Sharif Digital Repository

In this paper we propose a new algorithm for learning low-dimensional linear subspaces. Our proposed algorithm performs by sequentially finding some low-dimensional subspaces on which a set of training data lies. Each subspace is found in such a way that the number of signals lying on (or near to) it is maximized. Once we found a subset of the training data that is sufficiently close to a subspace, then we omit these signals from the set of training signals and repeat the procedure for the remaining signals until all training signals are assigned to a subspace. This data reduction procedure results in a significant improvement to the runtime of our algorithm. We then propose a robust version... 

In this paper Long Term Memory (LTM) process during leftward and rightward orientation recalling have been analyzed using Magnetoencephalogram (MEG) signals. This paper presents a novel criterion for decision making using union subspace based classifier. The proposed method involves the Eigenvalues from Singular Value Decomposition (SVD) of each subspace not only to select basis for each subspace but also to weight the decision making criterion to discriminate two classes. The proposed method has provided orientation detection from recalling signal with 6.75 percent increase in classification accuracy compared to better results on this data  

Let be a ring and be the set of all non-trivial left ideals of. The intersection graph of ideals of, denoted by, is a graph with the vertex set and two distinct vertices and are adjacent if and only if. In this paper, we classify all rings (not necessarily commutative) whose domination number of the intersection graph of ideals is at least 2. Moreover, some results on the intersection graphs of ideals of matrix algebras over a finite field are given. For instance, we determine the domination number, the clique number and the independence number of. We prove that if is a positive integer and, then the domination number of is. Among other results, we show that if, where is a positive integer... 

In this paper we address the problem of learning low-dimensional subspaces using a given set of training data. To this aim, we propose an algorithm that performs by sequentially fitting a number of low-dimensional subspaces to the training data. Once we found a subset of the training data that is sufficiently near a fitted subspace, we omit these signals from the set of training signals and repeat the same procedure for the remaining signals until all training signals are assigned to a subspace. We then propose a robust version of the algorithm to address the situation in which the training signals are contaminated by additive white Gaussian noise (AWGN). Experimental results on both... 

One limitation of vector-based LDA and its matrix-based extension is that they cannot deal with heteroscedastic data. In this paper, we present a novel two-dimensional feature extraction technique for face recognition which is capable of handling the heteroscedastic data in the dataset. The technique is a general form of two-dimensional linear discriminant analysis. It generalizes the interclass scatter matrix of two-dimensional LDA by applying the Chernoff distance as a measure of separation of every pair of clusters with the same index in different classes. By employing the new distance, our method can capture the discriminatory information presented in the difference of covariance... 

Traditional learning algorithms cannot perform well in scenarios where training data (source domain data) that are used to learn the model have a different distribution with test data (target domain data). The domain adaptation that intends to compensate this problem is an important capability for an intelligent agent. This paper presents a domain adaptation method which learns to adapt the data distribution of the source domain to that of the target domain where no labeled data of the target domain is available (and just unlabeled data are available for the target domain). Our method jointly learns a low dimensional representation space and an adaptive classifier. In fact, we try to find a... 

There is a growing attention in subspace learning using tensor-based approaches in high dimensional spaces. In this paper we first indicate that these methods suffer from the Heteroscedastic problem and then propose a new approach called Heteroscedastic Multilinear Discriminant Analysis (HMDA). Our method can solve this problem by utilizing the pairwise chernoff distance between every pair of clusters with the same index in different classes. We also show that our method is a general form of Multilinear Discriminant Analysis (MDA) approach. Experimental results on CMU-PIE, AR and AT&T face databases demonstrate that the proposed method always perform better than MDA in term of classification... 

A cognitive radio provides access to a licensed spectrum for unlicensed users opportunistically provided that they are not harmful for licensed users (primary users). We call a cognitive radio user (CR user) harmful, when it generates interference for primary users (PU) or occupies spectrum holes excessively. This paper discusses the spectrum management policy against harmful CR users. For this, we design a jammer signal which ruins transmission of harmful CR users and forces them to leave the spectrum without damaging the communication of PUs. This signal is designed using group subspace technique for both synchronous and asynchronous channels. Our simulation results show that the designed... 

Discriminative subspace analysis is a popular approach for a variety of applications. There is a growing interest in subspace learning techniques for face recognition. Principal component analysis (PCA) and eigenfaces are two important subspace analysis methods have been widely applied in a variety of areas. However, the excessive dimension of data space often causes the curse of dimensionality dilemma, expensive computational cost, and sometimes the singularity problem. In this paper, a new supervised discriminative subspace analysis is presented by encoding face image as a high order general tensor. As face space can be considered as a nonlinear submanifold embedded in the tensor space, a... 

In this article, we investigate the limiting spectral distribution of the sample covariance matrix (SCM) of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We obtain an approximation for the spectral distribution of the SCM obtained from windowed data. We also determine a condition on the coefficients of the window, under which the fragmentation of the support of noise eigenvalues can be avoided, in the noise-only data case. For the commonly used exponential window, we derive an explicit expression for the l.s.d of the noise-only data. In addition, we present a method to... 

We provide an analytical investigation of the entanglement dynamics for a system composed of an arbitrary number of qubits dissipating into a common environment. Specifically, we consider product initial states with a given number of excitations whose evolution remains confined on low-dimensional subspaces of the operators space. We then find for which pairs of qubits entanglement can be generated and can persist at a steady state. Finally, we determine the stationary distribution of entanglement as well as its scaling versus the total number of qubits in the system  

We propose an ℓ1 criterion for dictionary learning for sparse signal representation. Instead of directly searching for the dictionary vectors, our dictionary learning approach identifies vectors that are orthogonal to the subspaces in which the training data concentrate. We study conditions on the coefficients of training data that guarantee that ideal normal vectors deduced from the dictionary are local optima of the criterion. We illustrate the behavior of the criterion on a 2D example, showing that the local minima correspond to ideal normal vectors when the number of training data is sufficient. We conclude by describing an algorithm that can be used to optimize the criterion in higher... 

The problem of signal detection using a flexible and general model is considered. Owing to applicability and flexibility of sparse signal representation and approximation, it has attracted a lot of attention in many signal processing areas. In this study, the authors propose a new detection method based on sparse decomposition in a union of subspaces model. Their proposed detector uses a dictionary that can be interpreted as a bank of matched subspaces. This improves the performance of signal detection, as it is a generalisation for detectors. Low-rank assumption for the desired signals implies that the representations of these signals in terms of some proper bases would be sparse. Their... 

The algebraic multigrid (AMG) algorithm as a preconditioner to the Krylov subspace methods has drawn the attention of many researchers in solving fluid flow and heat transfer problems. However, the efficient employment of this solver needs experience, because users have to quantify several important parameters. In this work, we choose a hybrid finite-volume element method and quantify the optimum magnitudes for those parameters. To generalize our results, two sets of fluid flow governing equations, the thermobuoyant flow and confined diffusion flame, are studied and the optimum values are determined. The results indicate that the AMG can be very effective if a proper storage method is chosen...