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Hyperspectral image analysis often requires selecting the most informative bands instead of processing the whole data without losing the key information. Existing band reduction (BR) methods have the capability to reveal the nonlinear…

Recent advance in Dense Retrieval (DR) techniques has significantly improved the effectiveness of first-stage retrieval. Trained with large-scale supervised data, DR models can encode queries and documents into a low-dimensional dense space…

Color information is the most commonly used prior knowledge for depth map super-resolution (DSR), which can provide high-frequency boundary guidance for detail restoration. However, its role and functionality in DSR have not been fully…

The goal of dimension reduction tools is to construct a low-dimensional representation of high-dimensional data. These tools are employed for a variety of reasons such as noise reduction, visualization, and to lower computational costs.…

Single image rain streaks removal has recently witnessed substantial progress due to the development of deep convolutional neural networks. However, existing deep learning based methods either focus on the entrance and exit of the network…

One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in…

Recent advances in machine learning allow us to analyze and describe the content of high-dimensional data like text, audio, images or other signals. In order to visualize that data in 2D or 3D, usually Dimensionality Reduction (DR)…

Data-driven problem solving in many real-world applications involves analysis of time-dependent multivariate data, for which dimensionality reduction (DR) methods are often used to uncover the intrinsic structure and features of the data.…

Synthetic Aperture Radar (SAR) imagery enables all-weather, day-and-night Earth observation; however, it remains difficult to interpret due to speckle noise and other intrinsic imaging artifacts. Sentinel-1 (S1) constitutes one of the most…

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…

Three-dimensional (3D) object reconstruction based on differentiable rendering (DR) is an active research topic in computer vision. DR-based methods minimize the difference between the rendered and target images by optimizing both the shape…

High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…

Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we…

We describe an efficient domain decomposition-based framework for nonlinear multiscale PDE problems. The framework is inspired by manifold learning techniques and exploits the tangent spaces spanned by the nearest neighbors to compress…

A numerical framework is developed to solve various types of PDEs on complicated domains, including steady and time-dependent, non-linear and non-local PDEs, with different boundary conditions that can also include non-linear and non-local…

Deep diffeomorphic registration faces significant challenges for high-dimensional images, especially in terms of memory limits. Existing approaches either downsample original images, or approximate underlying transformations, or reduce…

Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…

Neural rendering has garnered substantial attention owing to its capacity for creating realistic 3D scenes. However, its applicability to extensive scenes remains challenging, with limitations in effectiveness. In this work, we propose the…

Dimensionality reduction can distort vector space properties such as orthogonality and linear independence, which are critical for tasks including cross-modal retrieval, clustering, and classification. We propose a Relationship Preserving…

With the proliferation of Graph Neural Network (GNN) methods stemming from contrastive learning, unsupervised node representation learning for graph data is rapidly gaining traction across various fields, from biology to molecular dynamics,…