Singular values/vectors for all occasions: from Seismology to Information Retrieval
Osni MarquesLawrence Berkeley National Laboratory (LBNL)
National Energy Research Scientific Computing Center (NERSC)
Berkeley, CA 94720
July 12 - 3.00 p.m. CERFACS Conference Room
Abstract :
Many applications are solved by means of techniques based on subspaces formed by singular vectors. A (partial) singular value decomposition (SVD) allows the computation of generalized inverses, which are used in the solution of various inverse problems. In some cases, given a set of (physical) data, the goal is to estimate a set of model parameters describing the problem at hand. Travel time of sound waves generated by earthquakes, for instance, are used to estimate parameters for a model describing the internal structure of the Earth (the underlying models usually lead to sparse matrices larger than 10^6-by-10^5). In this case, it is important to determine estimates of uncertainties. The SVD can also be used in information retrieval applications, in the context of the latent semantic indexing (LSI). Now, the data is related to a list of terms (key words, for instance) and documents (books and journals, for instance). Then, the idea is to compute a (partial) SVD to 'extract' information contained in the data. As an extension of that idea one could use the SVD to 'extract' information contained in the World Wide Web (the list of terms corresponds to a good part of the words in a dictionary, the documents correspond to home-pages, and the sparse matrices that result therein have dimensions of several millions). In the talk we will describe the aforementioned applications and the main computational issues related to their solutions using NERSC's supercomputers.
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