The on-line curvilinear component analysis (onCCA) for real-time data reduction

Real time pattern recognition applications often deal with high dimensional data, which require a data reduction step which is only performed offline. However, this loses the possibility of adaption to a changing environment. This is also true for other applications different from pattern recognition, like data visualization for input inspection. Only linear projections, like the principal component analysis, can work in real time by using iterative algorithms while all known nonlinear techniques cannot be implemented in such a way and actually always work on the whole database at each epoch. Among these nonlinear tools, the Curvilinear Component Analysis (CCA), which is a non-convex technique based on the preservation of the local distances into the lower dimensional space, plays an important role. This paper presents the online version of CCA. It inherits the same features of CCA, is adaptive in real time and tracks non-stationary high dimensional distributions. It is composed of neurons with two weights: one, pointing to the input space, quantizes the data distribution, and the other, pointing to the output space, represents the projection of the first weight. This on-line CCA has been conceived not only for the previously cited applications, but also as a basic tool for more complex supervised neural networks for modelling very complex high dimensional data. This algorithm is tested on 2-D and 3-D synthetic data and on an experimental database concerning the bearing faults of an electrical motor, with the goal of novelty (fault) detection.