Expectation propagation (EP) is a powerful algorithm for signal recovery in compressed sensing. This letter proposes correction of a variance message before denoising to improve the performance of EP in the high signal-to-noise ratio (SNR) regime for finite-sized systems. The variance massage is replaced by an observation-dependent consistent estimator of the mean-square error in estimation before denoising. Massive multiple-input multiple-output (MIMO) is considered to verify the effectiveness of the proposed correction. Numerical simulations show that the proposed variance correction improves the high SNR performance of EP for massive MIMO with a few hundred transmit and receive antennas.

In this paper, we propose a robust parameters estimation algorithm for channel coded systems based on the low-density parity-check (LDPC) code over fading channels with impulse noise. The estimated parameters are then used to generate bit log-likelihood ratios (LLRs) for a soft-inputLDPC decoder. The expectation-maximization (EM) algorithm is used to estimate the parameters, including the channel gain and the parameters of the Bernoulli-Gaussian (B-G) impulse noise model. The parameters can be estimated accurately and the average number of iterations of the proposed algorithm is acceptable. Simulation results show that over a wide range of impulse noise power, the proposed algorithm approaches the optimal performance under different Rician channel factors and even under Middleton class-A (M-CA) impulse noise models.

This paper addresses pilot contamination in massive multiple-input multiple-output (MIMO) uplink. Pilot contamination is caused by reuse of identical pilot sequences in adjacent cells. To solve pilot contamination, the base station utilizes differences between the transmission frames of different users, which are detected via joint channel and data estimation. The joint estimation is regarded as a bilinear inference problem in compressed sensing. Expectation propagation (EP) is used to propose an iterative channel and data estimation algorithm. Initial channel estimates are attained via time-shifted pilots without exploiting information about large scale fading. The proposed EP modifies two points in conventional bilinear adaptive vector approximate message-passing (BAd-VAMP). One is that EP utilizes data estimates after soft decision in the channel estimation while BAd-VAMP uses them before soft decision. The other point is that EP can utilize the prior distribution of the channel matrix while BAd-VAMP cannot in principle. Numerical simulations show that EP converges much faster than BAd-VAMP in spatially correlated MIMO, in which approximate message-passing fails to converge toward the same fixed-point as EP and BAd-VAMP.

Sparse orthogonal matrices are proposed to improve the convergence property of expectation propagation (EP) for sparse signal recovery from compressed linear measurements subject to known dense and ill-conditioned multiplicative noise. As a typical problem, this letter addresses generalized spatial modulation (GSM) in over-loaded and spatially correlated multiple-input multiple-output (MIMO) systems. The proposed sparse orthogonal matrices are used in precoding and constructed efficiently via a generalization of the fast Walsh-Hadamard transform. Numerical simulations show that the proposed sparse orthogonal precoding improves the convergence property of EP in over-loaded GSM MIMO systems with known spatially correlated channel matrices.

Identifying the infection sources in a network, including the sponsor of a network rumor, the servers that inject computer virus into a computer network, or the zero-patient in an infectious disease network, plays a critical role in limiting the damage caused by the infection. A two-source estimator is firstly constructed on basis of partitions of infection regions in this paper. Meanwhile, the two-source estimation problem is transformed into calculating the expectation of permitted permutations count which can be simplified to a single-source estimation problem under determined infection region. A heuristic algorithm is also proposed to promote the estimator to general graphs in a Breadth-First-Search (BFS) fashion. Experimental results are provided to verify the performance of our method and illustrate variations of error detection in different networks.

Expectation propagation (EP) decoding is proposed for sparse superposition coding in orthogonal frequency division multiplexing (OFDM) systems. When a randomized discrete Fourier transform (DFT) dictionary matrix is used, the EP decoding has the same complexity as approximate message-passing (AMP) decoding, which is a low-complexity and powerful decoding algorithm for the additive white Gaussian noise (AWGN) channel. Numerical simulations show that the EP decoding achieves comparable performance to AMP decoding for the AWGN channel. For OFDM systems, on the other hand, the EP decoding is much superior to the AMP decoding while the AMP decoding has an error-floor in high signal-to-noise ratio regime.

Image boundary detection or image segmentation is an important step in image analysis. However, choosing appropriate parameters for boundary detection algorithms is necessary to achieve good boundary detection results. Image boundary detection fusion with unsupervised parameters can output a final consensus boundary, which is generally better than using unsupervised or supervised image boundary detection algorithms. In this study, we theoretically examine why image boundary detection fusion can work well and we propose a mixture model for image boundary detection fusion (MMIBDF) to achieve good consensus segmentation in an unsupervised manner. All of the segmentation algorithms are treated as new features and the segmentation results obtained by the algorithms are the values of the new features. The MMIBDF is designed to sample the boundary according to a discrete distribution. We present an inference method for MMIBDF and describe the corresponding algorithm in detail. Extensive empirical results demonstrate that MMIBDF significantly outperforms other image boundary detection fusion algorithms and the base image boundary detection algorithms according to most performance indices.

In this letter, robust sparse signal recovery is considered in the presence of heavy-tailed impulsive noise. Two Bayesian approaches are developed where a Bayesian framework is constructed by utilizing the Laplace distribution to model the noise. By rewriting the noise-fitting term as a reweighted quadratic function which is optimized in the sparse signal space, the Type I Maximum A Posteriori (MAP) approach is proposed. Next, by exploiting the hierarchical structure of the sparse prior and the likelihood function, we develop the Type II Evidence Maximization approach optimized in the hyperparameter space. The numerical results verify the effectiveness of the proposed methods in the presence of impulsive noise.

In this paper, an adaptive updating probabilistic model is proposed to track an object in real-world environment that includes motion blur, illumination changes, pose variations, and occlusions. This model adaptively updates tracker with the searching and updating process. The searching process focuses on how to learn appropriate tracker and updating process aims to correct it as a robust and efficient tracker in unconstrained real-world environments. Specifically, according to various changes in an object's appearance and recent probability matrix (TPM), tracker probability is achieved in Expectation-Maximization (EM) manner. When the tracking in each frame is completed, the estimated object's state is obtained and then fed into update current TPM and tracker probability via running EM in a similar manner. The highest tracker probability denotes the object location in every frame. The experimental result demonstrates that our method tracks targets accurately and robustly in the real-world tracking environments.

A novel virtual sensors-based positioning method has been presented in this paper, which can make use of both direct paths and indirect paths. By integrating the virtual sensor idea and Bayesian state and observation framework, this method models the indirect paths corresponding to persistent virtual sensors as virtual direct paths and further reformulates the wireless positioning problem as the maximum likelihood estimation of both the mobile terminal's positions and the persistent virtual sensors' positions. Then the method adopts the EM (Expectation Maximization) and the particle filtering schemes to estimate the virtual sensors' positions and finally exploits not only the direct paths' measurements but also the indirect paths' measurements to realize the mobile terminal's positions estimation, thus achieving better positioning performance. Simulation results demonstrate the effectiveness of the proposed method.

The modeling of random telegraph noise (RTN) of MOS transistors is becoming increasingly important. In this paper, a novel method is proposed for realizing automated estimation of two important RTN-model parameters: the number of interface-states and corresponding threshold voltage shift. The proposed method utilizes a Gaussian mixture model (GMM) to represent the voltage distributions, and estimates their parameters using the expectation-maximization (EM) algorithm. Using information criteria, the optimal estimation is automatically obtained while avoiding overfitting. In addition, we use a shared variance for all the Gaussian components in the GMM to deal with the noise in RTN signals. The proposed method improved estimation accuracy when the large measurement noise is observed.

We propose a speaker adaptation method based on the probabilistic principal component analysis (PPCA) of acoustic models. We define a training matrix which is represented in a two-way array and decompose the training models by PPCA to construct bases. In the two-way array representation, each training model is represented as a matrix and the columns of each training matrix are treated as training vectors. We formulate the adaptation equation in the maximum a posteriori (MAP) framework using the bases and the prior.

The k-error linear complexity of periodic sequences is an important security index of stream cipher systems. By using an interesting decomposing approach, we investigate the intrinsic structure for the set of 2n-periodic binary sequences with fixed complexity measures. For k ≤ 4, we construct the complete set of error vectors that give the k-error linear complexity. As auxiliary results we obtain the counting functions of the k-error linear complexity of 2n-periodic binary sequences for k ≤ 4, as well as the expectations of the k-error linear complexity of a random sequence for k ≤ 3. Moreover, we study the 2t-error linear complexity of the set of 2n-periodic binary sequences with some fixed linear complexity L, where t < n-1 and the Hamming weight of the binary representation of 2n-L is t. Also, we extend some results to pn-periodic sequences over Fp. Finally, we discuss some potential applications.

The cooperative orthogonal frequency-division multiplexing (OFDM) relaying system is widely regarded as a key design for future broadband mobile cellular systems. This paper focuses on channel estimation in such a system that uses amplify-and-forward (AF) as the relaying strategy. In the cooperative AF relaying, the destination requires the individual (disintegrated) channel state information (CSI) of the source-relay (S-R) and relay-destination (R-D) links for optimum combination of the signals received from source and relay. Traditionally, the disintegrated CSIs are obtained with two channel estimators: one at the relay and the other at the destination. That is, the CSI of the S-R link is estimated at relay and passed to destination, and the CSI of the R-D link is estimated at destination with the help of pilot symbols transmitted by relay. In this paper, a new disintegrated channel estimator is proposed; based on an expectation-maximization (EM) algorithm, the disintegrated CSIs can be estimated solely by the estimator at destination. Therefore, the new method requires neither signaling overhead for passing the CSI of the S-R link to destination nor pilot symbols for the estimation of the R-D link. Computer simulations show that the proposed estimator works well under the signal-to-noise ratios of interest.

Estimating the ratio of two probability density functions (a.k.a. the importance) has recently gathered a great deal of attention since importance estimators can be used for solving various machine learning and data mining problems. In this paper, we propose a new importance estimation method using a mixture of probabilistic principal component analyzers. The proposed method is more flexible than existing approaches, and is expected to work well when the target importance function is correlated and rank-deficient. Through experiments, we illustrate the validity of the proposed approach.

Quad-core cpus have been a common desktop configuration for today's office. The increasing number of processors on a single chip opens new opportunity for parallel computing. Our goal is to make use of the multi-core as well as multi-processor architectures to speed up large-scale data mining algorithms. In this paper, we present a general parallel learning framework, Cut-And-Stitch, for training hidden Markov chain models. Particularly, we propose two model-specific variants, CAS-LDS for learning linear dynamical systems (LDS) and CAS-HMM for learning hidden Markov models (HMM). Our main contribution is a novel method to handle the data dependencies due to the chain structure of hidden variables, so as to parallelize the EM-based parameter learning algorithm. We implement CAS-LDS and CAS-HMM using OpenMP on two supercomputers and a quad-core commercial desktop. The experimental results show that parallel algorithms using Cut-And-Stitch achieve comparable accuracy and almost linear speedups over the traditional serial version.

In this paper, the expectation maximization (EM) algorithm is used for unsupervised classification of polarimetric synthetic aperture radar (SAR) images. The EM algorithm provides an estimate of the parameters of the underlying probability distribution functions (pdf's) for each class. The feature vector is 9-dimensional, consisting of the six magnitudes and three angles of the elements of a coherency matrix. Each of the elements of the feature vector is assigned a specific parametric pdf. In this work, all the features are supposed to be statistically independent. Then we present a two-stage unsupervised clustering procedure. The EM algorithm is first run for a few iterations to obtain an initial partition of, for example, four clusters. A randomly selected sample of, for example, 2% pixels of the polarimetric SAR image may be used for unsupervised training. In the second stage, the EM algorithm may be run again to reclassify the first stage clusters into smaller sub-clusters. Each cluster from the first stage will be processed separately in the second stage. This approach makes further classification possible as shown in the results. The training cost is also reduced as the number of feature vector in a specific cluster is much smaller than the whole image.

This paper addresses the parameter estimation problem of an interval-based hybrid dynamical system (interval system). The interval system has a two-layer architecture that comprises a finite state automaton and multiple linear dynamical systems. The automaton controls the activation timing of the dynamical systems based on a stochastic transition model between intervals. Thus, the interval system can generate and analyze complex multivariate sequences that consist of temporal regimes of dynamic primitives. Although the interval system is a powerful model to represent human behaviors such as gestures and facial expressions, the learning process has a paradoxical nature: temporal segmentation of primitives and identification of constituent dynamical systems need to be solved simultaneously. To overcome this problem, we propose a multiphase parameter estimation method that consists of a bottom-up clustering phase of linear dynamical systems and a refinement phase of all the system parameters. Experimental results show the method can organize hidden dynamical systems behind the training data and refine the system parameters successfully.

This paper deals with minimum spanning tree problems where each edge weight is a fuzzy random variable. In order to consider the imprecise nature of the decision maker's judgment, a fuzzy goal for the objective function is introduced. A novel decision making model is constructed based on possibility theory and on a stochastic programming model. It is shown that the problem including both randomness and fuzziness is reduced to a deterministic equivalent problem. Finally, a polynomial-time algorithm is provided to solve the problem.