Reduction of Dimensionality

Abstract In data analysis, the expression “Reduction of dimensionality”, or “Dimensionality reduction”, refers to the process of mapping a set of high‐dimensional statistical units into a lower‐dimensional space, minimizing the approximation, or reconstruction, error and preserving, as much as possible, the structure and the features of the input data. Dimensionality reduction is usually performed in order to simplify multidimensional data, to clean them from noise, to visualize them, to identify patterns of statistical units, or as a preliminary step before other kinds of statistical analysis (e.g., prediction and supervised classification). Many different algorithms for dimensionality reduction exist; they differ as to the kind of input data (categorical, ordinal, or numerical), to the mathematical setting they are based on (e.g., linear and nonlinear procedures) and to the emphasis they put on minimizing the approximation error or on providing less precise but more easily interpretable results. Given the increasing availability of increasingly complex data systems, dimensionality reduction is often a key step in real‐world statistical and data science processes and is a lively area of multivariate statistical and machine learning research.