Incremental algorithm for finding principal curves

Principal curves are a non-linear generalisation of principal components. They are smooth curves that pass through the middle of a data set to provide a new representation of those data to make tasks, such as visualisation and dimensionality reduction easier and more accurate. The subspace constrained mean shift (SCMS) algorithm is a recently proposed technique to find principal curves. The algorithm assumes that the complete data set is available in advance and that new data points cannot be added to the data set during the process. The algorithm finds the points on the principal curves by using the complete data set. In this paper, the authors investigate the situation where the entire data set is not available in advance and instead are sampled sequentially. They propose an incremental version of the SCMS algorithm that trains using a sequence of observations. Simulation results show the effectiveness of the proposed algorithm to find a principal curve using a stream of observations.