Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets

We present a new strategy called ''curvilinear component analysis'' (CCA) for dimensionality reduction and representation of multidimensional datasets. 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.