An online algorithm for efficient and temporally consistent subspace clustering

We present an online algorithm for the efficient clustering of data drawn from a union of arbitrary dimensional, non-static subspaces. Our algorithm is based on an online min-Mahalanobis distance classifier, which simultaneously clusters and is updated from subspace data. In contrast to most existing methods, our algorithm can cope with large amounts of batch or sequential data and is temporally consistent when dealing with time varying data (i.e. time-series). Starting from an initial condition, the classifier provides a first estimate of the subspace clusters in the current time-window. From this estimate, we update the classifier using stochastic gradient descent. The updated classifier is applied back onto the data to refine the subspace clusters, while at the same time we recover the explicit rotations that align the subspaces between time-windows. The whole procedure is repeated until convergence, resulting in a fast, efficient and accurate algorithm. We have tested our algorithm on synthetic and three real datasets and compared with competing methods from literature. Our results show that our algorithm outperforms the competition with superior clustering accuracy and computation speed.