Related papers: Deep Diffusion Maps
Medical image segmentation is crucial for accurate clinical diagnoses, yet it faces challenges such as low contrast between lesions and normal tissues, unclear boundaries, and high variability across patients. Deep learning has improved…
This paper presents a novel approach that combines the Deep Ritz Method (DRM) with Fourier feature mapping to solve minimization problems comprised of multi-well, non-convex energy potentials. These problems present computational challenges…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…
Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often…
In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…
In this paper, we address the challenging task of achieving multi-view dimensionality reduction. The goal is to effectively use the availability of multiple views for extracting a coherent low-dimensional representation of the data. The…
Large high-dimensional datasets are becoming more and more popular in an increasing number of research areas. Processing the high dimensional data incurs a high computational cost and is inherently inefficient since many of the values that…
Unsupervised learning of feature representations is a challenging yet important problem for analyzing a large collection of multimedia data that do not have semantic labels. Recently proposed neural network-based unsupervised learning…
Diffusion models excel at creating visually-convincing images, but they often struggle to meet subtle constraints inherent in the training data. Such constraints could be physics-based (e.g., satisfying a PDE), geometric (e.g., respecting…
Computational imaging is crucial in many disciplines from autonomous driving to life sciences. However, traditional model-driven and iterative methods consume large computational power and lack scalability for imaging. Deep learning (DL) is…
The challenge of mapping indoor environments is addressed. Typical heuristic algorithms for solving the motion planning problem are frontier-based methods, that are especially effective when the environment is completely unknown. However,…
We introduce {\em vector diffusion maps} (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images and shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and…
This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…
Spectral clustering and diffusion maps are celebrated dimensionality reduction algorithms built on eigen-elements related to the diffusive structure of the data. The core of these procedures is the approximation of a Laplacian through a…
Kernel-based non-linear dimensionality reduction methods, such as Local Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores, with which one can construct and study a weighted graph…
We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…
Recently, deep learning-based denoising approaches have led to dramatic improvements in low sample-count Monte Carlo rendering. These approaches are aimed at path tracing, which is not ideal for simulating challenging light transport…
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other…
Embedding of large but redundant data, such as images or text, in a hierarchy of lower-dimensional spaces is one of the key features of representation learning approaches, which nowadays provide state-of-the-art solutions to problems once…