Efficient, high performance, subspace tracking for time-domain data

This paper describes two new algorithms for tracking the subspace spanned by the principal eigenvectors of the correlation matrix associated with time-domain (i.e., time series) data. The algorithms track the d principal N-dimensional eigenvectors of the data covariance matrix with a complexity of O(Nd²), yet they have performance comparable with algorithms having O(N²d) complexity. The computation reduction is achieved by exploiting the shift-invariance property of temporal data covariance matrices. Experiments are used to compare our algorithms with other well-known approaches of similar and/or lower complexity. Our new algorithms are shown to outperform the subset of the general approaches having the same complexity. The new algorithms are useful for applications such as subspace-based speech enhancement and low-rank adaptive filtering.