2 research outputs found
Randomized methods for matrix computations
The purpose of this text is to provide an accessible introduction to a set of
recently developed algorithms for factorizing matrices. These new algorithms
attain high practical speed by reducing the dimensionality of intermediate
computations using randomized projections. The algorithms are particularly
powerful for computing low-rank approximations to very large matrices, but they
can also be used to accelerate algorithms for computing full factorizations of
matrices. A key competitive advantage of the algorithms described is that they
require less communication than traditional deterministic methods
Randomized Clustered Nystrom for Large-Scale Kernel Machines
The Nystrom method is a popular technique for generating low-rank approximations of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected landmark points and the selection procedure. In this paper, we introduce a randomized algorithm for generating landmark points that is scalable to large high-dimensional data sets. The proposed method performs K-means clustering on low-dimensional random projections of a data set and thus leads to significant savings for high-dimensional data sets. Our theoretical results characterize the tradeoffs between accuracy and efficiency of the proposed method. Moreover, numerical experiments on classification and regression tasks demonstrate the superior performance and efficiency of our proposed method compared with existing approaches