How do you approach a machine learning problem with a large number of features?

When tackling a machine learning problem with a large number of features, there are three primary strategies to reduce the feature count if needed. This helps to avoid overfitting (caused by the curse of dimensionality) and to reduce computational complexity, thereby increasing efficiency.

1. Regularization and Sparsity

   If the model supports it, using L1 or ElasticNet regularization can help by effectively reducing the feature set. These techniques work by zeroing out less important features, creating a sparser model.

   
   

2. Feature Selection

   Various feature selection methods can help us identify the most useful features. Techniques include variance-based selection or more complex approaches like greedy search methods (e.g., sequential forward/backward selection), as well as genetic algorithms.

   
   

3. Feature Extraction

   Transforming the feature space to a lower-dimensional subspace is another way to manage high-dimensional data. A common technique is Principal Component Analysis (PCA), which is ideal for linear transformations but may struggle with non-linear data structures. For example, consider a dataset with two classes, represented by blue and red concentric circles.

   

Let’s assume the blue samples belong to one class, and the red circles belong to a second class. Our goal is to train a model for classification. Furthermore, we assume that this dataset has too many dimensions (okay, we only have 2 features here, but we need to keep it “simple” for visualization purposes). Now, we want to compress the data onto a lower-dimensional subspace, here: 1 dimension. Let’s start with “standard” PCA. Can you spot the problem?

The two classes are not separable anymore… Let’s use kernel PCA:

This is much better; we can now train a linear classifier to separate those two classes. However, the problem is that we introduce an additional hyperparameter (gamma) that needs to be tuned. Also, this “kernel trick” does not work for any dataset, and there are also many more manifold learning techniques that are “more powerful”/appropriate than kernel PCA. For example, locally linear embedding (LLE) to unfold the famous Swiss Roll: