<p>First of all, presumably you want the VC-dimension of your class of composed with the sign function, which yields a class of Boolean functions (otherwise, VC-dim is not defined). With that out of the way, the answer is: It's infinite. That will be the answer for any periodic function class that contains all possible frequencies and crosses the x-axis. For a concrete proof for this sine wave, see Theorem 9 here:
<a href="https://www.cs.bgu.ac.il/%7Ekaryeh/fat-add.pdf" rel="nofollow noreferrer">https://www.cs.bgu.ac.il/~karyeh/fat-add.pdf</a></p>

CC BY-SA 4.0
2020-11-25T11:46:45.920Z
2020-11-25T11:46:45.920Z
Aryeh
<p>I am searching for the VC-dimension of the following:</p>
<p>What is the VC-dimension of the infinite set of triangle wave functions with
amplitude 1 and period parameter p on points on the line?<br />
<strong>2πarcsin⁡(sin(2πx⁄p))</strong></p>

<reference-request><machine-learning><cg.comp-geom><lg.learning><vc-dimension>
VC-dimension of infinite set of triangle wave
amit
# VC-dimension of infinite set of triangle wave

(Asked by: username_0 on 2020-11-25)

I am searching for the VC-dimension of the following:

What is the VC-dimension of the infinite set of triangle wave functions with
amplitude 1 and period parameter p on points on the line?  
**2πarcsin⁡(sin(2πx⁄p))**

**Tags:** reference-request, machine-learning, cg.comp-geom, lg.learning, vc-dimension


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## 1 answers

### Answer by username_1 on 2020-11-25. Score: 1

First of all, presumably you want the VC-dimension of your class of composed with the sign function, which yields a class of Boolean functions (otherwise, VC-dim is not defined). With that out of the way, the answer is: It's infinite. That will be the answer for any periodic function class that contains all possible frequencies and crosses the x-axis. For a concrete proof for this sine wave, see Theorem 9 here:
[https://www.cs.bgu.ac.il/~karyeh/fat-add.pdf](https://www.cs.bgu.ac.il/%7Ekaryeh/fat-add.pdf)


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