Related papers: Dimension-free Concentration Bounds on Hankel Matr…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen-Ward, and they are similar in spirit to the results of…

Estimation of a sparse spectral precision matrix, the inverse of a spectral density matrix, is a canonical problem in frequency-domain analysis of high-dimensional time series (HDTS), with applications in neurosciences and environmental…

This letter introduces a pioneering, training-free and explainable framework for High-Resolution Range Profile (HRRP) automatic target recognition (ATR) utilizing large-scale pre-trained Large Language Models (LLMs). Diverging from…

Scattering obscures information carried by wave by producing a speckle pattern, posing a common challenge across various fields, including microscopy and astronomy. Traditional methods for extracting information from speckles often rely on…

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral…

Deep learning has established the state of the art in multiple fields, including hyperspectral image analysis. However, training large-capacity learners to segment such imagery requires representative training sets. Acquiring such data is…

We give an algorithm for learning a mixture of {\em unstructured} distributions. This problem arises in various unsupervised learning scenarios, for example in learning {\em topic models} from a corpus of documents spanning several topics.…

Spectral functions of large matrices contains important structural information about the underlying data, and is thus becoming increasingly important. Many times, large matrices representing real-world data are \emph{sparse} or \emph{doubly…

We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra…

This paper proposes a probabilistic deep metric learning (PDML) framework for hyperspectral image classification, which aims to predict the category of each pixel for an image captured by hyperspectral sensors. The core problem for…

The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…

Why depth yields a genuine computational advantage over shallow methods remains a central open question in learning theory. We study this question in a controlled high-dimensional Gaussian setting, focusing on compositional target…

Many canonical machine learning problems boil down to a convex optimization problem with a finite sum structure. However, whereas much progress has been made in developing faster algorithms for this setting, the inherent limitations of…

This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics;…

Hyperspectral imaging, also known as image spectrometry, is a landmark technique in geoscience and remote sensing (RS). In the past decade, enormous efforts have been made to process and analyze these hyperspectral (HS) products mainly by…

Random matrix theory, which characterizes spectral distributions of infinitely large matrices, plays a central role across diverse fields, including high-dimensional data analysis, ecology, neuroscience, and machine learning. Among its key…

Hyperspectral image (HSI) classification is one of the most active research topics and has achieved promising results boosted by the recent development of deep learning. However, most state-of-the-art approaches tend to perform poorly when…

This contribution revisits the classical approximate realization problem, which involves determining matrices of a state-space model based on estimates of a truncated series of Markov parameters. A Hankel matrix built up by these Markov…