Sharif Digital Repository

In this paper we address the problem of image interpolation using Gaussian Mixture Models (GMM) as a prior. Previous methods of image restoration with GMM have not considered spatial (geometric) distance between patches in clustering, failing to fully exploit the coherency of nearby patches. The GMM framework in our method for image interpolation is based on the assumption that the accumulation of similar patches in a neighborhood are derived from a multivariate Gaussian probability distribution with a specific covariance and mean. An Expectation Maximization-like (EM-like) algorithm is used in order to determine patches in a cluster and restore them. The results show that our image... 

A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity analysis in social networks. In this paper, we analyze the clusterability of BMMs from a theoretical perspective, when the number of clusters is unknown. In particular, we stipulate a set of conditions on the sample complexity and dimension of the model in order to guarantee the Probably Approximately Correct (PAC)-clusterability of a dataset. To the best of our knowledge, these findings are the first non-asymptotic bounds on the sample complexity of learning or... 

The predictions of the pair radial distribution function (RDF) at contact value, compressibility factor, and chemical potentials for binary and ternary hard-sphere mixtures obtained with the Barrio-Solana, the Santos et al., and the generalized Lebowitz mixing rules are compared using the Carnahan-Starling, Kolafa, and Khoshkbarchi-Vera one-component hard-sphere EOS. An expression for the pair RDF at contact value for Barrio-Solana mixing rule and the expressions for the chemical potentials in multicomponent hard-sphere fluids are derived. As a general rule, the equations of state obtained based on the generalized Lebowitz mixing rule predict better the pair RDF at contact value simulated... 

We apply the theory of optimal transport to study mathematical properties of mean field variational Bayesian approximation. It turns out that if K +C > 0 where C is the convexity coefficient of −log p and K is a lower bound for the Ricci curvature of the underlying parameter space, then the corresponding system of equations of variational Bayesian approximation admits a unique solution. The uniqueness property in presence of symmetry leads to preservation of mode. As an explicit application we correct Bayesian Gaussian Mixture model in such a way that it turns into a convex model while its (unique) maximum likelihood solution coincides asymptotically with the true solution. Using convexity... 

Cardiovascular Disease (CVD) is considered as one of the principal causes of death in the world. Over recent years, this field of study has attracted researchers' attention to investigate heart sounds' patterns for disease diagnostics. In this study, an approach is proposed for normal/abnormal heart sound classification on the Physionet challenge 2016 dataset. For the first time, a fixed length feature vector; called i-vector; is extracted from each heart sound using Mel Frequency Cepstral Coefficient (MFCC) features. Afterwards, Principal Component Analysis (PCA) transform and Variational Autoencoder (VAE) are applied on the i-vector to achieve dimension reduction. Eventually, the reduced... 

Point Set Registration (PSR) of anatomic parts is used in different fields such as Patient Specific Implant (PSI) design in Computer Assisted Surgery (CAS) procedure. We designed a modified rigid PSR method based on student's-t mixture model. The proposed method is compared with Coherent Point Drift (CPD) registration method. Higher convergence speed and the lower error value are the advantages of the suggested algorithm in compare with CPD. In our method, the number of iterations decreases by about 69%, and the final error improvement was about 7% in comparison with CPD. The robustness of the proposed algorithm makes it beneficial to be used in the procedure of designing PSI in both... 

In this paper, we focus on the mixing matrix estimation which is the first step of Sparse Component Analysis. We propose a novel algorithm based on Expectation- Maximization (EM) algorithm in the case of two-sensor set up. Then, a novel iterative Bayesian clustering is applied to yield better results in estimating the mixing matrix. Also, we compute the Maximum Likelihood (ML) estimates of the elements of the second row of the mixing matrix based on each cluster. The simulations show that the proposed method has better accuracy and less failure than the EM-Laplacian Mixture Model (EM-LMM) method. copyright by EURASIP  

Turbulent fully developed periodic condensation heat transfer and pressure drop in herringbone-type plate heat exchangers for R134a and steam were numerically investigated. A mixture model was introduced and the equations governing the two phase flow were simplified. Thus a single phase periodic flow with mixture properties was solved for R134a. For Steam a separate empirical model was used. The governing equations were solved numerically by a finite-volume method for elliptic flows in complex geometries using collocated variable arrangement. The influence of mass flux and vapor quality on frictional pressure drop for refrigerant was investigated. The heat transfer was studied using a... 

The long-term performance of LiFi networks significantly depends on the location of access points. The optimized placement can be determined based on the distribution of users in the room. In this paper, we investigate the placement optimization for average throughput maximization in the presence of asymmetric distributions. In particular, we represent users' distribution in the indoor environment by the Gaussian mixture model, which is powerful and computationally convenient. Then we obtain the optimized deployment for different scenarios using gradient ascent algorithm. The results show that optimization of deployment significantly improves the average throughput of the network. As the... 

This paper presents a method to solve hyperspectral unmixing problem based on the well-known linear mixing model. Hyperspectral unmixing is to decompose observed spectrum of a mixed pixel into its constituent spectra and a set of corresponding abundances. We use Nonnegative Matrix Factorization (NMF) to solve the problem in a single step. The proposed method is based on a projected gradient NMF algorithm. Moreover, we modify the NMF algorithm by adding a penalty term to include also the statistical independence of abundances. At the end, the performance of the method is compared to two other algorithms using both real and synthetic data. In these experiments, the algorithm shows interesting... 

In this paper, we address the problem of recovering degraded images using multivariate Gaussian mixture model (GMM) as a prior. The GMM framework in our method for image restoration is based on the assumption that the accumulation of similar patches in a neighborhood are derived from a multivariate Gaussian probability distribution with a specific covariance and mean. Previous methods of image restoration with GMM have not considered spatial (geometric) distance between patches in clustering. Our conducted experiments show that in the case of constraining Gaussian estimates into a finite-sized windows, the patch clusters are more likely to be derived from the estimated multivariate Gaussian... 

Forced convective of a nanofluid that consists of water and Al2O3 in horizontal tubes has been studied numerically. Computed results were validated with existing well established correlation. Two-phase Eulerian model has been implemented for the first time to study such a flow field. A single-phase model and two-phase mixture model formulations were also used for comparison. The comparison of calculated results with experimental values shows that the mixture model is more precise. It is illustrated that the single-phase model and the two-phase Eulerian model underestimates the Nusselt number. Effects of nanoparticles concentration on the thermal parameters are also discussed  

This paper introduces a probabilistic framework to quantify the spatial distribution of cracking and crushing in rectangular reinforced concrete shear walls at different drift ratios. In this research, a comprehensive probabilistic spatial analysis is conducted on an extensive collected database of reinforced concrete shear walls tested under the quasi-static cyclic loading. The database includes 235 images of 72 damaged walls with various geometry and material properties at different drift ratios between 0.0 and 4.0%. Various image processing filters are implemented to the images to highlight the wall areas that are more prone to cracking and crushing. Then, advanced statistical analysis is...