کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4605635 1337588 2006 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
From graph to manifold Laplacian: The convergence rate
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
From graph to manifold Laplacian: The convergence rate
چکیده انگلیسی

The convergence of the discrete graph Laplacian to the continuous manifold Laplacian in the limit of sample size N→∞ while the kernel bandwidth ε→0, is the justification for the success of Laplacian based algorithms in machine learning, such as dimensionality reduction, semi-supervised learning and spectral clustering. In this paper we improve the convergence rate of the variance term recently obtained by Hein et al. [From graphs to manifolds—Weak and strong pointwise consistency of graph Laplacians, in: P. Auer, R. Meir (Eds.), Proc. 18th Conf. Learning Theory (COLT), Lecture Notes Comput. Sci., vol. 3559, Springer-Verlag, Berlin, 2005, pp. 470–485], improve the bias term error, and find an optimal criteria to determine the parameter ε given N.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied and Computational Harmonic Analysis - Volume 21, Issue 1, July 2006, Pages 128-134