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Let $K/k$ be a finite Galois extension of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a way to verify the nonsplitting of the short exact sequence
Hyperspectral images (HSIs) denoising is a critical research area in image processing duo to its importance in improving the quality of HSIs, which has a negative impact on object detection and classi...
Let G be an unrami ed group over a p-adic eld. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for G and proves the corresponding base ...
These lectures describe Hecke algebra isomorphisms and types for depth-zero principal series blocks, a.k.a. Bernstein components Rs(G) for s = sχ = [T, χe]G, where χ is a depth-zero character on T(O...
Nonlinear principal component analysis (NLPCA) was performed to examine the total electron content (TEC) anomalies for the China Wenchuan earthquake of May 12, 2008 (= 7.9). This was applied to global...
The presence of ionospheric perturbations in possible association with two huge earthquakes (Noto-hanto peninsula and Niigata-chuetu-oki earthquakes) in 2007 was studied on the basis of a conventional...
The elements of a multivariate data set are often curves rather than single points. Functional principal components can be used to describe the modes of variation of such curves. If one has complete m...
Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However,PCA suffers from the fact that each principal component is a linear combination of all the or...
In regression problems where the number of predictors greatly exceeds the number of observations, conventional regression techniques may produce unsatisfactory results. We describe a technique called ...
In regression problems where the number of predictors greatly exceeds the number of observations, conventional regression techniques may produce unsatisfactory results. We describe a technique called ...
We present a penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix. We approximate the matrix X as X ˆ = k K=1 dkukvk T , where dk, uk, and vk m...
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. Contemporary data sets of...
Let x1 denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian varates. Equivalently, x1 is the largest principal component vari...
We propose a simple method to assess the number of subpopulations in multivariate data by projecting the data on its principal curve and then applying Silverman’s bandwidth test to the resulting uni...
Today, colour or multichannel satellite and aerial images are increasingly becoming available due to the commercial availability of multispectral digital sensors and pansharpening function of the co...

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