Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Multiscale Geometric Methods for Data Sets I: Multiscale SVD, Noise and Curvature

Large data sets are often modeled as being noisy samples from probability distributions μ in R, withD large. It has been noticed that oftentimes the supportM of these probability distributions seems to be well-approximated by low-dimensional sets, perhaps even by manifolds. We shall consider sets that are locally well approximated by k-dimensional planes, with k ≪ D, with k-dimensional manifold...

متن کامل

Multiscale Geometric Methods for Data Sets II: Geometric Multi-Resolution Analysis

Data sets are often modeled as point clouds in R, for D large. It is often assumed that the data has some interesting low-dimensional structure, for example that of a d-dimensional manifold M, with d much smaller than D. When M is simply a linear subspace, one may exploit this assumption for encoding efficiently the data by projecting onto a dictionary of d vectors in R (for example found by SV...

متن کامل

Multiscale Geometric Methods for Estimating Intrinsic Dimension

We present a novel approach for estimating the intrinsic dimension of certain point clouds: we assume that the points are sampled from a manifold M of dimension k, with k << D, and corrupted by D-dimensional noise. When M is linear, one may analyze this situation by PCA: with no noise one would obtain a rank k matrix, and noise may be treated as a perturbation of the covariance matrix. WhenM is...

متن کامل

Multiscale Geometric Dictionaries for Point-cloud Data

We develop a novel geometric multiresolution analysis for analyzing intrinsically low dimensional point clouds in high-dimensional spaces, modeled as samples from a d-dimensional set M (in particular, a manifold) embedded in R, in the regime d D. This type of situation has been recognized as important in various applications, such as the analysis of sounds, images, and gene arrays. In this pape...

متن کامل

Multiscale Algorithm for Atmospheric Data AssimilationPart I

A multiscale algorithm for the problem of optimal statistical interpolation of the observed data has been developed. This problem includes the calculation of the vector of the \analyzed" (best estimated) atmosphere ow eld w a by the formula w a = w f + P f H T y; where the quantity y is deened by the equation using the given model forecast rst guess w f and the vector of observations w o. H is ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Applied and Computational Harmonic Analysis

سال: 2017

ISSN: 1063-5203

DOI: 10.1016/j.acha.2015.09.009