<p>SVM looks to maximize the margin <span class="math-container">$ρ$</span> of support vectors to reduce the model's effective complexity for overfitting and improves its generalization ability. The bound <span class="math-container">$d_{VC}(ρ)≤d_{VC}(0)$</span> shows that while both SVM and PLA may have the same VC dimension for linear separators in worst case scenarios, the margin maximization in SVM effectively reduces its VC-dimension <em>on average</em> compared to PLA, making it a better choice for generalization.</p>

CC BY-SA 4.0
2024-12-15T08:49:05.067Z
2024-12-15T08:49:05.067Z
cinch
<p>For linear separators in <span class="math-container">$d$</span> dimensions, we have
<span class="math-container">$d_{VC}(\rho) \le d_{VC}(0) =d+1$</span> where <span class="math-container">$\rho$</span> is the margin.</p>
<p>Based on the above result, does that mean SVM consistently produces a classifier
with superior generalization performance compared to any linear separator derived from the Perceptron Learning Algorithm (PLA), as PLA does not maximize the separation margin between classes?</p>

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2024-12-15T22:18:31.927Z
Can you clarify what $d_{VC}(p)$ means? VC probably stands for the VC dimension, but can you describe function and number? I suppose that's the VC dimension of some function of an SVM, but please put that into words. Also, where did you take this formula from?
nbro
<support-vector-machine><vc-dimension><vc-theory>
Confusion about the use of VC in SVMs
DSPinfinity
# Confusion about the use of VC in SVMs

(Asked by: username_0 on 2024-12-14)

For linear separators in $d$ dimensions, we have
$d\_{VC}(\rho) \le d\_{VC}(0) =d+1$ where $\rho$ is the margin.

Based on the above result, does that mean SVM consistently produces a classifier
with superior generalization performance compared to any linear separator derived from the Perceptron Learning Algorithm (PLA), as PLA does not maximize the separation margin between classes?

**Tags:** support-vector-machine, vc-dimension, vc-theory

> **Comments:**
> **username_1**: Can you clarify what $d_{VC}(p)$ means? VC probably stands for the VC dimension, but can you describe function and number? I suppose that's the VC dimension of some function of an SVM, but please put that into words. Also, where did you take this formula from?  

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## 1 answers

### Answer by username_2 on 2024-12-15. Score: 1

SVM looks to maximize the margin $ρ$ of support vectors to reduce the model's effective complexity for overfitting and improves its generalization ability. The bound $d\_{VC}(ρ)≤d\_{VC}(0)$ shows that while both SVM and PLA may have the same VC dimension for linear separators in worst case scenarios, the margin maximization in SVM effectively reduces its VC-dimension *on average* compared to PLA, making it a better choice for generalization.


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