Bridging the Gap Between Numerical Linear Algebra , Theoretical Computer Science , and Data Applications
چکیده
The Workshop on Algorithms for Modern Massive Data Sets (MMDS 2006), sponsored by the National Science Foundation, Yahoo! Research, and Ask.com, was held at Stanford University, June 21–24. The objectives were to explore novel techniques for modeling and analyzing massive, high-dimensional, and nonlinearly structured data sets, and to bring together computer scientists, computational and applied mathematicians, statisticians, and practitioners to promote cross-fertilization of ideas. The program, with 45 talks and 24 poster presentations, drew 232 participants—far exceeding the anticipated 75! MMDS 2006 grew out of discussions among the four organizers (who are also the authors of this article) about the complementary perspectives brought by the numerical linear algebra (NLA) and the theoretical computer science (TCS) communities to linear algebra and matrix computations. These discussions were motivated by data applications, and, in particular, by technological developments over the last two decades (in both scientific and Internet domains) that permit the automatic generation of very large data sets. Such data are often modeled as matrices: An m × n real-valued matrix A provides a natural structure for encoding information about m objects, each of which is described by n features. In genetics, for example, microarray expression data can be represented in such a framework, with Aij representing the expression level of the ith gene in the jth experimental condition. Similarly, term–document matrices can be constructed in many Internet applications, with Aij indicating the frequency of the jth term in the ith document. Such data matrices often have structural properties that present challenges and opportunities for researchers in both NLA and TCS. The workshop was loosely organized around six hour-long tutorials that introduced participants to the major themes of the workshop.