Other Ques From: Ch.1 from the 'Hundred-Page Machine Learning Book'
Feature dimensionality affects SVM performance in both positive and negative ways, depending on the balance between number of features and number of training samples.
🔹 1. Positive Effect — High Dimensions Can Help
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In higher-dimensional spaces, data points are more likely to become linearly separable.
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This is why SVMs often perform better with more features, especially when the original space is not separable.
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The kernel trick can implicitly create such high-dimensional feature spaces.
Example:
In 2D, two intertwined spirals may be inseparable, but in 3D after a transformation, a plane can separate them.
🔹 2. Negative Effect — Curse of Dimensionality
When the number of features greatly exceeds the number of training samples:
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SVM might overfit — the model finds boundaries that perfectly classify the training set but fail on new data.
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The margin can become unstable because distances in high dimensions tend to lose meaning (all points look equally far apart).
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More dimensions = higher computation cost.
🔹 3. Impact on Margin
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SVM tries to maximize the margin between classes.
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In very high dimensions, the margin can shrink or become noisy if irrelevant features are present.
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This makes feature selection and regularization (via
C,gamma) crucial.
🔹 4. Practical Tips
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If features are high-dimensional: Use regularization (
Cin SVM) to avoid overfitting. -
If data is sparse: Linear SVM (with a linear kernel) often works better.
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If many irrelevant features exist: Apply feature selection (e.g., PCA, mutual information).
✅ Summary Table:
| Dimensionality Change | Effect on SVM | Risk |
|---|---|---|
| Moderate increase | Easier separation | Higher computation |
| Large increase (> samples) | Overfitting risk | Poor generalization |
| Many irrelevant features | Noisy margin | Reduced accuracy |
If you want, I can make you a diagram showing how increasing feature dimensions changes the SVM decision boundary and margin.
Do you want me to create that?
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