Image denoising based on a probabilistic model of local image patches has been employed by various researchers, and recently a deep (denoising) autoencoder has been proposed by Burger et al. [2012] and Xie et al. [2012] as a good model for this. In this paper, we propose that another popular family of models in the field of deep learning, called Boltzmann machines, can perform image denoising as well as, or in certain cases of high level of noise, better than denoising autoencoders. We empirically evaluate the two models on three different sets of images with different types and levels of noise. Throughout the experiments we also examine the effect of the depth of the models. The experiments confirmed our claim and revealed that the performance can be improved by adding more hidden layers, especially when the level of noise is high.

Recently, the deep-belief-networks (DBN) based voice activity detection (VAD) has been proposed. It is powerful in fusing the advantages of multiple features, and achieves the state-of-the-art performance. However, the deep layers of the DBN-based VAD do not show an apparent superiority to the shallower layers. In this paper, we propose a denoising-deep-neural-network (DDNN) based VAD to address the aforementioned problem. Specifically, we pre-train a deep neural network in a special unsupervised denoising greedy layer-wise mode, and then fine-tune the whole network in a supervised way by the common back-propagation algorithm. In the pre-training phase, we take the noisy speech signals as the visible layer and try to extract a new feature that minimizes the reconstruction cross-entropy loss between the noisy speech signals and its corresponding clean speech signals. Experimental results show that the proposed DDNN-based VAD not only outperforms the DBN-based VAD but also shows an apparent performance improvement of the deep layers over shallower layers.

This paper investigates the concept of symmetry and its role in problem solving. It first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given precise definitions of problems, it is relatively straightforward to construct a search process for finding solutions. Finally this paper attempts to exploit the concept of symmetry in improving problem solving.

Modeling spike firing assumes that spiking statistics are Poisson, but real data violates this assumption. To capture non-Poissonian features, in order to fix the inevitable inherent irregularity, researchers rescale the time axis with tedious computational overhead instead of searching for another distribution. Spikes or action potentials are precisely-timed changes in the ionic transport through synapses adjusting the synaptic weight, successfully modeled and developed as a memristor. Memristance value is multiples of initial resistance. This reminds us with the foundations of quantum mechanics. We try to quantize potential and resistance, as done with energy. After reviewing Planck curve for blackbody radiation, we propose the quantization equations. We introduce and prove a theorem that quantizes the resistance. Then we define the tyke showing its basic characteristics. Finally we give the basic transformations to model spiking and link an energy quantum to a tyke. Investigation shows how this perfectly models the neuron spiking, with over 97% match.

Negation as failure and incomplete information in logic programs have been studied by many researchers, mainly because of their role in the foundations of declarative reading of logic programming. This paper gives a review of some of the definitions of the concepts related to of the declarative reading of logic programming. Then, the paper provides a framework to overcome misleads and to solve a misleading case study. The paper begins with reviewing the relevant work of contributions to logic programming emphasizing many concepts such as negation as failure, closed world assumption, incomplete information, and their consequences (Section 2). Then we comment on the standard definitions of the relevant logic programming concepts such as: compound terms, substitution, common instance, facts, rules, reduction, variables quantification, unifier, Most General Unifier (MGU), computation, and structured data (Section 3). Then we briefly discuss the semantics of logic programming. A logic program can have many semantics according the point of view. The common semantics are operational, denotational, and declarative (Section 4).

Covering is an important type of data structure while covering-based rough sets provide an efficient and systematic theory to deal with covering data. In this paper, we use boolean matrices to represent and axiomatize three types of covering approximation operators. First, we define two types of characteristic matrices of a covering which are essentially square boolean ones, and their properties are studied. Through the characteristic matrices, three important types of covering approximation operators are concisely equivalently represented. Second, matrix representations of covering approximation operators are used in boolean matrix decomposition. We provide a sufficient and necessary condition for a square boolean matrix to decompose into the boolean product of another one and its transpose. And we develop an algorithm for this boolean matrix decomposition. Finally, based on the above results, these three types of covering approximation operators are axiomatized using boolean matrices. In a word, this work borrows extensively from boolean matrices and present a new view to study covering-based rough sets.

We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we show that it is non-trivial to select a good estimator without knowledge about the distributions of the random variables. We investigate and bound the bias and variance of the aforementioned estimators and prove consistency. The variance of cross validation can be significantly reduced, but not without risking a large bias. The bias and variance of different variants of cross validation are shown to be very problem-dependent, and a wrong choice can lead to very inaccurate estimates.

Imaging devices such as telescopes and microscopes collect incoming light using lenses or mirrors of finite size. This finite size imposes a finite aperture on the light that reaches the optical system, leading to effects of diffraction. In particular, diffraction ensures that the image of a point can never be a point. For instance, an imaging system using a lens with an F -number f/D (where f is the focal length, and D is the diameter of the circular aperture) has an impulse response function (Airy disk) whose radius is 1.22λf/D on the sensor, where λ is the wave length of the light (for simplicity, assumed to be monochromatic). Another way to express the same insight uses the transfer function. For a lens focused at infinity, the transfer function is constant within a circle of radius ν 1/(2λf/D), and zero outside [23, p. 136]. This means, in a nutshell, that if we try to image a sinusoidal pattern with spatial frequency larger than ν, diffraction will annihilate that pattern. Likewise, if we decompose a general object into spatial frequencies by Fourier analysis, all components larger than ν will vanish. This article has been accepted for publication at the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Portland, 2013.

In recent years, the problem of detecting communities in networks has received a large amount of attention, with important applications in the social and biological sciences, among others (Fortunato, 2010). The vast majority of this expansive literature focuses on developing realistic models of (random) networks (Albert and Barabási, 2002; Barabási and Albert, 1999), on designing methods for extracting communities from such networks (Girvan and Newman, 2002; Newman, 2006; Reichardt and Bornholdt, 2006) and on fitting models to network data (Bickel et al., 2011). The underlying model is that of graph G (E,V), where E is the set of edges and V is the set of nodes. For example, in a social network, a node would represent an individual and an edge between two nodes would symbolize a friendship or kinship of some sort shared by these two individuals. In the literature just mentioned, almost all the methodology has concentrated on devising graph partitioning methods, with the end goal of clustering the nodes in V into groups with strong inner-connectivity and weak inter-connectivity (Bickel and Chen, 2009; Lancichinetti and Fortunato, 2009; Newman and Girvan, 2004).

Motivated by social balance theory, we develop a theory of link classification in signed networks using the correlation clustering index as measure of label regularity. We derive learning bounds in terms of correlation clustering within three fundamental transductive learning settings: online, batch and active. Our main algorithmic contribution is in the active setting, where we introduce a new family of efficient link classifiers based on covering the input graph with small circuits. These are the first active algorithms for link classification with mistake bounds that hold for arbitrary signed networks.