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As human–machine teams are being considered for a variety of mixed‐initiative tasks, detecting and being responsive to human cognitive states, in particular systematic cognitive states, is among the most critical capabilities for artificial systems to ensure smooth interactions with humans and high overall team performance. Various human physiological parameters, such as heart rate, respiration rate, blood pressure, and skin conductance, as well as brain activity inferred from functional near‐infrared spectroscopy or electroencephalogram, have been linked to different systemic cognitive states, such as workload, distraction, or mind–wandering among others. Whether these multimodal signals are indeed sufficient to isolate such cognitive states across individuals performing tasks or whether additional contextual information (e.g., about the task state or the task environment) is required for making appropriate inferences remains an important open problem. In this paper, we introduce an experimental and machine learning framework for investigating these questions and focus specifically on using physiological and neurophysiological measurements to learn classifiers associated with systemic cognitive states like cognitive load, distraction, sense of urgency, mind wandering, and interference. Specifically, we describe a multitasking interactive experimental setting used to obtain a comprehensive multimodal data set which provided the foundation for a first evaluation of various standard state‐of‐the‐art machine learning techniques with respect to their effectiveness in inferring systemic cognitive states. While the classification success of these standard methods based on just the physiological and neurophysiological signals across subjects was modest, which is to be expected given the complexity of the classification problem and the possibility that higher accuracy rates might not in general be achievable, the results nevertheless can serve as a baseline for evaluating future efforts to improve classification, especially methods that take contextual aspects such as task and environmental states into account. As human‐machine teams are being considered for a variety of mixed‐initiative tasks, detecting and being responsive to human systematic cognitive states is among the most critical capabilities for artificial systems to ensure smooth interactions with humans and high overall team performance. We introduce an experimental and machine learning framework for investigating whether physiological and neurophysiological measurements are sufficient for learning classifiers associated with systemic cognitive states like cognitive load, distraction, sense of urgency, mind wandering, and interference. [ABSTRACT FROM AUTHOR]

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its elements selected uniformly at random. We propose a fast iterative algorithm, called Tubal-AltMin, that is inspired by a similar approach for low-rank matrix completion. The unknown low-tubal-rank tensor is represented as the product of two much smaller tensors with the low-tubal-rank property being automatically incorporated, and Tubal-AltMin alternates between estimating those two tensors using tensor least squares minimization. First, we note that tensor least squares minimization is different from its matrix counterpart and nontrivial as the circular convolution operator of the low-tubal-rank tensor model is intertwined with the sub-sampling operator. Secondly, the theoretical performance guarantee is challenging since Tubal-AltMin is iterative and nonconvex. We prove that 1) Tubal-AltMin generates a best rank- $r$ approximate up to any predefined accuracy $\epsilon $ at an exponential rate, and 2) for an $n \times n \times k$ tensor $\mathcal {M}$ with tubal-rank $r \ll n$ , the required sampling complexity is $O((nr^{2}k ||\mathcal {M}||_{F}^{2} \log ^{3}~n) / \overline {\sigma }_{rk}^{2})$ , where $\overline {\sigma }_{rk}$ is the $rk$ -th singular value of the block diagonal matrix representation of $\mathcal {M}$ in the frequency domain, and the computational complexity is $O(n^{2}r^{2}k^{3} \log n \log (n/\epsilon))$. Finally, on both synthetic data and real-world video data, evaluation results show that compared with tensor-nuclear norm minimization using alternating direction method of multipliers (TNN-ADMM), Tubal-AltMin-Simple (a simplified implementation of Tubal-AltMin) improves the recovery error by several orders of magnitude. In experiments, Tubal-AltMin-Simple is faster than TNN-ADMM by a factor of 5 for a $200 \times 200 \times 20$ tensor. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the problem of completion of multidimensional arrays (also referred to as tensors), in particular three-dimensional (3-D) arrays, from limited sampling. Our approach is based on a recently proposed tensor algebraic framework where 3-D tensors are treated as linear operators over the set of 2-D tensors. In this framework, one can obtain a factorization for 3-D data, referred to as the tensor singular value decomposition (t-SVD), which is similar to the SVD for matrices. t-SVD results in a notion of rank referred to as the tubal-rank. Using this approach we consider the problem of sampling and recovery of 3-D arrays with low tubal-rank. We show that by solving a convex optimization problem, which minimizes a convex surrogate to the tubal-rank, one can guarantee exact recovery with high probability as long as number of samples is of the order $O(rnk \log (nk))$ , given a tensor of size $n\times n\times k$ with tubal-rank $r$ . The conditions under which this result holds are similar to the incoherence conditions for low-rank matrix completion under random sampling. The difference is that we define incoherence under the algebraic setup of t-SVD, which is different from the standard matrix incoherence conditions. We also compare the numerical performance of the proposed algorithm with some state-of-the-art approaches on real-world datasets. [ABSTRACT FROM PUBLISHER]

In this paper, we present methods and strategies for robust detection and slowness estimation of weak compressional (P) and shear (S) waves in borehole sonic logging in noisy environments such as while logging while drilling, by proposing methods for enhancing the semblance used in the slowness time coherence method used in the logging. In this direction our contributions are two fold. First, we propose a novel class of shrinkage estimators in the discrete Radon transform domain derived from data semblance, for waveform de-noising to combat random additive noise and reflections. In this context we also identify necessary and sufficient conditions for the optimality of the proposed estimator. Our second contribution lies in developing a novel method to cancel energy propagating at the slowness of borehole modes, chiefly Stoneley, and to a lesser extent, shear, that significantly lowers the semblance of the weaker head wave arrivals. This approach is based on representing the data using time-frequency compact space-time propagators. Finally, we present an algorithm that combines the space time shrinkage in the discrete Radon transform domain and the proposed interference cancelation strategies for enhanced compressional and shear detection via semblance processing. The algorithm is validated on synthetic data and demonstrated to enhance performance on real logging while drilling field data sets. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a broadband method to extract the dispersion curves for multiple overlapping dispersive modes from borehole acoustic data under limited spatial sampling. The proposed approach exploits a first order Taylor series approximation of the dispersion curve in a band around a given (center) frequency in terms of the phase and group slowness at that frequency. Under this approximation, the acoustic signal in a given band can be represented as a superposition of broadband propagators each of which is parameterized by the slowness pair above. We then formulate a sparsity penalized reconstruction framework as follows. These broadband propagators are viewed as elements from an overcomplete dictionary representation and under the assumption that the number of modes is small compared to the size of the dictionary, it turns out that an appropriately reshaped support image of the coefficient vector synthesizing the signal (using the given dictionary representation) exhibits column sparsity. Our main contribution lies in identifying this feature and proposing a complexity regularized algorithm for support recovery with an \ell1 type simultaneous sparse penalization. Note that support recovery in this context amounts to recovery of the broadband propagators comprising the signal and hence extracting the dispersion, namely, the group and phase slownesses of the modes. In this direction we present a novel method to select the regularization parameter based on Kolmogorov–Smirnov (KS) tests on the distribution of residuals for varying values of the regularization parameter. We evaluate the performance of the proposed method on synthetic as well as real data and show its performance in dispersion extraction under presence of heavy noise and strong interference from time overlapped modes. [ABSTRACT FROM PUBLISHER]

We consider the problem of distributed target tracking in a sensor network under communication constraints between the sensor nodes, a problem that has recently received significant attention. Communication constraints limit sensor data fusion in two ways. It significantly constrains sensor communication across large distances and substantially limits the number of sensors participating in data fusion at any time instant. We explore sensor management policies, i.e., sensor selection under communication constraints, for distributed target tracking. The coupled problem of track estimation and sensor management is generally intractable and significant effort has been devoted towards proposing simple strategies under various performance criteria. In this paper, we adopt a certainty equivalent approach and separate the tasks of track estimation and sensor management. Our approach is an adaptive dynamic strategy for sensor selection that seeks to optimize a tradeoff between tracking error and communications cost. We formulate the sensor management problem for the limiting case of infinite sensor density and derive sensor selection policies for different classes of target dynamics and sensor measurements. Under assumptions of a regular dense network with homogeneous sensors, the optimal strategy is a hybrid switching strategy, where the fusion center location and reporting sensors are held stationary unless the target estimates move outside of a threshold radius around the sensors. We simulate different tracking scenarios to illustrate the performance of our algorithms on sensor networks. We show that the computational as well as the communication costs are constant and do not scale with network size. We also perform different parametric studies to illustrate the validity of our approximations. [ABSTRACT FROM AUTHOR]

This paper deals with throughput scaling laws for random ad hoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio λ(n) of achievable net- work sum capacity to the sum of the point-to-point capacities of source-destinations (S-D) pairs operating in isolation. Our focus in this paper is on fixed signal-to-noise ratio (SNR) networks, i.e., networks where the worst case SNR over the S-D pairs is fixed independent of n. For such fixed SNR networks, which include fixed area networks as a special case, we show that collaborative strategies yield a scaling law of λ(n) = Ω(1/n1/3) in contrast to multihop strategies which yield a scaling law of λ(n) = ϴ(1/√n). While networks where worst case SNR goes to zero do not preclude the possibility of collaboration, multihop strategies achieve optimal throughput. The plausible reason is that the gains due to collaboration cannot offset the effect of vanishing receive SNR. This suggests that for fixed SNR networks, a network designer should look for network protocols that exploit collaboration. [ABSTRACT FROM AUTHOR]

Highlights • We propose a TT-PCA algorithm for estimating structured subspace from the data. • TT-PCA is empirically shown to be more robust to noise as compared to PCA or Tucker-PCA. • The approach is validated on Extended YaleFace Dataset B. • Storage, computation, and classification performance tradeoffs are investigated. Abstract Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a notion of Tensor Train subspace and in this paper we propose a TT-PCA algorithm for estimating this structured subspace from the given data. By maintaining low rank tensor structure, TT-PCA is empirically more robust to noise as compared to PCA or Tucker-PCA. This is borne out numerically by testing the proposed approach on the Extended YaleFace Dataset B, MINIST Dataset, CIFAR-10 dataset. This paper shows that the TT-PCA methods achieve less storage requirements, and have computationally faster online implementation with improved classification performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose a tensor train neighborhood preserving embedding (TTNPE) to embed multidimensional tensor data into low-dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate a novel tradeoff gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior tradeoff in classification, computation, and dimensionality reduction in MNIST handwritten digits, Weizmann face datasets, and financial market datasets. [ABSTRACT FROM AUTHOR]

In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays . To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K -nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. [ABSTRACT FROM AUTHOR]

• Inspired by multi-view representation learning, we propose a scheme casting adversarial examples as a secondary view. • We propose and analyze our loss for learning representations with shared information between clean and adversarial samples. • We demonstrate that our method achieves improved robust vs. natural accuracy tradeoffs over several attacks and datasets. We consider the problem of improving the adversarial robustness of neural networks while retaining natural accuracy. Motivated by the multi-view information bottleneck formalism, we seek to learn a representation that captures the shared information between clean samples and their corresponding adversarial samples while discarding these samples' view-specific information. We show that this approach leads to a novel multi-objective loss function, and we provide mathematical motivation for its components towards improving the robust vs. natural accuracy tradeoff. We demonstrate enhanced tradeoff compared to current state-of-the-art methods with extensive evaluation on various benchmark image datasets and architectures. Ablation studies indicate that learning shared representations is key to improving performance. [ABSTRACT FROM AUTHOR]

The framework of optimal transport has been leveraged to extend the notion of rank to the multivariate setting as corresponding to an optimal transport map, while preserving desirable properties of the resulting goodness-of-fit (GoF) statistics. In particular, the rank energy (RE) and rank maximum mean discrepancy (RMMD) are distribution-free under the null, exhibit high power in statistical testing, and are robust to outliers. In this paper, we point to and alleviate some of the shortcomings of these GoF statistics that are of practical significance, namely high computational cost, curse of dimensionality in statistical sample complexity, and lack of differentiability with respect to the data. We show that all these issues are addressed by defining multivariate rank as an entropic transport map derived from the entropic regularization of the optimal transport problem, which we refer to as the soft rank. We consequently propose two new statistics, the soft rank energy (sRE) and soft rank maximum mean discrepancy (sRMMD). Given n sample data points, we provide non-asymptotic convergence rates for the sample estimate of the entropic transport map to its population version that are essentially of the order n-1/2 when the source measure is subgaussian and the target measure has compact support. This result is novel compared to existing results which achieve a rate of n-1 but crucially rely on both measures having compact support. In contrast, the corresponding convergence rate of estimating an optimal transport map, and hence the rank map, is exponential in the data dimension. We leverage these fast convergence rates to show that the sample estimates of sRE and sRMMD converge rapidly to their population versions. Combined with the computational efficiency of methods in solving the entropy-regularized optimal transport problem, these results enable efficient rank-based GoF statistical computation, even in high dimensions. Furthermore, the sample estimates of sRE and sRMMD are differentiable with respect to the data and amenable to popular machine learning frameworks that rely on gradient methods. We leverage these properties towards showcasing their utility for generative modeling on two important problems: image generation and generating valid knockoffs for controlled feature selection. [ABSTRACT FROM AUTHOR]

Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to a set of one dimensional empirical distribution functions computed from the raw input data. Interpreting this mapping in terms of Radon-type projections provides an analytical connection between the data and the density with many very useful properties including stable invertibility, fast computation, and significant theoretical grounding. Using results from the literature in geometric inverse problems we give uniqueness results and stability estimates for our methods. We subsequently extend the ideas to address problems in manifold learning and density estimation on manifolds. We introduce two new algorithms which can be readily applied to implement density estimation using Radon transforms in low dimensions or on low dimensional manifolds embedded in R d. The code for our algorithms can be found here . We test our algorithms performance on a range of synthetic 2-D density estimation problems, designed with a mixture of sharp edges and smooth features. We show that our algorithm can offer a consistently competitive performance when compared to the state–of–the–art density estimation methods from the literature. [ABSTRACT FROM AUTHOR]

Robots interacting with humans in assistive contexts have to be sensitive to human cognitive states to be able to provide help when it is needed and not overburden the human when the human is busy. Yet, it is currently still unclear which sensing modality might allow robots to derive the best evidence of human workload. In this work, we analyzed and modeled data from a multi-modal simulated driving study specifically designed to evaluate different levels of cognitive workload induced by various secondary tasks such as dialogue interactions and braking events in addition to the primary driving task. Specifically, we performed statistical analyses of various physiological signals including eye gaze, electroencephalography, and arterial blood pressure from the healthy volunteers and utilized several machine learning methodologies including k-nearest neighbor, naive Bayes, random forest, support-vector machines, and neural network-based models to infer human cognitive workload levels. Our analyses provide evidence for eye gaze being the best physiological indicator of human cognitive workload, even when multiple signals are combined. Specifically, the highest accuracy (in %) of binary workload classification based on eye gaze signals is 80.45 ∓ 3.15 achieved by using support-vector machines, while the highest accuracy combining eye gaze and electroencephalography is only 77.08 ∓ 3.22 achieved by a neural network-based model. Our findings are important for future efforts of real-time workload estimation in the multimodal human-robot interactive systems given that eye gaze is easy to collect and process and less susceptible to noise artifacts compared to other physiological signal modalities. [ABSTRACT FROM AUTHOR]

Research in tensor representation and analysis has been rising in popularity in direct response to a) the increased ability of data collection systems to store huge volumes of multidimensional data and b) the recognition of potential modeling accuracy that can be provided by leaving the data and/or the operator in its natural, multidimensional form. In recent work [1] , the authors introduced the notion of the t-product, a generalization of matrix multiplication for tensors of order three, which can be extended to multiply tensors of arbitrary order [2] . The multiplication is based on a convolution-like operation, which can be implemented efficiently using the Fast Fourier Transform (FFT). The corresponding linear algebraic framework from the original work was further developed in [3] , and it allows one to elegantly generalize all classical algorithms from numerical linear algebra. In this paper, we extend this development so that tensor–tensor products can be defined in a so-called transform domain for any invertible linear transform. In order to properly motivate this transform-based approach, we begin by defining a new tensor–tensor product alternative to the t-product. We then show that it can be implemented efficiently using DCTs, and that subsequent definitions and factorizations can be formulated by appealing to the transform domain. Using this new product as our guide, we then generalize the transform-based approach to any invertible linear transform. We introduce the algebraic structures induced by each new multiplication in the family, which is that of C ⁎ -algebras and modules. Finally, in the spirit of [4] , we give a matrix–algebra based interpretation of the new family of tensor–tensor products, and from an applied perspective, we briefly discuss how to choose a transform. We demonstrate the convenience of our new framework within the context of an image deblurring problem and we show the potential for using one of these new tensor–tensor products and resulting tensor-SVD for hyperspectral image compression. [ABSTRACT FROM AUTHOR]

Metabolomic data processing pipelines have been improving in recent years, allowing for greater feature extraction and identification. Lately, machine learning and robust statistical techniques to control false discoveries are being incorporated into metabolomic data analysis. In this paper, we introduce one such recently developed technique called aggregate knockoff filtering to untargeted metabolomic analysis. When applied to a publicly available dataset, aggregate knockoff filtering combined with typical p-value filtering improves the number of significantly changing metabolites by 25% when compared to conventional untargeted metabolomic data processing. By using this method, features that would normally not be extracted under standard processing would be brought to researchers' attention for further analysis. [ABSTRACT FROM AUTHOR]

Summary: The tensor SVD (t‐SVD) for third‐order tensors, previously proposed in the literature, has been applied successfully in many fields, such as computed tomography, facial recognition, and video completion. In this paper, we propose a method that extends a well‐known randomized matrix method to the t‐SVD. This method can produce a factorization with similar properties to the t‐SVD, but it is more computationally efficient on very large data sets. We present details of the algorithms and theoretical results and provide numerical results that show the promise of our approach for compressing and analyzing image‐based data sets. We also present an improved analysis of the randomized and simultaneous iteration for matrices, which may be of independent interest to the scientific community. We also use these new results to address the convergence properties of the new and randomized tensor method as well. [ABSTRACT FROM AUTHOR]

Significance: We demonstrated the potential of using domain adaptation on functional near-infrared spectroscopy (fNIRS) data to classify different levels of n-back tasks that involve working memory. Aim: Domain shift in fNIRS data is a challenge in the workload level alignment across different experiment sessions and subjects. To address this problem, two domain adaptation approaches—Gromov–Wasserstein (G-W) and fused Gromov–Wasserstein (FG-W) were used. Approach: Specifically, we used labeled data from one session or one subject to classify trials in another session (within the same subject) or another subject. We applied G-W for session-by-session alignment and FG-W for subject-by-subject alignment to fNIRS data acquired during different n-back task levels. We compared these approaches with three supervised methods: multiclass support vector machine (SVM), convolutional neural network (CNN), and recurrent neural network (RNN). Results: In a sample of six subjects, G-W resulted in an alignment accuracy of 68 % ± 4 % (weighted mean ± standard error) for session-by-session alignment, FG-W resulted in an alignment accuracy of 55 % ± 2 % for subject-by-subject alignment. In each of these cases, 25% accuracy represents chance. Alignment accuracy results from both G-W and FG-W are significantly greater than those from SVM, CNN, and RNN. We also showed that removal of motion artifacts from the fNIRS data plays an important role in improving alignment performance. Conclusions: Domain adaptation has potential for session-by-session and subject-by-subject alignment of mental workload by using fNIRS data. [ABSTRACT FROM AUTHOR]