A Scalable CUR Matrix Decomposition Algorithm: Lower Time Complexity and Tighter Bound

The CUR matrix decomposition is an important extension of Nystr\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advantages over the existing relative-error CUR algorithms that it possesses tighter theoretical bound and lower time complexity, and that it can avoid maintaining the whole data matrix in main memory. Finally, experiments on several real-world datasets demonstrate significant improvement over the existing relative-error algorithms.Comment: accepted by NIPS 201

A New Method for Evaluating Spatial Variability of Soil Strains Developed during Earthquakes Based on Electrical Resistivity Concepts Using Green’s Function

A new method for evaluating spatial variability of soil strains during earthquakes is developed. The idea is based on electrical resisitivity concepts. By solving the classic Maxwell’s equations applying Green’s function for the boundary conditions, we obtained a closed form solution relating the electric potential measurements to the soil’s displacements during earthquakes. The displacement information can be further used to obtain soil strains. In centrifuge models, the displacement measurements using an electrode switching system have been demonstrated to have spatial and temporal resolutions of 1 mm and 1 ms. Based on the high resolution of the displacement that is obtainable, strains of the soil matrix can be computed. The scheme of the method is to establish electromagnetic fields in saturated soil by injecting low-frequency alternating currents through electrodes in a designed mesh and the displacement of the soil is related to the change of electrical potential measured on the electrode located at that point. The viability of the technique is demonstrated by measuring the liquefaction-induced displacements of objects in a geotechnical centrifuge model test. This method is considered to be a useful technique for monitoring strain distributions in physical centrifuge models and has practical application potentials in the field