In many applications, like function approximation, pattern recognition, time series prediction, and data mining, one has to build a model relating some features describing the data to some response value. Often, the features that are relevant for building the model are not known in advance. Feature selection methods allow removing irrelevant and/or redundant features to only keep the feature subset that are most useful to build a prediction model. The model is simpler and easier to interpret, reducing the risks of overfitting, non-convergence, etc. By contrast with other dimensionality reduction techniques such as principal component analysis or more recent nonlinear projection techniques (Lee & Verleysen 2007), which build a new, smaller set of features, the features that are selected by feature selection methods preserve their initial meaning, potentially bringing extra information about the process being modeled (Guyon 2006). Recently, the advent of high-dimensional data has raised new challenges for feature selection methods, both from the algorithmic point of view and the conceptual point of view (Liu & Motoda 2007). The problem of feature selection is exponential in nature, and many approximate algorithms are cubic with respect to the initial number of features, which may be intractable when the dimensionality of the data is large. Furthermore, high-dimensional data are often highly redundant, and two distinct subsets of features may have very similar predictive power, which can make it difficult to identify the best subset.
This section discusses the concepts of relevance and redundancy, which are central to any feature selection method, and propose a step-by-step methodology along with some recommendations for feature selection on real, high-dimensional, and noisy data.