Related papers: Nonlinear Dimensionality Reduction with Diffusion …

Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…

Dimensionality reduction (DR) is characterized by two longstanding trade-offs. First, there is a global-local preservation tension: methods such as t-SNE and UMAP prioritize local neighborhood preservation, yet may distort global manifold…

In this paper, we consider an inverse problem for a nonlinear wave equation with a damping term and a general nonlinear term. This problem arises in nonlinear acoustic imaging and has applications in medical imaging and other fields. The…

Dimensionality reduction has become an important research topic as demand for interpreting high-dimensional datasets has been increasing rapidly in recent years. There have been many dimensionality reduction methods with good performance in…

Understanding the surrounding environment is fundamental in autonomous driving and robotic perception. Distinguishing between known classes and previously unseen objects is crucial in real-world environments, as done in Anomaly…

Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression,…

Deep generative models have emerged as promising tools for detecting arbitrary anomalies in data, dispensing with the necessity for manual labelling. Recently, autoregressive transformers have achieved state-of-the-art performance for…

Multispectral image analysis is a relatively promising field of research with applications in several areas, such as medical imaging and satellite monitoring. A considerable number of current methods of analysis are based on parametric…

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…

Nuclei segmentation is a fundamental but challenging task in the quantitative analysis of histopathology images. Although fully-supervised deep learning-based methods have made significant progress, a large number of labeled images are…

An active learning algorithm for the classification of high-dimensional images is proposed in which spatially-regularized nonlinear diffusion geometry is used to characterize cluster cores. The proposed method samples from estimated cluster…

This paper presents a novel methodology for generating realistic abundance maps from hyperspectral imagery using an unsupervised, deep-learning-driven approach. Our framework integrates blind linear hyperspectral unmixing with…

The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…

Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often…

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…

Remote sensing image change description represents an innovative multimodal task within the realm of remote sensing processing.This task not only facilitates the detection of alterations in surface conditions, but also provides…

This paper presents a principled approach for detecting out-of-distribution (OOD) samples in deep neural networks (DNN). Modeling probability distributions on deep features has recently emerged as an effective, yet computationally cheap…

Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…