Daniel Boley

Principal Direction Divisive Partitioning

We propose a new algorithm capable of partitioning a set of documents or other samples based on an embedding in a high dimensional Euclidean space (i.e., in which every document is a vector of real numbers). The method is unusual in that it is divisive, as opposed to agglomerative, and operates by repeatedly splitting clusters into smaller clusters. The documents are assembled into a matrix which is very sparse. It is this sparsity that permits the algorithm to be very efficient. The performance of the method is illustrated with a set of text documents obtained from the World Wide Web. Some possible extensions are proposed for further investigation.

Optical Flow Estimation: An Error Analysis of Gradient-Based Methods with Local Optimization

Multiple views of a scene can provide important information about the structure and dynamic behavior of three-dimensional objects. Many of the methods that recover this information require the determination of optical flow-the velocity, on the image, of visible points on object surfaces. An important class of techniques for estimating optical flow depend on the relationship between the gradients of image brightness. While gradient-based methods have been widely studied, little attention has been paid to accuracy and reliability of the approach. Gradient-based methods are sensitive to conditions commonly encountered in real imagery. Highly textured surfaces, large areas of constant brightness, motion boundaries, and depth discontinuities can all be troublesome for gradient-based methods. Fortunately, these problematic areas are usually localized can be identified in the image. In this paper we examine the sources of errors for gradient-based techniques that locally solve for optical flow. These methods assume that optical flow is constant in a small neighborhood. The consequence of violating in this assumption is examined. The causes of measurement errors and the determinants of the conditioning of the solution system are also considered. By understanding how errors arise, we are able to define the inherent limitations of the technique, obtain estimates of the accuracy of computed values, enhance the performance of the technique, and demonstrate the informative value of some types of error.

Partitioning-based clustering for Web document categorization

Abstract Clustering techniques have been used by many intelligent software agents in order to retrieve, filter, and categorize documents available on the World Wide Web. Clustering is also useful in extracting salient features of related Web documents to automatically formulate queries and search for other similar documents on the Web. Traditional clustering algorithms either use a priori knowledge of document structures to define a distance or similarity among these documents, or use probabilistic techniques such as Bayesian classification. Many of these traditional algorithms, however, falter when the dimensionality of the feature space becomes high relative to the size of the document space. In this paper, we introduce two new clustering algorithms that can effectively cluster documents, even in the presence of a very high dimensional feature space. These clustering techniques, which are based on generalizations of graph partitioning, do not require pre-specified ad hoc distance functions, and are capable of automatically discovering document similarities or associations. We conduct several experiments on real Web data using various feature selection heuristics, and compare our clustering schemes to standard distance-based techniques, such as hierarchical agglomeration clustering , and Bayesian classification methods, such as AutoClass .

WebACE: a Web agent for document categorization and exploration

We propose an agent for exploring and categorizing documents on the World Wide Web based on a user pro le. The heart of the agent is an automatic categorization of a set of documents, combined with a process for generating new queries used to search for new related documents and ltering the resulting documents to extract the set of documents most closely related to the starting set. The document categories are not given a-priori. The resulting document set could also be used to update the initial set of documents. We present the overall architecture and describe two novel algorithms which provide signi cant improvement over traditional clustering algorithms and form the basis for the query generation and search component of the agent.

A survey of matrix inverse eigenvalue problems

In this paper, we present a survey of some recent results regarding direct methods for solving certain symmetric inverse eigenvalue problems. The problems we discuss in this paper are those of generating a symmetric matrix, either Jacobi, banded, or some variation thereof, given only some information on the eigenvalues of the matrix itself and some of its principal submatrices. Much of the motivation for the problems discussed in this paper came about from an interest in the inverse Sturm-Liouville problem. A preliminary version of this report was issued as a technical report of the Computer Science Department, University of Minnesota, TR 86-20, May 1986.

Document Categorization and Query Generation on the World Wide WebUsing WebACE

We present WebACE, an agent for exploring and categorizing documents onthe World Wide Web based on a user profile. The heart of the agent is anunsupervised categorization of a set of documents, combined with a processfor generating new queries that is used to search for new relateddocuments and for filtering the resulting documents to extract the onesmost closely related to the starting set. The document categories are notgiven a priori. We present the overall architecture and describe twonovel algorithms which provide significant improvement over HierarchicalAgglomeration Clustering and AutoClass algorithms and form the basis forthe query generation and search component of the agent. We report on theresults of our experiments comparing these new algorithms with moretraditional clustering algorithms and we show that our algorithms are fastand sacalable.

Adaptive control of a class of slowly time-varying plants

Abstract An adaptive control system of the type considered earlier by the author, which is designed to be stable under the assumption that the unknown plant parameters are constant, is shown to maintain stability when the plant parameters are slowly time varying.

A Lanczos-type method for multiple starting vectors

Given a square matrix and single right and left starting vectors, the classical nonsymmetric Lanczos process generates two sequences of bior- thogonal basis vectors for the right and left Krylov subspaces induced by the given matrix and vectors. In this paper, we propose a Lanczos-type algorithm that extends the classical Lanczos process for single starting vectors to mul- tiple starting vectors. Given a square matrix and two blocks of right and left starting vectors, the algorithm generates two sequences of biorthogonal basis vectors for the right and left block Krylov subspaces induced by the given data. The algorithm can handle the most general case of right and left start- ing blocks of arbitrary sizes, while all previously proposed extensions of the Lanczos process are restricted to right and left starting blocks of identical sizes. Other features of our algorithm include a built-in deation procedure to detect and delete linearly dependent vectors in the block Krylov sequences, and the option to employ look-ahead to remedy the potential breakdowns that may occur in nonsymmetric Lanczos-type methods.

Local Linear Convergence of the Alternating Direction Method of Multipliers on Quadratic or Linear Programs

We introduce a novel matrix recurrence yielding a new spectral analysis of the local transient convergence behavior of the alternating direction method of multipliers (ADMM), for the particular case of a quadratic program or a linear program. We identify a particular combination of vector iterates whose convergence can be analyzed via a spectral analysis. The theory predicts that ADMM should go through up to four convergence regimes, such as constant step convergence or linear convergence, ending with the latter when close enough to the optimal solution if the optimal solution is unique and satisfies strict complementarity.

Krylov space methods on state-space control models

We give an overview of various Lanczos/Krylov space methods and the way in which they are being used for solving certain problems in Control Systems Theory based on state-space models. The matrix methods used are based on Krylov sequences and are closely related to modern iterative methods for standard matrix problems such as sets of linear equations and eigenvalue calculations. We show how these methods can be applied to problems in Control Theory such as controllability, observability, and model reduction. All the methods are based on the use of state-space models, which may be very sparse and of high dimensionality. For example, we show how one may compute an approximate solution to a Lyapunov equation arising from a discrete-time linear dynamic system with a large sparse system matrix by the use of the Arnoldi algorithm, and so obtain an approximate Gramian matrix. This has applications in model reduction. The close relation between the matrix Lanczos algorithm and the algebraic structure of linear control systems is also explored.