Which kernel method is effective for data with many more examples than features?

The Gaussian radial basis function (RBF) kernel is particularly effective for datasets where the number of examples significantly exceeds the number of features. This situation is common in many practical applications, such as text classification or image recognition, where the number of observations can vastly outnumber the features used to describe them.

The RBF kernel functions by measuring the similarity between data points based on their distance in a high-dimensional space. Because it maps the input features into an infinite-dimensional space, it is capable of capturing complex relationships in the data while remaining computationally efficient. This ability allows the RBF kernel to generalize well when there are many examples available, helping to effectively model the underlying patterns without overfitting, which can be a risk if the feature space is too small relative to the volume of data.

In contrast, although linear kernels work well in high-dimensional spaces, they may not capture more intricate patterns unless the data is linearly separable. Polynomial kernels can become computationally intensive as the feature space grows, making them less efficient in scenarios with a high number of examples compared to features. Sigmoid kernels, based on neural network concepts, can lead to convergence issues and are not as commonly used in practice as RBF kernels for standard classification tasks.

Thus