due to the coding gain. In this paper, a channel model including time-varying fading, multipath and additive noise for the shallow water acoustic channels is built. Based on the channel model, the Probability Density Function (PDF) of initial decoding messages with Belief Propagation (BP) algorithm of LowDensity Parity-Check (LDPC) codes is deduced. The performance of the LDPC codes with BP algorithm is simulated, and the effects of multipath, fading velocity and channel interleaver on the decoding performance are studied. As the result, the following conclusions can be given: The performance of LDPC codes is excellent (Bit Error Rate (BER) is less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> ) over three-multipath shallow water acoustic channels, with 3~5 iterative decoding times and about 1000 bits code lengths; The BER of LDPC codes degrades with the increasing of the number of multipath; The BER of LDPC codes degrades slowly with the decreasing of the fading velocity, which shows the proposed channel code is not sensitive to the fading velocity of the channel.

For industrial application of load monitoring techniques, it is important to establish high-performance state estimators of low-cost and low frequency smart meters (SM) and sensors in a power system, which can run under resource-constrained computing units. Because household electronic appliances often tap power from fixed sockets, a finite state table for the corresponding sensors is suitable and convenient. However, SM in the main line may have an enormous state table. In this study, we propose a belief propagation (BP) algorithm to calculate the power consumption of electronic appliances in a semi-intrusive load monitoring (SILM) system whose SM and sensors have state tables with sizes varying largely. The novelty of the proposed method lies in a continuous approximation to a large state table and a switching scheme between discrete and continuous parts of the SILM system. With datasets from numerical simulations and a real-world experimental SILM system in a set of high-density school buildings within a secondary distribution network, the proposed BP algorithm is compared with relevant state-of-the-art algorithms. The results show that the proposed algorithm achieves a percentage of error (8&#x0025;), which outperforms the percentage achieved by the other methods, a linear state estimation of 99&#x0025;, a hidden Markov model of 21&#x0025;, and a full-discrete BP algorithm of 11&#x0025;. In addition, the complexity of the proposed algorithm is the least of all methods, and the proposed algorithm can run by SoC on concentrators.

It has been shown that the stable fixed points of belief propagation (BP) algorithms correspond to extrema of the Bethe free energy. In this paper, we describe the dual problem for the minimization of the Bethe free energy and solve it using simple nonlinear block Gauss-Seidel and Jacobi algorithms. The use of the nonlinear block Gauss-Seidel algorithm corresponds to serial scheduling for the BP algorithm. In addition, it is shown that applying the nonlinear block Jacobi algorithm on the dual of the Bethe free energy corresponds to the parallel BP algorithm.

Generic wrap-around shape optimisation technology is presented, and is applied to a helicopter rotor in hover, using compressible CFD as the aerodynamic model. An efficient domain element shape parameterisation method is used as the surface control and deformation method, and is linked to a radial basis function global interpolation, to provide direct transfer of domain element movements into deformations of the design surface and the CFD volume mesh. This method is independent of mesh type and size, and optimisation independence from the flow solver is achieved by obtaining sensitivity information for an advanced parallel gradient-based algorithm by finite-difference. The method is applied here to a two-bladed hovering rotor, with transonic tip speed, comparing the effects of global twist parameters and more local planform parameters. Significant torque reductions are achieved in both cases, and it is shown that using only three global twist parameters are extremely effective. Using 63 local and global parameters, large geometric changes are demonstrated, with both induced power and wave drag reduced.

In this paper, we describe a new method for improving cooperative spectrum sensing in cognitive radio. We introduce a new block based on belief propagation algorithm in the conventional structure of cooperative spectrum sensing. The belief propagation block allows propagation of correct beliefs over a network of secondary users and thus in turn improves the primary user detection. We consider the network of secondary users as Tanner graph [1] and propose a scheme based on belief propagation over these graphs to improve the local decisions at the secondary users before sending the decisions to the fusion center. We demonstrate the improvement in probability of detection, P d using our belief propagation block by simulating the performance of cooperative spectrum sensing using energy detection over Rayleigh fading channels. The proposed scheme provides improvement over conventional cooperative spectrum sensing for both soft combination and hard combination schemes.

The belief propagation (BP) algorithm is a widely adopted iterative decoding method for Luby transform (LT) codes. However, the conventional log-likelihood ratio BP (LLR-BP) decoder exhibits inherent limitations in additive white Gaussian noise (AWGN) channels. These limitations include high computational complexity, slow convergence speed, and limited decoding efficiency. To address these challenges, we propose a variable-order threshold serial belief propagation (VOT-SBP) algorithm. The proposed algorithm integrates the serial belief propagation (SBP) method with a reliability metric for check nodes, enabling accurate determination of the sequence for message updates. In addition, by introducing an adaptive threshold for correcting check node information, the algorithm effectively eliminates redundant update actions throughout the decoding process. Simulation results demonstrate a 63.6% reduction in iteration count compared to BP for long-length codes at medium to high signal-to-noise ratio (SNR) and a 17.4% decrease in computational overhead. This approach enhances both decoding performance and convergence efficiency.