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 isperformed using the linear discriminant analysis, due to its high performance, speed andability to project unseen (out-of-sample) patterns. The map is defined in an efficient way byassigning the proper output value to each square (or pixel) in the 2D map. The experimentsshow that the maps defined by both methods: (1) allow to understand visually the datadistribution of a classification or regression problem; (2) their performances are very nearto 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.