The embedding dimension of Laplacian eigenfunction maps

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

The embedding dimension of Laplacian eigenfunction maps

Any closed, connected Riemannian manifold M can be smoothly embedded by its Laplacian eigenfunction maps into Rm for some m. We call the smallest such m the maximal embedding dimension of M. We show that the maximal embedding dimension of M is bounded from above by a constant depending only on the dimension of M, a lower bound for injectivity radius, a lower bound for Ricci curvature, and a vol...

متن کامل

Signed Laplacian Embedding for Supervised Dimension Reduction

Manifold learning is a powerful tool for solving nonlinear dimension reduction problems. By assuming that the high-dimensional data usually lie on a low-dimensional manifold, many algorithms have been proposed. However, most algorithms simply adopt the traditional graph Laplacian to encode the data locality, so the discriminative ability is limited and the embedding results are not always suita...

متن کامل

Discriminant Laplacian Embedding

Many real life applications brought by modern technologies often have multiple data sources, which are usually characterized by both attributes and pairwise similarities at the same time. For example in webpage ranking, a webpage is usually represented by a vector of term values, and meanwhile the internet linkages induce pairwise similarities among the webpages. Although both attributes and pa...

متن کامل

on numerical semigroups with embedding dimension three

let $fneq1,3$ be a positive integer‎. ‎we prove that there exists a numerical semigroup $s$ with embedding dimension three such that $f$ is the frobenius number of $s$‎. ‎we also show that‎ ‎the same fact holds for affine semigroups in higher dimensional monoids‎.

متن کامل

Stratified Structure of Laplacian Eigenmaps Embedding

We construct a locality preserving weight matrix for Laplacian eigenmaps algorithm used in dimension reduction. Our point cloud data is sampled from a low dimensional stratified space embedded in a higher dimension. Specifically, we use tools developed in local homology, persistence homology for kernel and cokernels to infer a weight matrix which captures neighborhood relations among points in ...

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: 2014

ISSN: 1063-5203

DOI: 10.1016/j.acha.2014.03.002