Efficient and Accurate Rectangular Window Subspace Tracking

In this paper, we describe a rectangular window subspace tracking algorithm, which tracks the r largest singular values and corresponding left singular vectors of a sequence of n times c matrices in O(nr
²
) time. This algorithm is designed to track rapidly changing subspaces. It uses a rectangular window to include a finite number of approximately stationary data columns. This algorithm is based on the improved fast adaptive subspace tracking (IFAST) algorithm of Toolan and Tufts, but reforms the rth order eigendecomposition with an alternative method that takes advantage of matrix structure. This matrix is a special rank-six modification of a diagonal matrix, so its eigendecomposition can be determined with only a single O(r
³
) matrix product to rotate its eigenvectors, and all other computation is O(r
²
). Methods for implementing this algorithm in a numerically stable way are also discussed