<p>In the paper <code>Belkin, Mikhail, and Partha Niyogi. "Laplacian eigenmaps and spectral techniques for embedding and clustering." In NIPS, vol. 14, pp. 585-591. 2001</code> The author uses methods from spectral geometry, specifically <strong>Laplace-Beltrami operator</strong>, after searching around about the topic of spectral geometry I found the lectures and books beyond my background. What are the background materials I need to study/read (Lecture notes-references-...) before reading a book or a lecture about spectral geometry?</p>

CC BY-SA 3.0
2014-07-16T05:32:01.463Z
Looking at the paper, it is not clear to me how much spectral geometry you want to learn vs. just sticking to spectral graph theory. For spectral graph theory, check Fan Chung's book. For spectral geometry, I am not an expert, and it really depends what your background is. You might have to learn some basic differential geometry first, e.g. something like this text http://www.amazon.com/Introduction-Smooth-Manifolds-Graduate-Mathematics/dp/0387954481.
Sasho Nikolov
CC BY-SA 3.0
2014-07-16T11:29:55.863Z
Thanks a lot for your reply, concerning the amount I want to learn, I just wanted to gain enough intuition (geometric/algebraic) to justify the use of the operator.
Magellanea
<soft-question><spectral-graph-theory>
introduction to spectral geometry
Magellanea
# introduction to spectral geometry

(Asked by: username_0 on 2014-07-14)

In the paper `Belkin, Mikhail, and Partha Niyogi. "Laplacian eigenmaps and spectral techniques for embedding and clustering." In NIPS, vol. 14, pp. 585-591. 2001` The author uses methods from spectral geometry, specifically **Laplace-Beltrami operator**, after searching around about the topic of spectral geometry I found the lectures and books beyond my background. What are the background materials I need to study/read (Lecture notes-references-...) before reading a book or a lecture about spectral geometry?

**Tags:** soft-question, spectral-graph-theory

> **Comments:**
> **username_1**: Looking at the paper, it is not clear to me how much spectral geometry you want to learn vs. just sticking to spectral graph theory. For spectral graph theory, check Fan Chung's book. For spectral geometry, I am not an expert, and it really depends what your background is. You might have to learn some basic differential geometry first, e.g. something like this text http://www.amazon.com/Introduction-Smooth-Manifolds-Graduate-Mathematics/dp/0387954481.  
> **username_0**: Thanks a lot for your reply, concerning the amount I want to learn, I just wanted to gain enough intuition (geometric/algebraic) to justify the use of the operator.  

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