<p>For $L$-Lipschitz functions on a metric space $(X,\rho)$ with $\epsilon$-packing number $M(\epsilon)$, the $\gamma$-shattering dimension is $M(2\gamma/L)$, as proved here:
<a href="http://ieeexplore.ieee.org/document/6867374/" rel="nofollow noreferrer">http://ieeexplore.ieee.org/document/6867374/</a></p>

CC BY-SA 3.0
2017-04-01T19:43:04.023Z
Are there any more examples?
Meni
CC BY-SA 3.0
2017-04-01T20:20:13.870Z
The $\gamma$-shattering dimension of hyperplanes on a ball of radius $R$ is $(R/\gamma)^2$.
Aryeh
CC BY-SA 3.0
2017-04-01T20:42:22.657Z
Care for a proof or s link to one? :-)
Meni
CC BY-SA 3.0
2017-04-01T22:20:03.720Z
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.6950
Aryeh
CC BY-SA 3.0
2017-04-01T22:20:31.840Z
See Theorem 1.6
Aryeh
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2017-03-30T09:22:16.573Z
2017-03-30T09:22:16.573Z
Aryeh
<p>What are some good examples for analysis of a class's Fat-Shattering dimension?</p>

<p>By (<a href="http://www.tau.ac.il/~nogaa/PDFS/learn3.pdf" rel="nofollow noreferrer" title="Alon et al">Alon et al</a>) I know that the Fat-Shattering Dimension characterizes the learnability of real-valued function classes but I didn't find any proper examples of function class with a proof for a bound on the Fat-Shattering Dimension of the class.</p>

<machine-learning><lg.learning><computing-over-reals>
Examples of Fat-Shattering Dimension
Meni
# Examples of Fat-Shattering Dimension

(Asked by: username_0 on 2017-03-29)

What are some good examples for analysis of a class's Fat-Shattering dimension?

By ([Alon et al](http://www.tau.ac.il/~nogaa/PDFS/learn3.pdf "Alon et al")) I know that the Fat-Shattering Dimension characterizes the learnability of real-valued function classes but I didn't find any proper examples of function class with a proof for a bound on the Fat-Shattering Dimension of the class.

**Tags:** machine-learning, lg.learning, computing-over-reals


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## 1 answers

### Answer by username_1 on 2017-03-30. Score: 2 | Accepted answer

For $L$-Lipschitz functions on a metric space $(X,\rho)$ with $\epsilon$-packing number $M(\epsilon)$, the $\gamma$-shattering dimension is $M(2\gamma/L)$, as proved here:
<http://ieeexplore.ieee.org/document/6867374/>

> **Comments:**
> **username_0**: Are there any more examples?  
> **username_1**: The $\gamma$-shattering dimension of hyperplanes on a ball of radius $R$ is $(R/\gamma)^2$.  
> **username_0**: Care for a proof or s link to one? :-)  
> **username_1**: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.6950  
> **username_1**: See Theorem 1.6  

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