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Recently, Hyperspectral Image (HSI) classification has attracted increasing attention in remote sensing. However, HSI data are inherently high-dimensional but low-rank, with discriminative information concentrated on a low-dimensional…

The human brain can be considered as complex networks, composed of various regions that continuously exchange their information with each other, forming the brain network graph, from which nodes and edges are extracted using resting-state…

This paper focuses on hyperspectral image (HSI) super-resolution that aims to fuse a low-spatial-resolution HSI and a high-spatial-resolution multispectral image to form a high-spatial-resolution HSI (HR-HSI). Existing deep learning-based…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

Other than vector representations, the direct objects of human cognition are generally high-order tensors, such as 2D images and 3D textures. From this fact, two interesting questions naturally arise: How does the human brain represent…

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…

The reconstruction of a high resolution image given a low resolution observation is an ill-posed inverse problem in imaging. Deep learning methods rely on training data to learn an end-to-end mapping from a low-resolution input to a…

Hyperspectral images (HSI) contain a wealth of information over hundreds of contiguous spectral bands, making it possible to classify materials through subtle spectral discrepancies. However, the classification of this rich spectral…

Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…

Classifying hyperspectral images (HSIs) is a complex task in remote sensing due to the high-dimensional nature and volume of data involved. To address these challenges, we propose the Spectral-Spatial non-Linear Model, a novel framework…

Understanding the reasons for the success of deep neural networks trained using stochastic gradient-based methods is a key open problem for the nascent theory of deep learning. The types of data where these networks are most successful,…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…

Classical nonlinear dimensionality reduction (NLDR) techniques like t-SNE, Isomap, and LLE excel at creating low-dimensional embeddings for data visualization but fundamentally lack the ability to map these embeddings back to the original…

Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…

Recent work in Deep Learning has re-imagined the representation of data as functions mapping from a coordinate space to an underlying continuous signal. When such functions are approximated by neural networks this introduces a compelling…

Learning-based single image super-resolution (SISR) methods are continuously showing superior effectiveness and efficiency over traditional model-based methods, largely due to the end-to-end training. However, different from model-based…

Deep learning models for medical data are typically trained using task specific objectives that encourage representations to collapse onto a small number of discriminative directions. While effective for individual prediction problems, this…

Hyperspectral Imaging (HSI) captures rich spectral information across contiguous wavelength bands, supporting applications in precision agriculture, environmental monitoring, and autonomous driving. However, its high dimensionality poses…

High-dimensional hyperspectral imaging (HSI) enables the visualization of ultrafast molecular dynamics and complex, heterogeneous spectra. However, applying this capability to resolve spatially varying vibrational couplings in…