Related papers: Diffusion Maps is not Dimensionality Reduction
A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make…
Recently, diffusion models have demonstrated impressive capabilities in text-guided and image-conditioned image generation. However, existing diffusion models cannot simultaneously generate an image and a panoptic segmentation of objects…
UMAP is a non-parametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) Compute a…
Color-guided depth map super-resolution (CDSR) improve the spatial resolution of a low-quality depth map with the corresponding high-quality color map, benefiting various applications such as 3D reconstruction, virtual reality, and…
We present a method to estimate dense depth by optimizing a sparse set of points such that their diffusion into a depth map minimizes a multi-view reprojection error from RGB supervision. We optimize point positions, depths, and weights…
Machine learning (ML) facilitates rapid channel modeling for 5G and beyond wireless communication systems. Many existing ML techniques utilize a city map to construct the radio map; however, an updated city map may not always be available.…
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…
This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear…
Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions. Notice…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
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…
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…
This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional DeepParticle (BDP) method to learn and generate solutions…
Multi-arm motion planning is fundamental for enabling arms to complete complex long-horizon tasks in shared spaces efficiently but current methods struggle with scalability due to exponential state-space growth and reliance on large…
Probabilistic Diffusion Models (PDMs) have recently emerged as a very promising class of generative models, achieving high performance in natural image generation. However, their performance relative to non-natural images, like radar-based…
This is the second article in a series of two which report on a matrix approach for ultrasound imaging in heterogeneous media. This article describes the quantification and correction of aberration, i.e. the distortion of an image caused by…
In this paper, we investigate Dimensionality reduction (DR) maps in an information retrieval setting from a quantitative topology point of view. In particular, we show that no DR maps can achieve perfect precision and perfect recall…
Discrete delta functions define the limits of attainable spatial resolution for all imaging systems. Here we construct broad, multi-dimensional discrete functions that replicate closely the action of a Dirac delta function under aperiodic…
Diffusion models have recently gained recognition for generating diverse and high-quality content, especially in image synthesis. These models excel not only in creating fixed-size images but also in producing panoramic images. However,…
We introduce a new methodology for forecasting which we call Signal Diffusion Mapping. Our approach accommodates features of real world financial data which have been ignored historically in existing forecasting methodologies. Our method…