Feature selection and feature extraction are both techniques used in machine learning for dimensionality reduction. However, they differ in their approaches and goals.

  Feature selection, as the name suggests, is the process of selecting a subset of the original features from the dataset. The aim is to choose the most informative and relevant features that contribute the most to the prediction task. The selected features are kept as is, and the rest are discarded. This approach helps in reducing the complexity of the model, improving its interpretability, and alleviating the curse of dimensionality. Feature selection methods can be categorized into three types: filter methods, wrapper methods, and embedded methods. Filter methods evaluate the relevance of features independently of any machine learning algorithm. Wrapper methods use the performance of the learning algorithm as a guide to evaluate the subsets of features. Embedded methods perform feature selection during the training process of the learning algorithm itself.

  On the other hand, feature extraction aims to transform the original dataset into a lower-dimensional space by creating new features that capture the relevant information. It involves creating a set of new features (also known as latent variables) that are a combination or projection of the original features. Feature extraction techniques, such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), or Non-Negative Matrix Factorization (NMF), find the directions in the data where the variation or discriminative information is maximized. These derived features are often more informative and less correlated than the original features. Feature extraction can be particularly useful when facing high-dimensional, redundant, or noisy data.

  In summary, feature selection and feature extraction are both dimensionality reduction techniques, but their goals and approaches differ. Feature selection aims to choose the most important features from the original dataset, while feature extraction creates new features that capture relevant information by transforming the original dataset. The choice between the two techniques depends on the specific problem, the dataset characteristics, and the desired trade-off between interpretability and performance.