Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2000. / Includes bibliographical references (p. 99-102) and index.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 117-121).

Dimitri P. Bertsekas, Didier El Baz. / Bibliography: p. 22-23. / "October 1984." / "...supported by the National Science Foundation under Contract NSF ECS-8217668..." "...supported by...the Defense Advanced Research Projects Agency under Contract ONR-N00014-84-K-0357."

John N. Tsitsiklis. / "September 1985." / Bibliography: p. 22.

No description available.

Data clustering is a process of grouping unlabeled objects based on the imformation describing their relationship. And it has obtained a lot of attentions in data mining for its wide applications in life. For example, in marketing, companys are interested in finding groups of customers with similar purchase behavior, which will help them to make suitable plans to gain more profits. Besides, in biology, we can make use of data clustering to distinguish planets and animals given their features. Whats more, in earthquake analysis, by clustering observed earthquake epicenters, dangerous area can be identified, it would be helpful for people to take measures to protect them from earthquake in advance. In general, there isnt one clustering algorithm which can solve all the problems. Algorithms are specifically designed to analyze different data categories. In this thesis, we study several novel numerical algorithms for data clustering mainly applied on multi-view data and tensor data. More accurate clustering result can be achieved on multi-view data by integrating information from multiple graphs. However, Most existing multi-view clustering method assume the degree of association among all the graphs are the same. One significant truth is some graphs may be strongly or weakly associated with other graphs in reality. Determining the degree of association between graphs is a key issue when clustering multi-view data. In Chapter 2, 3 and 4, we propose three different models to solve this problem. In chapter 2, a block signed matrix is constructed to integrate information in each graph with association among graphs together. Then we apply spectral clustering on it to seek different cluster structure for each graph respectively and determine the degree of association among graphs using their own cluster structure at the same time. Numerical experiments including simulations, neuron activity data and gene expression data are conducted to illustrate the state-of-art performance of algorithm in clustering and graph association. In Chapter 3, we further consider multiple graphs clustering with graph association solved by self-consistent field iterative algorithm. By using the block graph clustering framework, graphs association are considered to enhance clustering result, and then better clustering result would be used to calculate more accurate association. Self-consistent field iterative method is employed to solve this problem, and the convergence analysis is also presented. Simulations are also carried out to demonstrate the outperformance of our method. Two gene expression data are used to evaluate the effectiveness of proposed model. In Chapter 4, we formulate the multiple graphs clustering problem with the graph association as an objective function, and the graph association is considered as a term in the objective function. The proposed model can be solved efficiently by using gradient flow method. We also present its convergence analysis. Experiments on synthetic data sets and two gene expression data are given to show the efficiency in clustering and capability in graphs association. In the last three chapters, we use multiple graphs to represent the multi-view data. A key challenge is high dimensionality when the number of graphs or objects is large-scale. Moreover, tensor is another common technique to describe multi-view data. Thus tensor decomposition method can be used to learn a low-dimensional representation for high dimensional data firstly and then perform clustering efficiently, which has attract worldwide attention of researchers. In Chapter 5, we propose an orthogonal nonnegative Tucker decomposition method to decompose high-dimensional nonnegative tensor into tensor with smaller size for dimension reduction, and then perform clustering analysis. A convex relaxation algorithm of the augmented Lagrangian function is devoloped to solve the optimization problem and the convergence of the algorithm is discussed. We employ our proposed method on several real image data sets from different real world application, including face recognition, image representation and hyperspectral unmixing problem to illustrate the effectiveness of proposed algorithm.

The numerical solutions of many types of problems are generally obtained by solving approximating linear algebraic systems. Moreover, in solving a nonlinear problem, one may replace it by a sequence of linear systems providing progressively improved approximations. For the study of these linear systems of equations a geometric terminology with the compact symbolism of vectors and matrices is useful. A resume of the basic principles of higher algebra necessary for the development of the material to follow is therefore included. / "A Paper." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Paul J. McCarthy, Professor Directing Paper. / "May, 1958." / At head of title: Florida State University. / Typescript. / Includes bibliographical references.

A number of significant problems require the solution of a system of linear equations Ax = b in which A is large, highly sparse, nonsymmetric, and unstructured. Several iterative methods which are applicable to nonsymmetric and indefinite problems are applied to a suite of test problems derived from simulations of actual bipolar circuits and to a viscous flow problem. Methods tested include Craig’s method, GMRES(k), BiCGSTAB, QMR, KACZ (a row-projection method) and LSQR. The convergence rates of these methods may be improved by use of a suitable preconditioner. Several such techniques are considered, including incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence statistics are given for each iterative method and preconditioner. / Master of Science

An optical image feedback system utilizing a cavity with a phase-conjugate mirror (PCM) has been studied. A new theory, based on operators, is developed to describe the steady-state output of the cavity. The use of operators allows one to describe the various optical operations and transformations needed in the optical implementation of iterative algorithms. The characteristics of the cavity are discussed using an expansion of the cavity fields in the cavity eigenfunctions. Several image processing applications using a PCM cavity are proposed and are studied using computer simulations. These theoretical studies indicate that a PC11 cavity can be useful in many applications. Optical phase conjugation was realized using a single crystal of photorefractive BaTi0₃ in a degenerated four-wave mixing geometry. The reflectivity gain from the PCM was optimized experimentally by the geometrical parameters and by the beamintensity ratios. The ability of the PCM to remove phase distortion as predicted theoretically, was demonstrated experimentally. The output of a PCM cavity can be substantially influenced by self-oscillations of the cavity above threshold. This was experimentally studied by observing the time evolution of the input. To avoid the influence of self-oscillation, the cavity must be operated below threshold. It is found that the cavity decay time constant diverges at and about threshold. This can be used as an indicator to show whether the cavity has crossed the threshold or to measure how close to threshold the cavity operates. To verify that a PCM cavity can be used in iterative image processing, an experiment was set up to implement an image restoration scheme based on the Gerchberg algorithm. It is shown that an optical implementation of the Gerchberg algorithm is feasible for objects made of few pixels. The experiment confirmed .that image iteration in a PCm cavity is possible. The limitations of the cavity and the technical difficulties are discussed. / Ph. D.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1981. / Bibliography: leaf 85. / by Art O'Leary. / Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1981.