Figure 1

Reduction of two complex datasets A (a roll) and B (a helicoidal tore) with two methods, classical linear method (PCA) versus nonlinear method (ISOMAP). PCA relies on projections: original data (left) are represented in a three-dimensional space. PCA projected data into a two-dimensional space along their principal axes and the neighboring relationships are not preserved (center). ISOMAP properly unfolds the data while preserving true neighbors (right). ‘True’ neighbors are dots of similar colors: the dimensionality reduction technique does not respect neighboring relationships when a red dot lies next to a blue dot.