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The notion of local intrinsic dimensionality (LID) is an important advancement in data dimensionality analysis, with applications in data mining, machine learning and similarity search problems. Existing distance-based LID estimators were…

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential…

This article introduces the Tensor Network B-spline model for the regularized identification of nonlinear systems using a nonlinear autoregressive exogenous (NARX) approach. Tensor network theory is used to alleviate the curse of…

Network Intrusion Detection (NID) remains a key area of research within the information security community, while also being relevant to Machine Learning (ML) practitioners. The latter generally aim to detect attacks using network features,…

Nuclear Magnetic Resonance (NMR) spectroscopy, which is modeled as the sum of damped exponential signals, has become an indispensable tool in various scenarios, such as the structure and function determination, chemical analysis, and…

Low-rank matrix recovery has found many applications in science and engineering such as machine learning, signal processing, collaborative filtering, system identification, and Euclidean embedding. But the low-rank matrix recovery problem…

This paper studies the problem of, given the structure of a linear-time invariant system and a set of possible inputs, finding the smallest subset of input vectors that ensures system's structural controllability. We refer to this problem…

In this paper, we study the problem of recovering two unknown signals from their convolution, which is commonly referred to as blind deconvolution. Reformulation of blind deconvolution as a low-rank recovery problem has led to multiple…

Node classification in structural networks has been proven to be useful in many real world applications. With the development of network embedding, the performance of node classification has been greatly improved. However, nearly all the…

Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…

The singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields. Myriad applications including clustering, classification, and dimensionality reduction involve studying and exploiting the geometric…

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…

Trained neural networks (NN) are attractive as surrogate models to replace costly calculations in physical simulations, but are often unknowingly applied to states not adequately represented in the training dataset. We present the novel…

Detection of surgical instruments plays a key role in ensuring patient safety in minimally invasive surgery. In this paper, we present a novel method for 2D vision-based recognition and pose estimation of surgical instruments that…

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…

Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is…

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…

We address the problem of learning the parameters of a mean square stable switched linear systems (SLS) with unknown latent space dimension, or \textit{order}, from its noisy input--output data. In particular, we focus on learning a good…