The improvement in VAS pain scores after LES injections correlated well with the changes in the SPI except in those patients classified on MRI as severe LSS and more than 3 lumbar levels affected. That patient group is unlikely to benefit from LES injections.
Hyperspectral images of a scene or object are a rich data source, often encoding a hundred or more spectral bands of reflectance at each pixel. Despite being very high-dimensional, these images typically encode latent low-dimensional structure that can be exploited for material discrimination. However, due to an inherent trade-off between spectral and spatial resolution, many hyperspectral images are generated at a coarse spatial scale, and single pixels may correspond to spatial regions containing multiple materials. This article introduces the Diffusion and Volume maximization-based Image Clustering (D-VIC ) algorithm for unsupervised material discrimination. D-VIC locates cluster modes-high-density, high-purity pixels in the hyperspectral image that are far in diffusion distance (a data-dependent distance metric) from other high-density, high-purity pixels-and assigns these pixels unique labels, as these points are meant to exemplify underlying material structure. Non-modal pixels are labeled according to their diffusion distance nearest neighbor of higher density and purity that is already labeled. By directly incorporating pixel purity into its modal and non-modal labeling, D-VIC upweights pixels that correspond to a spatial region containing just a single material, yielding more interpretable clusterings. D-VIC is shown to outperform baseline and comparable state-of-the-art methods in extensive numerical experiments on a range of hyperspectral images, implying that it is well-equipped for material discrimination and clustering of these data.
Clustering algorithms partition a dataset into groups of similar points. The clustering problem is very general, and different partitions of the same dataset could be considered correct and useful. To fully understand such data, it must be considered at a variety of scales, ranging from coarse to fine. We introduce the Multiscale Environment for Learning by Diffusion (MELD) data model, which is a family of clusterings parameterized by nonlinear diffusion on the dataset. We show that the MELD data model precisely captures latent multiscale structure in data and facilitates its analysis. 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. We provide theoretical guarantees for the algorithm's performance and establish its computational efficiency. Finally, we show that the M-LUND clustering algorithm detects the latent structure in a range of synthetic and real datasets.
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