Related papers: Learning Low-Dimensional Nonlinear Structures from…

Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…

This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…

High-dimensional data are ubiquitous, with examples ranging from natural images to scientific datasets, and often reside near low-dimensional manifolds. Leveraging this geometric structure is vital for downstream tasks, including signal…

The profusion of spectral bands generated by the acquisition process of hyperspectral images generally leads to high computational costs. Such difficulties arise in particular with nonlinear unmixing methods, which are naturally more…

This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…

Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel…

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…

This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

Two-dimensional electronic spectroscopy (2DES) has enabled significant discoveries in both biological and synthetic energy-transducing systems. Although deriving chemical information from 2DES is a complex task, machine learning (ML) offers…

This paper introduces a novel nonparametric framework for data imputation, coined multilinear kernel regression and imputation via the manifold assumption (MultiL-KRIM). Motivated by manifold learning, MultiL-KRIM models data features as a…

A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…

Noiseless subsystems offer a general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. A paradigmatic class of error models displaying non-trivial symmetries emerges under…

Network embedding is the process of learning low-dimensional representations for nodes in a network, while preserving node features. Existing studies only leverage network structure information and focus on preserving structural features.…

We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the…

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…

While neural networks have made significant strides in many AI tasks, they remain vulnerable to a range of noise types, including natural corruptions, adversarial noise, and low-resolution artifacts. Many existing approaches focus on…