This thesis consists of five chapters, and focuses on two main problems: the graph realization problem with its applications to localization of sensor network and structural biology, and the low-rank matrix completion problem. Chapter 1 is a brief introduction to rigidity theory and supplies

the products are identified initially, but for readability, the trademark symbols are not repeated throughout the report. Upgrading of Low-Rank Coals Cover images: (upper left) The ENCOAL demonstration site near Gillette, Wyoming, and (lower right)

Exact recovery from contaminated visual data plays an important role in various tasks. By assuming the observed data matrix as the addition of a low-rank matrix and a sparse matrix, theoretic guarantee exists under mild con-ditions for exact data recovery. Practically matrix nuclear norm is adopted

We study the common problem of approximating a target matrix with a matrix of lower rank. We provide a simple and e#cient (EM) algorithm for solving weighted low-rank approximation problems, which, unlike their unweighted version, do not admit a closedform solution in general. We analyze

We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving weighted low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general

We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving weighted low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general

Abstract not found

Sparse models have attracted great attention from the research community due to their

Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, but obtaining

We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperform-ing