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Image set recognition has been widely applied in many practical problems like real-time video retrieval and image caption tasks. Due to its superior performance, it has grown into a significant topic in recent years. However, images with complicated variations, e.g., postures and human ages, are difficult to address, as these variations are continuous and gradual with respect to image appearance. Consequently, the crucial point of image set recognition is to mine the intrinsic connection or structural information from the image batches with variations. In this work, a Discriminant Residual Analysis (DRA) method is proposed to improve the classification performance by discovering discriminant features in related and unrelated groups. Specifically, DRA attempts to obtain a powerful projection which casts the residual representations into a discriminant subspace. Such a projection subspace is expected to magnify the useful information of the input space as much as possible, then the relation between the training set and the test set described by the given metric or distance will be more precise in the discriminant subspace. We also propose a nonfeasance strategy by defining another approach to construct the unrelated groups, which help to reduce furthermore the cost of sampling errors. Two regularization approaches are used to deal with the probable small sample size problem. Extensive experiments are conducted on benchmark databases, and the results show superiority and efficiency of the new methods. [ABSTRACT FROM AUTHOR]

In Gaussian measurement models, the measurements are given by a known function of the unknown parameter vector, contaminated by additive zero-mean Gaussian noise. When the function is linear, the resulting maximum likelihood estimate (MLE) is well-known to be efficient [unbiased, with a mean square estimation error (MSE) matrix attaining the Cramér–Rao lower bound (CRLB)]. However, when the function is nonlinear, the MLE is only asymptotically efficient. The classical derivation of its asymptotic efficiency uses a first-order perturbation analysis, relying on a “small-errors” assumption, which under subasymptotic conditions turns inaccurate, rendering the MLE generally biased and inefficient. Although a more accurate (higher-order) performance analysis for such cases is of considerable interest, the associated derivations are rather involved, requiring cumbersome notations and indexing. Building on the recent assimilation of tensor computations into signal processing literature, we exploit the tensor formulation of higher-order derivatives to derive a tractable formulation of a higher (up to third-) order perturbation analysis, predicting the bias and MSE matrix of the MLE of parameter vectors in general nonlinear models under subasymptotic conditions. We provide explicit expressions depending on the first three derivatives of the nonlinear measurement function, and demonstrate the resulting ability to predict the “efficiency gap” (relative excess MSE beyond the CRLB) in simulation experiments. We also provide MATLAB code for easy computation of our resulting expressions. [ABSTRACT FROM AUTHOR]

Sign information is the key for overcoming the inevitable saturation error in compressive sensing system, which causes loss of information and may result in great bias. For sparse signal recovery from saturation, we propose to use linear loss to improve the effectiveness from the existing methods that utilize hard constraints/hinge loss for sign consistency. Due to the use of linear loss, analytical solution in the update progress is obtained and some nonconvex penalties are applicable, e.g., minimax concave penalty, $\ell _0$ norm, and sorted $\ell _1$ norm. Theoretical analysis reveals that the estimation error can still be bounded. Generally, with linear loss and nonconvex penalties, the recovery performance can be significantly improved and the computational time is also largely saved, which is verified by the numerical experiments. [ABSTRACT FROM AUTHOR]

This paper proposes a rigorous anomaly detection scheme, developed to spot power system operational changes which are inconsistent with the models used by operators. This novel technique relies on a state observer, with guaranteed estimation error convergence, suitable to be implemented in real time, and it has been developed to fully address this important issue in power systems. The proposed method is fitted to the highly nonlinear characteristics of the network, with the states of the nonlinear generator model being estimated by means of a linear time-varying estimation scheme. Given the reliance of the existing dynamic security assessment tools in industry on nominal power system models, the suggested methodology addresses cases when there is deviation from assumed system dynamics, enhancing operators’ awareness of system operation. It is based on a decision scheme relying on analytical computation of thresholds, not involving empirical criteria which are likely to introduce inaccurate outcomes. Since false-alarms are guaranteed to be absent, the proposed technique turns out to be very useful for system monitoring and control. The effectiveness of the anomaly detection algorithm is shown through detailed realistic case studies in two power system models. [ABSTRACT FROM AUTHOR]

In this paper, we propose an open-loop unequal-error-protection querying policy based on superposition coding for the noisy 20 questions problem. In this problem, a player wishes to successively refine an estimate of the value of a continuous random variable by posing binary queries and receiving noisy responses. When the queries are designed non-adaptively as a single block and the noisy responses are modeled as the output of a binary symmetric channel, the 20 questions problem can be mapped to an equivalent problem of channel coding with unequal error protection (UEP). A new non-adaptive querying strategy based on UEP superposition coding is introduced, whose estimation error decreases with an exponential rate of convergence that is significantly better than that of the UEP repetition coding introduced by Variani et al. (2015). With the proposed querying strategy, the rate of exponential decrease in the number of queries matches the rate of a closed-loop adaptive scheme, where queries are sequentially designed with the benefit of feedback. Furthermore, the achievable error exponent is significantly better than that of random block codes employing equal error protection. [ABSTRACT FROM AUTHOR]

Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in \mathbb R^d with an optimal number of samples. We generalize this problem to the case of spatial signals, where the sampling cost is a function of both the number of samples taken and the distance traveled during estimation. This is motivated by our work studying regions of low oxygen concentration in the Great Lakes. We show that for one-dimensional threshold classifiers, a tradeoff between the number of samples taken and distance traveled can be achieved using a generalization of binary search, which we refer to as quantile search. We characterize both the estimation error after a fixed number of samples and the distance traveled in the noiseless case, as well as the estimation error in the case of noisy measurements. We illustrate our results in both simulations and experiments and show that our method outperforms existing algorithms in a large range of sampling scenarios. [ABSTRACT FROM AUTHOR]

We show that the rate regions achieved by linear-feedback coding schemes over dual multi-antenna Gaussian multi-access channels (MACs) and broadcast channels (BCs) with independent noises coincide. By dual here we mean: •

the channel matrices of the MAC and the BC are transposes of each other and [ABSTRACT FROM PUBLISHER]

This paper establishes a nearly optimal algorithm for denoising a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary. We show how to compute the estimator via semidefinite programming and provide guarantees on its mean-squared error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semidefinite programming approach outperforms three classical spectral estimation techniques. [ABSTRACT FROM PUBLISHER]