This paper presents the results of an experimental study of some common document clustering techniques: agglomerative hierarchical clustering and K-means. (We used both a “standard” K-means algorithm and a “bisecting ” K-means algorithm.) Our results indicate that the bisecting K-means technique is better than the standard K-means approach and (somewhat surprisingly) as good or better than the hierarchical approaches that we tested.

The naive Bayes classifier, currently experiencing a renaissance in machine learning, has long been a core technique in information retrieval. We review some of the variations of naive Bayes models used for text retrieval and classification, focusing on the distributional assump- tions made about word occurrences in documents.

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

Text data in the Internet can be partitioned into many databases naturally. Efficient retrieval of desired data can be achieved if we can accurately predict the usefulness of each database, because with such information, we only need to retrieve potentially useful documents from useful databases. In this paper, we propose two new methods for estimating the usefulness of text databases. For a given query, the usefulness of a text database in this paper is defined to be the number of documents in the database that are sufficiently similar to the query. Such a usefulness measure enables naive-users to make informed decision about which databases to search. We also consider the collection fusion problem. Because local databases may employ similarity functions that are different from that used by the global database, the threshold used by a local database to determine whether a document is potentially useful may be different from that used by the global database. We provide techniques that ...

Discriminant analysis has been used for decades to extract features that preserve class separability. It is commonly defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters. The requirement that one of these matrices be nonsingular limits its application to data sets with certain relative dimensions. We examine a number of optimization criteria, and extend their applicability by using the generalized singular value decomposition to circumvent the nonsingularity requirement. The result is a generalization of discriminant analysis that can be applied even when the sample size is smaller than the dimension of the sample data. We use classification results from the reduced representation to compare the effectiveness of this approach with some alternatives, and conclude with a discussion of their relative merits. 1

Abstract Dimension reduction in today's vector space based information retrieval system is essential for improvingcomputational efficiency in handling massive amounts of data. A mathematical framework for lower dimensional representation of text data in vector space based information retrieval is proposed using minimizationand a matrix rank reduction formula. We illustrate how the commonly used Latent Semantic Indexing based on the Singular Value Decomposition (LSI/SVD) can be derived as a method for dimension reduction fromour mathematical framework. Then two new methods for dimension reduction based on the centroids of data clusters are proposed and shown to be more efficient and effective than LSI/SVD when we have a prioriinformation on the cluster structure of the data. Several advantages of the new methods in terms of computational efficiency and data representation in the reduced space, as well as their mathematical properties arediscussed. Experimental results are presented to illustrate the effectiveness of our methods on certain classificationproblems in a reduced dimensional space. The results indicate that for a successful lower dimensional representation of the data, it is important to incorporate a priori knowledge in the dimension reductionalgorithms.

In this paper, we present a statistical method to estimate the usefulness of a search engine for any given query. The estimates can be used by a metasearch engine to choose local search engines to invoke. For a given query, the usefulness of a search engine in this paper is defined to be a combination of the number of documents in the search engine that are sufficiently similar to the query and the average similarity of these documents. Experimental results indicate that the proposed estimation method is quite accurate. 1 Introduction Many search engines have been created on the Internet to help ordinary users find desired data. Each search engine has a corresponding database that defines the set of documents that can be searched by the search engine. Usually, an index for all documents in the database is created and stored in the search engine to speed up query processing. The amount of data in the Internet is huge (it is believed that by the end of 1997, there were more than 300 mil...

In this paper we compare the performance of local detectors and descriptors in the context of object class recognition. Recently, many detectors / descriptors have been evaluated in the context of matching as well as invariance to viewpoint changes [20]. However, it is unclear if these results can be generalized to categorization problems, which require different properties of features. We evaluate 5 stateof-the-art scale invariant region detectors and 5 descriptors. Local features are computed for 20 object classes and clustered using hierarchical agglomerative clustering. We measure the quality of appearance clusters and location distributions using entropy as well as precision. We also measure how the clusters generalize from training set to novel test data. Our results indicate that extended SIFT descriptors [22] computed on Hessian-Laplace [20] regions perform best. Second score is obtained by Salient regions [11]. The results also show that these two detectors provide complementary features. The new detectors/descriptors significantly improve the performance of a state-of-the art recognition approach [16] in pedestrian detection task. 1.

Abstract. In today’s vector space information retrieval systems, dimension reduction is imperative for efficiently manipulating the massive quantity of data. To be useful, this lower-dimensional representation must be a good approximation of the full document set. To that end, we adapt and extend the discriminant analysis projection used in pattern recognition. This projection preserves cluster structure by maximizing the scatter between clusters while minimizing the scatter within clusters. A common limitation of trace optimization in discriminant analysis is that one of the scatter matrices must be nonsingular, which restricts its application to document sets in which the number of terms does not exceed the number of documents. We show that by using the generalized singular value decomposition (GSVD), we can achieve the same goal regardless of the relative dimensions of the term-document matrix. In addition, applying the GSVD allows us to avoid the explicit formation of the scatter matrices in favor of working directly with the data matrix, thus improving the numerical properties of the approach. Finally, we present experimental results that confirm the effectiveness of our approach.

Abstract—An optimization criterion is presented for discriminant analysis. The criterion extends the optimization criteria of the classical Linear Discriminant Analysis (LDA) through the use of the pseudoinverse when the scatter matrices are singular. It is applicable regardless of the relative sizes of the data dimension and sample size, overcoming a limitation of classical LDA. The optimization problem can be solved analytically by applying the Generalized Singular Value Decomposition (GSVD) technique. The pseudoinverse has been suggested and used for undersampled problems in the past, where the data dimension exceeds the number of data points. The criterion proposed in this paper provides a theoretical justification for this procedure. An approximation algorithm for the GSVD-based approach is also presented. It reduces the computational complexity by finding subclusters of each cluster and uses their centroids to capture the structure of each cluster. This reduced problem yields much smaller matrices to which the GSVD can be applied efficiently. Experiments on text data, with up to 7,000 dimensions, show that the approximation algorithm produces results that are close to those produced by the exact algorithm. Index Terms—Classification, clustering, dimension reduction, generalized singular value decomposition, linear discriminant analysis, text mining. 1