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Power consumption has become one of the primary challenges to meetMoore’s law. For reducing power consumption, single-electron transistor (SET) at room temperature has been demonstrated as a promising device for extending Moore’s law due to its ultralow power consumption in operation. Previous works have proposed automated mapping approaches for SET arrays that focused on minimizing the number of hexagons in the SET arrays. However, the area of an SET array is the product of the bounded height and the bounded width, and the height usually equals the number of inputs in the Boolean function. Consequently, in this paper, we focus on the width minimization to reduce the overall area in the mapping of the SET arrays. Our approach consists of techniques of product term minimization, branch-then-share (BTS)-aware variable reordering, SET array architecture relaxation, and BTS-aware product term reordering. The experimental results on a set of MCNC and IWLS 2005 benchmarks show that the proposed approach saves 45% of width compared with the work by Chiang et al., which focused on hexagon count minimization, and also saves 13% of width compared with the work by Chen et al., which focused on width minimization. [ABSTRACT FROM AUTHOR]

Sparse representation-based visual tracking approaches have attracted increasing interests in the community in recent years. The main idea is to linearly represent each target candidate using a set of target and trivial templates, while imposing a sparsity constraint onto the representation coefficients. After we obtain the coefficients using \ell 1 -norm minimization methods, the candidate with the lowest error, when it is reconstructed using only the target templates and the associated coefficients, is considered as the tracking result. In spite of promising system performance widely reported, it is unclear if the performance of these trackers can be maximized. In addition, computational complexity caused by the dimensionality of the feature space limits these algorithms in real-time applications. In this paper, we propose a real-time visual tracking method based on structurally random projection (RP) and weighted least squares (WLS) techniques. In particular, to enhance the discriminative capability of the tracker, we introduce background templates to the linear representation framework. To handle appearance variations over time, we relax the sparsity constraint using a WLS method to obtain the representation coefficients. To further reduce the computational complexity, structurally RP is used to reduce the dimensionality of the feature space, while preserving the pairwise distances between the data points in the feature space. Experimental results show that the proposed approach outperforms several state-of-the-art tracking methods. [ABSTRACT FROM AUTHOR]

In recent years, low-rank tensor completion (LRTC) problems have received a significant amount of attention in computer vision, data mining, and signal processing. The existing trace norm minimization algorithms for iteratively solving LRTC problems involve multiple singular value decompositions of very large matrices at each iteration. Therefore, they suffer from high computational cost. In this paper, we propose a novel trace norm regularized CANDECOMP/PARAFAC decomposition (TNCP) method for simultaneous tensor decomposition and completion. We first formulate a factor matrix rank minimization model by deducing the relation between the rank of each factor matrix and the mode- n rank of a tensor. Then, we introduce a tractable relaxation of our rank function, and then achieve a convex combination problem of much smaller-scale matrix trace norm minimization. Finally, we develop an efficient algorithm based on alternating direction method of multipliers to solve our problem. The promising experimental results on synthetic and real-world data validate the effectiveness of our TNCP method. Moreover, TNCP is significantly faster than the state-of-the-art methods and scales to larger problems. [ABSTRACT FROM PUBLISHER]

This paper proposes an interval type-2 neural fuzzy classifier learned through soft margin minimization (IT2NFC-SMM) and applies it to human body posture classification. The IT2NFC-SMM consists of interval type-2, zero-order Takagi–Sugeno (T–S) fuzzy rules established through online structure learning. The antecedent part of the IT2NFC-SMM uses interval type-2 fuzzy sets to decrease the number of rules and manage noisy data. For parameter learning, the consequent parameters are learned through a linear support vector machine (SVM) for soft margin minimization to improve the generalization ability. The proposed SVM-based learning addresses the problem that the orders of the fuzzy rules in computing the outputs of an interval type-2 fuzzy system depend on the consequent values that are unknown in advance. To address this problem, the IT2NFC-SMM uses weighted bound-set boundaries to simplify the type-reduction operation and a novel crisp-to-interval linear SVM learning algorithm. Based on the soft margin minimization, the antecedent parameters are tuned using the gradient descent algorithm. The IT2NFC-SMM is applied to a vision-based human body posture classification system. The system uses two cameras and novel classification features extracted from a silhouette of the human body to classify the four postures of standing, bending, sitting, and lying. The classification performance of the IT2NFC-SMM is verified through results in clean and noisy classification examples and through the posture classification problem, as well as through comparisons with various type-1 and type-2 fuzzy classifiers. The overall result shows that the IT2NFC-SMM achieves higher classification rates with a smaller or similar model size than the classifiers used for comparison, especially for noisy classification problems. [ABSTRACT FROM PUBLISHER]

Performance guarantees for the algorithms deployed to solve underdetermined linear systems with sparse solutions are based on the assumption that the involved system matrix has the form of an incoherent unit norm tight frame. Learned dictionaries, which are popular in sparse representations, often do not meet the necessary conditions for signal recovery. In compressed sensing (CS), recovery rates have been improved substantially with optimized projections; however, these techniques do not produce binary matrices, which are more suitable for hardware implementation. In this paper, we consider an underdetermined linear system with sparse solutions and propose a preconditioning technique that yields a system matrix having the properties of an incoherent unit norm tight frame. While existing work in preconditioning concerns greedy algorithms, the proposed technique is based on recent theoretical results for standard numerical solvers such as BP and OMP. Our simulations show that the proposed preconditioning improves the recovery rates both in sparse representations and CS; the results for CS are comparable to optimized projections. [ABSTRACT FROM AUTHOR]

We show that solving the LP relaxation of the min-sum labeling problem (also known as MAP inference problem in graphical models, discrete energy minimization, or valued constraint satisfaction) is not easier than solving any linear program. Precisely, every polytope is linear-time representable by a local marginal polytope and every LP can be reduced in linear time to a linear optimization (allowing infinite costs) over a local marginal polytope. The reduction can be done (though with a higher time complexity) even if the local marginal polytope is restricted to have a planar structure. [ABSTRACT FROM PUBLISHER]

In this paper, a distributed convex optimization framework is developed for energy trading between islanded microgrids. More specifically, the problem consists of several islanded microgrids that exchange energy flows by means of an arbitrary topology. Due to scalability issues and in order to safeguard local information on cost functions, a subgradient-based cost minimization algorithm that converges to the optimal solution in a practical number of iterations and with limited communication overhead is proposed. Furthermore, this approach allows for a very intuitive economics interpretation that explains the algorithm iterations in terms of a “supply–demand model” and “market clearing.” Numerical results are given in terms of the convergence rate of the algorithm and the attained costs for different network topologies. [ABSTRACT FROM PUBLISHER]

We consider the problem of estimating a deterministic finite alphabet vector f from underdetermined measurements y= A f , where A is a given (random) n \times N matrix. Two new convex optimization methods are introduced for the recovery of finite alphabet signals via \ell _{1} -norm minimization. The first method is based on regularization. In the second approach, the problem is formulated as the recovery of sparse signals after a suitable sparse transform. The regularization-based method is less complex than the transform-based one. When the alphabet size p$ equals 2 and $(n,N)$ grows proportionally, the conditions under which the signal will be recovered with high probability are the same for the two methods. When $p > 2$ , the behavior of the transform-based method is established. Experimental results support this theoretical result and show that the transform method outperforms the regularization-based one. [ABSTRACT FROM AUTHOR]

This paper investigates the minimization problem of fuzzy automata, aiming to obtain a procedure for finding a minimal state fuzzy automaton equivalent to a given one. The decision version of the minimization problem is as follows: Given a fuzzy automaton \cal A and a natural number k, i.e., a pair \langle {\cal A}, k\rangle, is there a k$-state fuzzy automaton equivalent to \cal A? We prove that the above problem is decidable for fuzzy automata over totally ordered lattices and then obtain a procedure for minimizing a given fuzzy automaton. To this end, we introduce the concept of systems of fuzzy polynomial equations, present a procedure for finding solutions of these systems and, finally, reduce the above decision problem to finding a solution of a system of fuzzy polynomial equations. It is worth pointing out that although some algorithms in the literature were claimed to be minimization algorithms, the term “minimization” there did not mean state minimization in our sense, since these algorithms did not aim at a minimal fuzzy automaton but found “reasonably” small fuzzy automata. [ABSTRACT FROM AUTHOR]

Constrained energy minimization (CEM) has been widely used for subpixel detection. It takes advantage of inverting the global sample correlation matrix R to suppress background so as to enhance detection of targets of interest. This paper presents a progressive band processing of CEM (PBP-CEM) which can perform CEM for target detection progressively band by band according to band sequential format. In doing so, a new concept, called causal band correlation matrix (CBCM), is introduced to replace the global sample correlation matrix R. It is a global correlation matrix formed by only those bands that were already visited up to the band currently being processed while excluding bands yet to be visited in the future. The proposed PBP-CEM allows CEM to be processed whenever bands are available, without waiting for completing band collection. With such an advantage, CEM has potential in data transmission and communication, specifically in satellite data processing. [ABSTRACT FROM PUBLISHER]

In this paper, we obtain performance guarantees for modified-CS and for its improved version, modified-CS-Add-LS-Del, for recursive reconstruction of a time sequence of sparse signals from a reduced set of noisy measurements available at each time. Under mild assumptions, we show that the support recovery error of both algorithms is bounded by a time-invariant and small value at all times. The same is also true for the reconstruction error. Under a slow support change assumption: 1) the support recovery error bound is small compared with the support size and 2) our results hold under weaker assumptions on the number of measurements than what \ell 1 minimization for noisy data needs. We first give a general result that only assumes a bound on support size, number of support changes, and number of small magnitude nonzero entries at each time. Later, we specialize the main idea of these results for two sets of signal change assumptions that model the class of problems in which a new element that is added to the support either gets added at a large initial magnitude or its magnitude slowly increases to a large enough value within a finite delay. Simulation experiments are shown to back up our claims. [ABSTRACT FROM PUBLISHER]

A crucial aspect of time?frequency (TF) analysis is the identification of separate components in a multicomponent signal. The Wigner?Ville distribution is the classical tool for representing such signals, but it suffers from cross-terms. Other methods, which are members of Cohen?s class of distributions, also aim to remove the cross-terms by masking the ambiguity function (AF), but they result in reduced resolution. Most practical time-varying signals are in the form of weighted trajectories on the TF plane, and many others are sparse in nature. Therefore, in recent studies the problem is cast as TF distribution reconstruction using a subset of AF domain coefficients and sparsity assumption. Sparsity can be achieved by constraining or minimizing the l1 norm. In this article, an l1 minimization approach based on projections onto convex sets is proposed to obtain a high-resolution, cross-term-free TF distribution for a given signal. The new method does not require any parameter adjustment to obtain a solution. Experimental results are presented. [ABSTRACT FROM AUTHOR]

Tailoring nearest neighbors algorithms to boosting is an important problem. Recent papers study an approach, unn, which provably minimizes particular convex surrogates under weak assumptions. However, numerical issues make it necessary to experimentally tweak parts of the unn algorithm, at the possible expense of the algorithm’s convergence and performance. In this paper, we propose a lightweight Newton-Raphson alternative optimizing proper scoring rules from a very broad set, and establish formal convergence rates under the boosting framework that compete with those known for unn. To the best of our knowledge, no such boosting-compliant convergence rates were previously known in the popular Gentle Adaboost’s lineage. We provide experiments on a dozen domains, including Caltech and SUN computer vision databases, comparing our approach to major families including support vector machines, (Ada)boosting and stochastic gradient descent. They support three major conclusions: (i) gnnb significantly outperforms unn , in terms of convergence rate and quality of the outputs, (ii) gnnb performs on par with or better than computationally intensive large margin approaches, (iii) on large domains that rule out those latter approaches for computational reasons, gnnb provides a simple and competitive contender to stochastic gradient descent. Experiments include a divide-and-conquer improvement of gnnb exploiting the link with proper scoring rules optimization. [ABSTRACT FROM AUTHOR]

In the last few years, image classification has become an incredibly active research topic, with widespread applications. Most methods for visual recognition are fully supervised, as they make use of bounding boxes or pixelwise segmentations to locate objects of interest. However, this type of manual labeling is time consuming, error prone and it has been shown that manual segmentations are not necessarily the optimal spatial enclosure for object classifiers. This paper proposes a weakly-supervised system for multi-label image classification. In this setting, training images are annotated with a set of keywords describing their contents, but the visual concepts are not explicitly segmented in the images. We formulate the weakly-supervised image classification as a low-rank matrix completion problem. Compared to previous work, our proposed framework has three advantages: (1) Unlike existing solutions based on multiple-instance learning methods, our model is convex. We propose two alternative algorithms for matrix completion specifically tailored to visual data, and prove their convergence. (2) Unlike existing discriminative methods, our algorithm is robust to labeling errors, background noise and partial occlusions. (3) Our method can potentially be used for semantic segmentation. Experimental validation on several data sets shows that our method outperforms state-of-the-art classification algorithms, while effectively capturing each class appearance. [ABSTRACT FROM AUTHOR]

Bounded Component Analysis (BCA) is a recent framework which enables development of methods for the separation of dependent as well as independent sources from their mixtures. This paper extends a recent geometric BCA approach introduced for the instantaneous mixing problem to the convolutive mixing problem. The paper proposes novel deterministic convolutive BCA frameworks for the blind source extraction and blind source separation of convolutive mixtures of sources which allows the sources to be potentially nonstationary. The global maximizers of the proposed deterministic BCA optimization settings are proved to be perfect separators. The paper also illustrates that the iterative algorithms corresponding to these frameworks are capable of extracting/separating convolutive mixtures of not only independent sources but also dependent (even correlated) sources in both component (space) and sample (time) dimensions through simulations based on a Copula distributed source system. In addition, even when the sources are independent, it is shown that the proposed BCA approach have the potential to provide improvement in separation performance especially for short data records based on the setups involving convolutive mixtures of digital communication sources. [ABSTRACT FROM PUBLISHER]

The class of Fourier matrices is of special importance in compressed sensing (CS). This paper concerns deterministic construction of CS matrices from Fourier matrices. Using Katz’ character sum estimation, we are able to design a deterministic procedure to select rows from a Fourier matrix to form a good CS matrix for sparse recovery. The sparsity bound in our construction is similar to that of binary CS matrices constructed by DeVore, which greatly improves previous results for CS matrices from Fourier matrices. Our approach also provides more flexibility in terms of the dimension of CS matrices. This paper also contains a useful improvement to Katz’ character sum estimation for quadratic extensions, with an elementary and transparent proof. Based on this improvement, we construct a class of special CS matrices consisting of partial Fourier matrices whose columns are a union of orthonormal bases. As a consequence, our construction yields an approximately mutually unbiased bases from Fourier matrices which is of particular interest to quantum information theory. Some numerical examples are also included. [ABSTRACT FROM PUBLISHER]

We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same size and block length. Examples of these universally optimal codes include Hamming, Golay, and Reed-Solomon codes, among many others, and this helps to explain their robustness as the channel model varies. Universal optimality of these codes is equivalent to minimality of their binomial moments, which has been proved in many cases by Ashikhmin and Barg. We highlight connections with mathematical physics and the analogy between these results and previous work by Cohn and Kumar in the continuous setting, and we develop a framework for optimizing the linear programming bounds. Furthermore, we show that if these bounds prove a code is universally optimal, then the code remains universally optimal even if one codeword is removed. [ABSTRACT FROM AUTHOR]

Automatic target detection is an important application in the hyperspectral image processing field. It is currently known that any test pixels in hyperspectral images can be represented within a spectral dictionary using appropriate sparse coefficients. Based on this assumption, some sparsity-based algorithms are developed for hyperspectral detection. This kind of sparse learning method attempts to find the sparse representation from a spectral library, i.e., a dictionary data set from which useful information is extracted. Among these algorithms, the iteratively reweighted least squares (IRLS) strategy is believed to be a simple and useful tool for sparse representation. However, when dealing with the hyperspectral data, the dictionary for sparse learning is usually high-dimensional which dramatically increases the scale and complexity of sparse learning. In such cases, most sparsity-based algorithms including the IRLS strategy lost their efficacy. To deal with this situation, we propose a discriminative IRLS algorithm, called inner-product-based discriminative IRLS detector (IDIRLSD), which decreases the scale and complexity problem by discriminatively seeking a subdictionary that retains the most critical information. Also, IDIRLSD applies a convex minimization for approximately solving the sparse recovery problem. A weighted ${{\mmb {\ell}}_{\bf 1}}$ minimization is relaxed and solved by IRLS strategy. The proposed algorithm applies an inner-product-based function for constructing the small-scale weighted ${{\mmb {\ell}}_{\bf 1}}$ minimization with respect to the subdictionary. The solution provided by IDIRLSD is then applied to label the test pixel as target or background. Experimental results from both synthetic and real hyperspectral data demonstrate the improved efficacy of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a reweighted low-rank matrix recovery method and demonstrate its application for robust image restoration. In the literature, principal component pursuit solves low-rank matrix recovery problem via a convex program of mixed nuclear norm and \ell1 norm. Inspired by reweighted \ell1 minimization for sparsity enhancement, we propose reweighting singular values to enhance low rank of a matrix. An efficient iterative reweighting scheme is proposed for enhancing low rank and sparsity simultaneously and the performance of low-rank matrix recovery is prompted greatly. We demonstrate the utility of the proposed method both on numerical simulations and real images/videos restoration, including single image restoration, hyperspectral image restoration, and background modeling from corrupted observations. All of these experiments give empirical evidence on significant improvements of the proposed algorithm over previous work on low-rank matrix recovery. [ABSTRACT FROM PUBLISHER]