Abstract:
This submission considers the problem of updating the rank-$k$
truncated Singular Value Decomposition (SVD) of matrices subject to
the addition of new rows and/or columns over time. Such matrix
problems represent an important computational kernel in applications
such as Latent Semantic Indexing and Recommender Systems. Nonetheless,
the proposed framework is purely algebraic and
targets general updating problems. The algorithm presented in this paper
undertakes a projection viewpoint and focuses on building a pair of
subspaces which approximate the linear span of the sought singular vectors
of the updated matrix. We discuss and analyze two different choices to
form the projection subspaces. Results on matrices from real applications
suggest that the proposed algorithm can lead to higher accuracy,
especially for the singular triplets associated with the largest modulus
singular values. Several practical details and key differences with other
approaches are also discussed.
