# Ultra Fast Classification and Regression of High-Dimensional Problems Projected on 2D

We propose the two-dimensional visual map classifier and regressor, which project the high-dimensional patterns on a 2D map, for human visualization and understanding of the data, and afterwards define a classification or regression map that predicts, for each 2D pattern, the class label (in classification) or the output value (in regression). The 2D projection is performed using the linear discriminant analysis, due to its high performance, speed and ability to project unseen (out-of-sample) patterns. The map is defined in an efficient way by assigning the proper output value to each square (or pixel) in the 2D map. The experiments show that the maps defined by both methods: (1) allow to understand visually the data distribution of a classification or regression problem; (2) their performances are very near to the state-of-the-art support vector classification and regression, including wrappers; and (3) they are very fast, between 1 and 5 orders of magnitude faster than the other approaches, spending less than 1 min to classify datasets with 5 million patterns. Matlab code is available.

keywords: Classification, Regression, Mapping, Data visualization, Dimensionality reduction, Linear discriminant analysis