Dimensionality reduction aims to reduce the number of features of a high dimensional dataset in order to overcome the difficulties that arise due to the curse of dimensionality.

There are two approaches: feature selection and feature extraction. Feature selection focuses on finding a subset of the original attributes. Whereas feature extraction transforms the original high-dimensional space into a lower dimensional one. Ideally, some structure in the data should remain in order to preserve enough information. Algorithms can be unsupervised (principal component analysis or PCA, independent component analysis or ICA) or supervised (linear discriminant analysis or LDA). In feature extraction, transformations can be linear (PCA, LDA) or non-linear (t-SNE, autoencoders).

There are plenty of applications such as hidden patterns visualization (by removing highly correlated attributes), noise reduction (removing irrelevant features), further exploration, data compression and storage, etc.

In fact, dimensionality reduction is usually applied as a preprocessing step for other machine learning and data mining algorithms. For instance, in unsupervised tasks with PCA + K-Means clustering, or in supervised tasks with LDA + K-Nearest Neighbors.