Implications for Feature Engineering
When you consider feature engineering in high-dimensional spaces, it is tempting to believe that adding more features will always improve your model. However, the curse of dimensionality reveals that this intuition can be misleading. As you increase the number of features, the data becomes increasingly sparse in the feature space. This sparsity means that data points are farther apart, and the density of points in any given region drops quickly. With each new feature, the volume of the space grows exponentially, but your dataset size usually stays the same, making it much less likely for points to be close to each other.
This sparsity leads to the phenomenon known as the vanishing middle. In high dimensions, most of the volume is concentrated near the edges of the space, and very little is in the center. As a result, the concept of similarity between points becomes less meaningful, and models may struggle to generalize. Adding features that are not highly informative can therefore worsen model performance, as the model may overfit to noise or irrelevant patterns in the data. This is why, despite the availability of more features, careful selection and dimensionality reduction techniques often become necessary to maintain model effectiveness.
If you add genuinely new, relevant, and independent features, they can provide additional signal that improves model performance, even in high dimensions;
Techniques such as L1/L2 regularization or embedded feature selection can help manage the risk of overfitting, allowing you to safely include more features;
If you have a dataset with a very high number of samples, the effects of sparsity are reduced, and adding features may still be beneficial;
Features that describe truly distinct facets of the underlying phenomenon may contribute positively, especially if they are not redundant.
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When you consider feature engineering in high-dimensional spaces, it is tempting to believe that adding more features will always improve your model. However, the curse of dimensionality reveals that this intuition can be misleading. As you increase the number of features, the data becomes increasingly sparse in the feature space. This sparsity means that data points are farther apart, and the density of points in any given region drops quickly. With each new feature, the volume of the space grows exponentially, but your dataset size usually stays the same, making it much less likely for points to be close to each other.
This sparsity leads to the phenomenon known as the vanishing middle. In high dimensions, most of the volume is concentrated near the edges of the space, and very little is in the center. As a result, the concept of similarity between points becomes less meaningful, and models may struggle to generalize. Adding features that are not highly informative can therefore worsen model performance, as the model may overfit to noise or irrelevant patterns in the data. This is why, despite the availability of more features, careful selection and dimensionality reduction techniques often become necessary to maintain model effectiveness.
If you add genuinely new, relevant, and independent features, they can provide additional signal that improves model performance, even in high dimensions;
Techniques such as L1/L2 regularization or embedded feature selection can help manage the risk of overfitting, allowing you to safely include more features;
If you have a dataset with a very high number of samples, the effects of sparsity are reduced, and adding features may still be beneficial;
Features that describe truly distinct facets of the underlying phenomenon may contribute positively, especially if they are not redundant.
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