Isomapping El Niño

Linear methods of dimensionality reduction are useful tools for handling and interpreting high dimensional data. However, the cumulative variance explained by each of the subspaces in which the data space is decomposed may show a slow convergence. This may difficult the selection of a proper minimum number of subspaces for representing the variability of the data. The use of nonlinear methods can improve the embedding of multivariate data into lower dimensional manifolds. In this talk, a nonlinear method for dimensionality reduction, Isomap, is explained and applied to several data sets showing dynamical or geometrical nonlinearities. In particular, Isomap will be applied to the sea surface temperature in the tropical Pacific Ocean, where the El Niño phenomenon and the annual cycle phenomena interact. Isomap gives a more accurate description of the manifold dimensionality of the physical system. This new description could help to enhance low dimensional models for El Niño and other extended nonlinear systems.