Related papers: Recovering Hidden Components in Multimodal Data wi…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
Learning multimodal representations is a fundamentally complex research problem due to the presence of multiple heterogeneous sources of information. Although the presence of multiple modalities provides additional valuable information,…
Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…
Many scientific areas are faced with the challenge of extracting information from large, complex, and highly structured data sets. A great deal of modern statistical work focuses on developing tools for handling such data. This paper…
We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…
Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
Manifold learning techniques for dynamical systems and time series have shown their utility for a broad spectrum of applications in recent years. While these methods are effective at learning a low-dimensional representation, they are often…
A key competence for open-ended learning is the formation of increasingly abstract representations useful for driving complex behavior. Abstract representations ignore specific details and facilitate generalization. Here we consider the…
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…
Multimodal representation learning has demonstrated remarkable potential in enabling models to process and integrate diverse data modalities, such as text and images, for improved understanding and performance. While the medical domain can…
Developing effective multimodal data fusion strategies has become increasingly essential for improving the predictive power of statistical machine learning methods across a wide range of applications, from autonomous driving to medical…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these…
Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve…
Representation of data on mixed variables, numerical and categorical types to get suitable feature map is a challenging task as important information lies in a complex non-linear manifold. The feature transformation should be able to…
We propose a compact and effective framework to fuse multimodal features at multiple layers in a single network. The framework consists of two innovative fusion schemes. Firstly, unlike existing multimodal methods that necessitate…
Multi-modal learning has shown exceptional performance in various tasks, especially in medical applications, where it integrates diverse medical information for comprehensive diagnostic evidence. However, there still are several challenges…
Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps…