Editor: Kernel based methods are increasingly being used for data modeling because of their conceptual simplicity and outstanding performance on many tasks. However, the kernel function is often chosen using trial-and-error heuristics. In this paper we address the problem of measuring the degree of agreement between a kernel and a learning task. A quantitative measure of agreement is important from both a theoretical and practical point of view. We propose a quantity to capture this notion, which we call Alignment. We study its theoretical properties, and derive a series of simple algorithms for adapting a kernel to the labels and vice versa. This produces a series of novel methods for clustering and transduction, kernel combination and kernel selection. The algorithms are tested on two publicly available datasets and are shown to exhibit good performance.

SUMMARIST is an attempt to create a robust automated text summarization system, based on the ‘equation’: summarization = topic identification interpretation generation. Each of these stages contains several independent modules, many of them trained on large corpora of text. We describe the system’s architecture and provide details of some of its modules.

Abstract. The evolution of digital libraries and the Internet has dramatically transformed the processing, storage, and retrieval of information. Efforts to digitize text, images, video, and audio now consume a substantial portion of both academic and industrial activity. Even when there is no shortage of textual materials on a particular topic, procedures for indexing or extracting the knowledge or conceptual information contained in them can be lacking. Recently developed information retrieval technologies are based on the concept of a vector space. Data are modeled as a matrix, and a user’s query of the database is represented as a vector. Relevant documents in the database are then identified via simple vector operations. Orthogonal factorizations of the matrix provide mechanisms for handling uncertainty in the database itself. The purpose of this paper is to show how such fundamental mathematical concepts from linear algebra can be used to manage and index large text collections. Key words. information retrieval, linear algebra, QR factorization, singular value decomposition, vector spaces

With the exponential growth of information on the World Wide Web, there is great demand for developing efficient and effective methods for organizing and retrieving the information available. Document clustering plays an important role in information retrieval and taxonomy management for the World Wide Web and remains an interesting and challenging problem in the field of web computing. In this paper we consider document clustering methods exploring textual information, hyperlink structure and co-citation relations. In particular, we apply the normalized-cut clustering method developed in computer vision to the task of hyperdocument clustering. We also explore some theoretical connections of the normalized-cut method to K-means method. We then experiment with normalized-cut method in the context of clustering query result sets for web search engines.

In several real-life data-mining... This paper proposes a relationship-based approach that alleviates both problems, side-stepping the "curse-of-dimensionality" issue by working in a suitable similarity space instead of the original high-dimensional attribute space. This intermediary similarity space can be suitably tailored to satisfy business criteria such as requiring customer clusters to represent comparable amounts of revenue. We apply efficient and scalable graph-partitioning-based clustering techniques in this space. The output from the clustering algorithm is used to re-order the data points so that the resulting permuted similarity matrix can be readily visualized in two dimensions, with clusters showing up as bands. While two-dimensional visualization of a similarity matrix is by itself not novel, its combination with the order-sensitive partitioning of a graph that captures the relevant similarity measure between objects provides three powerful properties: (i) the high-dimensionality of the data does not affect further processing once the similarity space is formed; (ii) it leads to clusters of (approximately) equal importance, and (iii) related clusters show up adjacent to one another, further facilitating the visualization of results. The visualization is very helpful for assessing and improving clustering. For example, actionable recommendations for splitting or merging of clusters can be easily derived, and it also guides the user toward the right number of clusters

A wide range of computational kernels in data mining and information retrieval from text collections involve techniques from linear algebra. These kernels typically operate on data that is presented in the form of large sparse term-document matrices (tdm). We present TMG, a research and teaching toolbox for the generation of sparse tdm’s from text collections and for the incremental modification of these tdm’s by means of additions or deletions. The toolbox is written entirely in MATLAB, a popular problem solving environment that is powerful in computational linear algebra, in order to streamline document preprocessing and prototyping of algorithms for information retrieval. Several design issues that concern the use of MATLAB sparse infrastructure and data structures are addressed. We illustrate the use of the tool in numerical explorations of the effect of stemming and different term-weighting policies on the performance of querying and clustering tasks.

. A common operation in scientific computing is the multiplication of a sparse, rectangular or structurally nonsymmetric matrix and a vector. In many applications the matrix-transposevector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioning bipartite graphs. We then introduce several algorithms for this partitioning problem and compare their performance on a set of test matrices. Key words. matrix partitioning, iterative method, parallel computing, rectangular matrix, structurally nonsymmetric matrix, bipartite graph AMS subject classifications. 05C50, 65F10, 65F50, 65Y05 1. Introduction. Matrix-vector and matrix-transpose-vector products that repeatedly involve the same large, sparse, structurally nonsymmetric or rectangular matrix arise in many iterative algorithms. Examples include algorithms for solving linear systems, least squares problems, and linear programs. To e...

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Abstract. A common operation in scientific computingis the multiplication of a sparse, rectangular, or structurally unsymmetric matrix and a vector. In many applications the matrix-transposevector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioningbipartite graphs. We then introduce several algorithms for this partitioning problem and compare their performance on a set of test matrices.

We review the time and storage costs of search and clustering algorithms. We exemplify these, based on case-studies in astronomy, information retrieval, visual user interfaces, chemical databases, and other areas. Sections 2 to 6 relate to nearest neighbor searching, an elemental form of clustering, and a basis for clustering algorithms to follow. Sections 7 to 11 review a number of families of clustering algorithm. Sections 12 to 14 relate to visual or image representations of data sets, from which a number of interesting algorithmic developments arise.