We motivate and develop a natural bicriteria measure for assessing the quality of a clustering which avoids the drawbacks of existing measures. A simple recursive heuristic has poly-logarithmic worst-case guarantees under the new measure. The main result of the paper is the analysis of a popular spectral algorithm. One variant of spectral clustering turns out to have effective worst-case guarantees

Two-dimensional contingency or co-occurrence tables arise frequently in important applications such as text, web-log and market-basket data analysis. A basic problem in contingency table analysis is co-clustering: simultaneous clustering of the rows and columns. A novel theoretical formulation views the contingency table as an empirical joint probability distribution of two discrete random variables and poses the co-clustering problem as an optimization problem in information theory -- the optimal co-clustering maximizes the mutual information between the clustered random variables subject to constraints on the number of row and column clusters.

Abstract—A large number of clustering approaches have been proposed for the analysis of gene expression data obtained from microarray experiments. However, the results from the application of standard clustering methods to genes are limited. This limitation is imposed by the existence of a number of experimental conditions where the activity of genes is uncorrelated. A similar limitation exists when clustering of conditions is performed. For this reason, a number of algorithms that perform simultaneous clustering on the row and column dimensions of the data matrix has been proposed. The goal is to find submatrices, that is, subgroups of genes and subgroups of conditions, where the genes exhibit highly correlated activities for every condition. In this paper, we refer to this class of algorithms as biclustering. Biclustering is also referred in the literature as coclustering and direct clustering, among others names, and has also been used in fields such as information retrieval and data mining. In this comprehensive survey, we analyze a large number of existing approaches to biclustering, and classify them in accordance with the type of biclusters they can find, the patterns of biclusters that are discovered, the methods used to perform the search, the approaches used to evaluate the solution, and the target applications. Index Terms—Biclustering, simultaneous clustering, coclustering, subspace clustering, bidimensional clustering, direct clustering, block clustering, two-way clustering, two-mode clustering, two-sided clustering, microarray data analysis, biological data analysis, gene expression data. 1

Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in mathematics, statistics, and numerical analysis. From a machine learning perspective clusters correspond to hidden patterns, the search for clusters is unsupervised learning, and the resulting system represents a data concept. From a practical perspective clustering plays an outstanding role in data mining applications such as scientific data exploration, information retrieval and text mining, spatial database applications, Web analysis, CRM, marketing, medical diagnostics, computational biology, and many others. Clustering is the subject of active research in several fields such as statistics, pattern recognition, and machine learning. This survey focuses on clustering in data mining. Data mining adds to clustering the complications of very large datasets with very many attributes of different types. This imposes unique

Consistency is a key property of statistical algorithms, when the data is drawn from some underlying probability distribution. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of a popular family of spectral clustering algorithms, which cluster the data with the help of eigenvectors of graph Laplacian matrices. We show that one of the two of major classes of spectral clustering (normalized clustering) converges under some very general conditions, while the other (unnormalized), is only consistent under strong additional assumptions, which, as we demonstrate, are not always satisfied in real data. We conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering in practical applications. We believe that methods used in our analysis will provide a basis for future exploration of Laplacian-based methods in a statistical setting.

We present a new method for transductive learning, which can be seen as a transductive version of the k nearest-neighbor classifier.

Fast and high-quality document clustering algorithms play an important role in providing intuitive navigation and browsing mechanisms by organizing large amounts of information into a small number of meaningful clusters. In particular, hierarchical clustering solutions provide a view of the data at different levels of granularity, making them ideal for people to visualize and interactively explore large document collections.

In recent years, we have witnessed a tremendous growth in the volume of text documents available on the Internet, digital libraries, news sources, and company-wide intranets. This has led to an increased interest in developing methods that can help users to effectively navigate, summarize, and organize this information with the ultimate goal of helping them to find what they are looking for. Fast and high-quality document clustering algorithms play an important role towards this goal as they have been shown to provide both an intuitive navigation/browsing mechanism by organizing large amounts of information into a small number of meaningful clusters as well as to greatly improve the retrieval performance either via cluster-driven dimensionality reduction, term-weighting, or query expansion. This ever-increasing importance of document clustering and the expanded range of its applications led to the development of a number of new and novel algorithms with different complexity-quality trade-offs. Among them, a class of clustering algorithms that have relatively low computational requirements are those that treat the clustering problem as an optimization process which seeks to maximize or minimize a particular clustering criterion function defined over the entire clustering solution.

We present an unsupervised technique for detecting unusual activity in a large video set using many simple features. No complex activity models and no supervised feature selections are used. We divide the video into equal length segments and classify the extracted features into prototypes, from which a prototype--segment co-occurrence matrix is computed. Motivated by a similar problem in documentkeyword analysis, we seek a correspondence relationship between prototypes and video segments which satisfies the transitive closure constraint. We show that an important sub-family of correspondence functions can be reduced to co-embedding prototypes and segments to N-D Euclidean space. We prove that an efficient, globally optimal algorithm exists for the co-embedding problem. Experiments on various real-life videos have validated our approach.

Inspired by the PageRank and HITS (hubs and authorities) algorithms for Web search, we propose a structural re-ranking approach to ad hoc information retrieval: we reorder the documents in an initially retrieved set by exploiting asymmetric relationships between them. Specifically, we consider generation links, which indicate that the language model induced from one document assigns high probability to the text of another; in doing so, we take care to prevent bias against long documents. We study a number of re-ranking criteria based on measures of centrality in the graphs formed by generation links, and show that integrating centrality into standard language-model-based retrieval is quite effective at improving precision at top ranks.