相关论文: Diffusion Self-Organizing Map on the Hypersphere

Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational…

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…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…

Diffusion-based generative methods have proven effective in modeling trajectories with offline datasets. However, they often face computational challenges and can falter in generalization, especially in capturing temporal abstractions for…

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…

We propose a variation of the self organizing map algorithm by considering the random placement of neurons on a two-dimensional manifold, following a blue noise distribution from which various topologies can be derived. These topologies…

Diffusion models have been successfully applied to robotics problems such as manipulation and vehicle path planning. In this work, we explore their application to end-to-end navigation -- including both perception and planning -- by…

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…

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…

Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…

The growing amount of data produced by simulations and observations of space physics processes encourages the use of methods rooted in Machine Learning for data analysis and physical discovery. We apply a clustering method based on…

Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric…

We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlocal diffusion operators in the basis of spherical harmonics,…

We describe the application of Semantic Segmentation by using the Self Organizing Map technique to an high spatial and spectral resolution dataset acquired along the H$\alpha$ line at 656.28 nm by the Interferometric Bi-dimensional…

In this paper, we address the problem of plausible object placement for the challenging task of realistic image composition. We propose DiffPop, the first framework that utilizes plausibility-guided denoising diffusion probabilistic model…

Diffusion-based motion planners are becoming popular due to their well-established performance improvements, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary…

Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…

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…

Problems in astrophysics, space weather research and geophysics usually need to analyze noisy big data on the sphere. This paper develops distributed filtered hyperinterpolation for noisy data on the sphere, which assigns the data fitting…