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We introduce a novel discrete signal processing framework, called discrete-lattice SP, for signals indexed by a finite lattice. A lattice is a partially ordered set that supports a meet (or join) operation that returns the greatest element below two given elements. Discrete-lattice SP chooses the meet as shift operation and derives associated notion of (meet-invariant) convolution, Fourier transform, frequency response, and a convolution theorem. Examples of lattices include sets of sets that are closed under intersection and trees.

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The spectral method is an important approach for signal esti- mation that is often used as an initialization to iterative methods as well as a stand-alone estimator, where the signal is estimated by the top eigenvector of certain carefully-constructed data matrix. A re- cent line of work has characterized the asymptotic behavior of such data matrices used in spectral methods, which reveals an interesting phase transition phenomenon: there exists a critical sampling thresh- old below which the estimate of the spectral method is uninforma- tive.

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Squared-loss mutual information (SMI) is a surrogate of Shannon mutual information that is more advantageous for estimation. On the other hand, the coherence matrix of a pair of random vectors, a power-normalized version of the sample cross-covariance matrix, is a well-known second-order statistic found in the core of fundamental signal processing problems, such as canonical correlation analysis (CCA).

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Gaining a better understanding of how people move about and interact with their environment is an important piece of understanding human behavior. Careful analysis of individuals’ deviations or variations in movement over time can provide an awareness about changes to their physical or mental state and may be helpful in tracking performance and well-being especially in workplace settings. We propose a technique for clustering and discovering patterns in human movement data by extracting motifs from the time series of durations where participants linger at different locations.

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Applications of signal processing and control are classically model-based, involving a two-step procedure for modeling and design: first a model is built from given data, and second, the estimated model is used for filtering, estimation, or control. Both steps typically involve optimization problems, but the combination of both is not necessarily optimal, and the modeling step often ignores the ultimate design objective. Recently, data-driven alternatives are receiving attention, which employ a direct approach combining the modeling and design into a single step.

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The paper introduces a novel family of deterministic signals, the orthogonal periodic sequences (OPSs), for the identification of functional link polynomial (FLiP) filters. The novel sequences share many of the characteristics of the perfect periodic sequences (PPSs). As the PPSs, they allow the perfect identification of a FLiP filter on a finite time interval with the cross-correlation method. In contrast to the PPSs, OPSs can identify also non-orthogonal FLiP filters, as the Volterra filters.

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In this paper, we address the fundamental problem of Sparse
Bayesian Learning (SBL), where the received signal is a high-order
tensor. We furthermore consider the problem of dictionary learning
(DL), where the tensor observations are assumed to be generated
from a Kronecker structured (KS) dictionary matrix multiplied by
the sparse coefficients. Exploiting the tensorial structure results in
a reduction in the number of degrees of freedom in the learning
problem, since the dimensions of each of the factor matrices are significantly

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