title: Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets.
abstract: We present a new strategy called "curvilinear component analysis" (CCA) for dimensionality reduction and representation of multidimensional data sets. The principle of CCA is a self-organized neural network performing two tasks: vector quantization (VQ) of the submanifold in the data set (input space); and nonlinear projection (P) of these quantizing vectors toward an output space, providing a revealing unfolding of the submanifold. After learning, the network has the ability to continuously map any new point from one space into another: forward mapping of new points in the input space, or backward mapping of an arbitrary position in the output space.
authors.affiliation: Lab. de Traitment d'Images et de Reconnaissance des Formes, Inst. Nat. Polytech. de Grenoble.
authors.forename: P
authors.initials: P
authors.lastname: Demartines
authors.forename: J
authors.initials: J
authors.lastname: Herault