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Found 20 papers, 9 papers with code
On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detection
This paper considers the use of recently proposed optimal transport-based multivariate test statistics, namely rank energy and its variant the soft rank energy derived from entropically regularized optimal transport, for the unsupervised nonparametric change point detection (CPD) problem.
Geometric Sparse Coding in Wasserstein Space
We show this approach leads to sparse representations in Wasserstein space and addresses the problem of non-uniqueness of barycentric representation.
Unsupervised Spatial-spectral Hyperspectral Image Reconstruction and Clustering with Diffusion Geometry
DSIRC then locates high-density, high-purity pixels far in diffusion distance (a data-dependent distance metric) from other high-density, high-purity pixels and treats these as cluster exemplars, giving each a unique label.
Unsupervised detection of ash dieback disease (Hymenoscyphus fraxineus) using diffusion-based hyperspectral image clustering
Ash dieback (Hymenoscyphus fraxineus) is an introduced fungal disease that is causing the widespread death of ash trees across Europe.
Active Diffusion and VCA-Assisted Image Segmentation of Hyperspectral Images
Hyperspectral images encode rich structure that can be exploited for material discrimination by machine learning algorithms.
Unsupervised Diffusion and Volume Maximization-Based Clustering of Hyperspectral Images
Hyperspectral images taken from aircraft or satellites contain information from hundreds of spectral bands, within which lie latent lower-dimensional structures that can be exploited for classifying vegetation and other materials.
Measure Estimation in the Barycentric Coding Model
Our first main result leverages the Riemannian geometry of Wasserstein-2 space to provide a procedure for recovering the barycentric coordinates as the solution to a quadratic optimization problem assuming access to the true reference measures.
Multivariate rank via entropic optimal transport: sample efficiency and generative modeling
We leverage this result to demonstrate fast convergence of sample sRE and sRMMD to their population version making them useful for high-dimensional GoF testing.
Multiscale Clustering of Hyperspectral Images Through Spectral-Spatial Diffusion Geometry
Clustering algorithms partition a dataset into groups of similar points.
A Multiscale Environment for Learning by Diffusion
To efficiently learn the multiscale structure observed in many real datasets, we introduce the Multiscale Learning by Unsupervised Nonlinear Diffusion (M-LUND) clustering algorithm, which is derived from a diffusion process at a range of temporal scales.
K-Deep Simplex: Deep Manifold Learning via Local Dictionaries
We theoretically analyze the proposed program by relating the weighted $\ell_1$ penalty in KDS to a weighted $\ell_0$ program.
Hyperspectral Image Clustering with Spatially-Regularized Ultrametrics
We propose a method for the unsupervised clustering of hyperspectral images based on spatially regularized spectral clustering with ultrametric path distances.
Diffusion State Distances: Multitemporal Analysis, Fast Algorithms, and Applications to Biological Networks
This article develops a theory for DSD based on the multitemporal emergence of mesoscopic equilibria in the underlying diffusion process.
Spatially regularized active diffusion learning for high-dimensional images
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.
Learning by Active Nonlinear Diffusion
This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs.
Spectral-Spatial Diffusion Geometry for Hyperspectral Image Clustering
The explicit incorporation of spatial regularity into the diffusion construction leads to smoother random processes that are more adapted for unsupervised machine learning than those based on spectra alone.
Learning by Unsupervised Nonlinear Diffusion
This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation.
Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms
We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters.
Unsupervised Clustering and Active Learning of Hyperspectral Images with Nonlinear Diffusion
The problem of unsupervised learning and segmentation of hyperspectral images is a significant challenge in remote sensing.
Superresolution of Noisy Remotely Sensed Images Through Directional Representations
We justify the use of shearlets mathematically, before presenting a denoising single-image superresolution algorithm that combines the shearlet transform with sparse mixing estimators (SME).
