Low power sensing networks often operate in open and potentially hostile environments. Ensuring that only legitimate devices communicate with the network is paramount. Authentication serves as the first line of defense in securing communication and data integrity, thereby protecting the network and devices from unauthorized access and data breaches. However, the ease of access to devices and sensors in the Internet-Of-Things (IoT) makes it easier for an attacker to replace legitimate devices and implant rogue ones in their stead; or physically tamper with devices (e.g., by moving them to another location). In this paper, we propose a resilient machine learning approach to uniquely identify deployment environments based on the link quality footprints of the devices that transmit from these environments. Our approach complements device identification based on unique RF transmission footprints. To the best of our knowledge, this is the first approach that attempts to uniquely identify the deployment environment despite considerable variations in both external and internal factors that affect signal propagation. We employ two different machine learning models, one based on a Convolutional Neural Network (CNN) and the other based on a Residual Network (ResNet). Through independent experiments involving actual deployments in five different environments in Miami, Florida (land, lake, Biscayne Bay, South Beach, and Crandon Beach), we attest that both models were able to uniquely identify the deployment environments with an average accuracy exceeding 99%. Furthermore, our models were able to distinguish between specific deployment configurations. In general, the ResNet model correctly identified the type of prototypes used with 100% accuracy (and CNN, with 98% accuracy). Both models were able to identify the types of radio used for transmission with 99% accuracy.

Hyperspectral images consist of large numbers of pixels across hundreds of spectral bands, making statistical analysis computationally challenging. However, these images often exhibit intrinsic structure that can be leveraged for efficient statistical and machine learning. We propose a novel nonlinear method for unmixing hyperspectral images. In contrast to classical methods which consider an additive linear model, we propose to represent hyperspectral spectra as probability distributions in Wasserstein space and characterize pure spectra as those that allow for typical observations to be reconstructed as entropic Wasserstein barycenters. This allows for the analysis and synthesis of hyperspectral spectra in a geometry-preserving fashion. Results on synthetic data and real HSI show important geometric features of hyperspectral spectra are preserved when utilizing our nonlinear Wasserstein unmixing scheme.

Hyperspectral images (HSI) capture rich information of large spatial scenes, yet generating labeled training data can be expensive and time-consuming. Unsupervised clustering of HSI allows for segmentation in the absence of labels and is an important problem in processing rapidly collected HSI. In order to accurately cluster noisy and high-dimensional HSI, meaningful data representations that capture latent intrinsic structure must be developed. We propose to leverage regularized dictionary learning in Wasserstein space to efficiently and accurately cluster HSI by modeling HSI pixels as probability distributions. We characterize pixels as similar if they can be synthesized as entropic Wasserstein barycenters with a common set of learned reference distributions. Our approach learns representations that preserve the geometry of the space of HSI spectra and our barycentric coding spectral clustering algorithm, which leverages these learned features, shows promise on benchmark HSI data.

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this paper, we aim to solve this problem given a minimal number of distance samples. To this end, we leverage continuous and non-convex rank minimization formulations of the problem and establish a local convergence guarantee for a variant of iteratively reweighted least squares (IRLS), which applies if a minimal random set of observed distances is provided. As a technical tool, we establish a restricted isometry property (RIP) restricted to a tangent space of the manifold of symmetric rank-$r$ matrices given random Euclidean distance measurements, which might be of independent interest for the analysis of other non-convex approaches. Furthermore, we assess data efficiency, scalability and generalizability of different reconstruction algorithms through numerical experiments with simulated data as well as real-world data, demonstrating the proposed algorithm's ability to identify the underlying geometry from fewer distance samples compared to the state-of-the-art. The Matlab code can be found at \href{https://github.com/ipsita-ghosh-1/EDG-IRLS}{github\_SEGRED}

We study the problem of determining the configuration of n points by using their distances to m nodes, referred to as anchor nodes. One sampling scheme is Nyström sampling, which assumes known distances between the anchors and between the anchors and the n points, while the distances among the n points are unknown. For this scheme, a simple adaptation of the Nyström method, which is often used for kernel approximation, is a viable technique to estimate the configuration of the anchors and the n points. In this manuscript, we propose a modified version of Nyström sampling, where the distances from every node to one central node are known, but all other distances are incomplete. In this setting, the standard Nyström approach is not applicable, necessitating an alternative technique to estimate the configuration of the anchors and the n points. We show that this problem can be framed as the recovery of a low-rank submatrix of a Gram matrix. Using synthetic and real data, we demonstrate that the proposed approach can exactly recover configurations of points given sufficient distance samples. This underscores that, in contrast to methods that rely on global sampling of distance matrices, the task of estimating the configuration of points can be done efficiently via structured sampling with well-chosen reliable anchors. Finally, our main analysis is grounded in a specific centering of the points. With this in mind, we extend previous work in Euclidean distance geometry by providing a general dual basis approach for points centered anywhere.

The unlabeled sensing problem is to solve a noisy linear system of equations under unknown permutation of the measurements. We study a particular case of the problem where the permutations are restricted to be r-local, i.e. the permutation matrix is block diagonal with r×r blocks. Assuming a Gaussian measurement matrix, we argue that the r-local permutation model is more challenging compared to a recent sparse permutation model. We propose a proximal alternating minimization algorithm for the general unlabeled sensing problem that provably converges to a first order stationary point. Applied to the r-local model, we show that the resulting algorithm is efficient. We validate the algorithm on synthetic and real datasets. We also formulate the 1-d unassigned distance geometry problem as an unlabeled sensing problem with a structured measurement matrix.

This paper considers the problem of measure estimation under the barycentric coding model (BCM), in which an unknown measure is assumed to belong to the set of Wasserstein-2 barycenters of a finite set of known measures. Estimating a measure under this model is equivalent to estimating the unknown barycentric coordinates. We provide novel geometrical, statistical, and computational insights for measure estimation under the BCM, consisting of three main results. Our first main result leverages the Riemannian geometry of Wasserstein-2 space to provide a procedure for recovering the barycentric coordinates as the solution to a quadratic optimization problem assuming access to the true reference measures. The essential geometric insight is that the parameters of this quadratic problem are determined by inner products between the optimal displacement maps from the given measure to the reference measures defining the BCM. Our second main result then establishes an algorithm for solving for the coordinates in the BCM when all the measures are observed empirically via i.i.d. samples. We prove precise rates of convergence for this algorithm—determined by the smoothness of the underlying measures and their dimensionality—thereby guaranteeing its statistical consistency. Finally, we demonstrate the utility of the BCM and associated estimation procedures in three application areas: (i) covariance estimation for Gaussian measures; (ii) image processing; and (iii) natural language processing.

A method for active learning of hyperspectral images (HSI) is proposed, which combines deep learning with diffusion processes on graphs. A deep variational autoencoder extracts smoothed, denoised features from a high-dimensional HSI, which are then used to make labeling queries based on graph diffusion processes. The proposed method combines the robust representations of deep learning with the mathematical tractability of diffusion geometry, and leads to strong performance on real HSI.

The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the problem can be formulated as a nuclear norm minimization problem. In this paper, this minimization program is recast as a matrix completion problem of a low-rank$r$Gram matrix with respect to a suitable basis. The well-known restricted isometry property cannot be satisfied in this scenario. Instead, a dual basis approach is introduced to theoretically analyze the reconstruction problem. If the Gram matrix satisfies certain coherence conditions with parameter$\nu $, the main result shows that the underlying configuration of$n$points can be recovered with very high probability from$O(nr\nu \log ^{2}(n))$uniformly random samples. Computationally, simple and fast algorithms are designed to solve the Euclidean distance geometry problem. Numerical tests on different 3-D data and protein molecules validate the effectiveness and efficiency of the proposed algorithms.