Panayiotis Tsaparas

Clustering aggregation

We consider the following problem: given a set of clusterings, find a clustering that agrees as much as possible with the given clusterings. This problem, clustering aggregation, appears naturally in various contexts. For example, clustering categorical data is an instance of the problem: each categorical variable can be viewed as a clustering of the input rows. Moreover, clustering aggregation can be used as a meta-clustering method to improve the robustness of clusterings. The problem formulation does not require a-priori information about the number of clusters, and it gives a natural way for handling missing values. We give a formal statement of the clustering-aggregation problem, we discuss related work, and we suggest a number of algorithms. For several of the methods we provide theoretical guarantees on the quality of the solutions. We also show how sampling can be used to scale the algorithms for large data sets. We give an extensive empirical evaluation demonstrating the usefulness of the problem and of the solutions.

Link analysis ranking: algorithms, theory, and experiments

The explosive growth and the widespread accessibility of the Web has led to a surge of research activity in the area of information retrieval on the World Wide Web. The seminal papers of Kleinberg [1998, 1999] and Brin and Page [1998] introduced Link Analysis Ranking, where hyperlink structures are used to determine the relative authority of a Web page and produce improved algorithms for the ranking of Web search results. In this article we work within the hubs and authorities framework defined by Kleinberg and we propose new families of algorithms. Two of the algorithms we propose use a Bayesian approach, as opposed to the usual algebraic and graph theoretic approaches. We also introduce a theoretical framework for the study of Link Analysis Ranking algorithms. The framework allows for the definition of specific properties of Link Analysis Ranking algorithms, as well as for comparing different algorithms. We study the properties of the algorithms that we define, and we provide an axiomatic characterization of the INDEGREE heuristic which ranks each node according to the number of incoming links. We conclude the article with an extensive experimental evaluation. We study the quality of the algorithms, and we examine how different structures in the graphs affect their performance.

Finding authorities and hubs from link structures on the World Wide Web

Recently, there have been a number of algorithms proposed for analyzing hypertext link structure so as to determine the best “authorities” for a given topic or query. While such analysis is usually combined with content analysis, there is a sense in which some algorithms are deemed to be “more balanced” and others “more focused”. We undertake a comparative study of hypertext link analysis algorithms. Guided by some experimental queries, we propose some formal criteria for evaluating and comparing link analysis algorithms.

LIMBO: Scalable Clustering of Categorical Data

Clustering is a problem of great practical importance in numerous applications. The problem of clustering becomes more challenging when the data is categorical, that is, when there is no inherent distance measure between data values. We introduce LIMBO, a scalable hierarchical categorical clustering algorithm that builds on the Information Bottleneck (IB) framework for quantifying the relevant information preserved when clustering. As a hierarchical algorithm, LIMBO has the advantage that it can produce clusterings of different sizes in a single execution. We use the IB framework to define a distance measure for categorical tuples and we also present a novel distance measure for categorical attribute values. We show how the LIMBO algorithm can be used to cluster both tuples and values. LIMBO handles large data sets by producing a memory bounded summary model for the data. We present an experimental evaluation of LIMBO, and we study how clustering quality compares to other categorical clustering algorithms. LIMBO supports a trade-off between efficiency (in terms of space and time) and quality. We quantify this trade-off and demonstrate that LIMBO allows for substantial improvements in efficiency with negligible decrease in quality.

Assessing data mining results via swap randomization

The problem of assessing the significance of data mining results on high-dimensional 0--1 datasets has been studied extensively in the literature. For problems such as mining frequent sets and finding correlations, significance testing can be done by standard statistical tests such as chi-square, or other methods. However, the results of such tests depend only on the specific attributes and not on the dataset as a whole. Moreover, the tests are difficult to apply to sets of patterns or other complex results of data mining algorithms. In this article, we consider a simple randomization technique that deals with this shortcoming. The approach consists of producing random datasets that have the same row and column margins as the given dataset, computing the results of interest on the randomized instances and comparing them to the results on the actual data. This randomization technique can be used to assess the results of many different types of data mining algorithms, such as frequent sets, clustering, and spectral analysis. To generate random datasets with given margins, we use variations of a Markov chain approach which is based on a simple swap operation. We give theoretical results on the efficiency of different randomization methods, and apply the swap randomization method to several well-known datasets. Our results indicate that for some datasets the structure discovered by the data mining algorithms is expected, given the row and column margins of the datasets, while for other datasets the discovered structure conveys information that is not captured by the margin counts.

Ranked join indices

A plethora of data sources contain data entities that could be ordered according to a variety of attributes associated with the entities. Such orderings result effectively in a ranking of the entities according to the values in the attribute domain. Commonly, users correlate such sources for query processing purposes through join operations. In query processing, it is desirable to incorporate user preferences towards specific attributes or their values. A way to incorporate such preferences is by utilizing scoring functions that combine user preferences and attribute values and return a numerical score for each tuple in the join result. Then, a target query, which we refer to as top-k join query, seeks to identify the k tuples in the join result with the highest scores. We propose a novel technique, which we refer to as ranked join index, to efficiently answer top-k join queries for arbitrary, user specified, preferences and a large class of scoring functions. Our rank join index requires small space (compared to the entire join result) and provides guarantees for its performance. Moreover, our proposal provides a graceful tradeoff between its space requirements and worst case search performance. We supplement our analytical results with a thorough experimental evaluation using a variety of real and synthetic data sets, demonstrating that, in comparison to other viable approaches, our technique offers significant performance benefits.

Information-theoretic tools for mining database structure from large data sets

Data design has been characterized as a process of arriving at a design that maximizes the information content of each piece of data (or equivalently, one that minimizes redundancy). Information content (or redundancy) is measured with respect to a prescribed model for the data, a model that is often expressed as a set of constraints. In this work, we consider the problem of doing data redesign in an environment where the prescribed model is unknown or incomplete. Specifically, we consider the problem of finding structural clues in an instance of data, an instance which may contain errors, missing values, and duplicate records. We propose a set of information-theoretic tools for finding structural summaries that are useful in characterizing the information content of the data, and ultimately useful in data design. We provide algorithms for creating these summaries over large, categorical data sets. We study the use of these summaries in one specific physical design task, that of ranking functional dependencies based on their data redundancy. We show how our ranking can be used by a physical data-design tool to find good vertical decompositions of a relation (decompositions that improve the information content of the design). We present an evaluation of the approach on real data sets.

Structured annotations of web queries

Queries asked on web search engines often target structured data, such as commercial products, movie showtimes, or airline schedules. However, surfacing relevant results from such data is a highly challenging problem, due to the unstructured language of the web queries, and the imposing scalability and speed requirements of web search. In this paper, we discover latent structured semantics in web queries and produce Structured Annotations for them. We consider an annotation as a mapping of a query to a table of structured data and attributes of this table. Given a collection of structured tables, we present a fast and scalable tagging mechanism for obtaining all possible annotations of a query over these tables. However, we observe that for a given query only few are sensible for the user needs. We thus propose a principled probabilistic scoring mechanism, using a generative model, for assessing the likelihood of a structured annotation, and we define a dynamic threshold for filtering out misinterpreted query annotations. Our techniques are completely unsupervised, obviating the need for costly manual labeling effort. We evaluated our techniques using real world queries and data and present promising experimental results.

Global similarity and local divergence in human and mouse gene co-expression networks

BackgroundA genome-wide comparative analysis of human and mouse gene expression patterns was performed in order to evaluate the evolutionary divergence of mammalian gene expression. Tissue-specific expression profiles were analyzed for 9,105 human-mouse orthologous gene pairs across 28 tissues. Expression profiles were resolved into species-specific coexpression networks, and the topological properties of the networks were compared between species.ResultsAt the global level, the topological properties of the human and mouse gene coexpression networks are, essentially, identical. For instance, both networks have topologies with small-world and scale-free properties as well as closely similar average node degrees, clustering coefficients, and path lengths. However, the human and mouse coexpression networks are highly divergent at the local level: only a small fraction (<10%) of coexpressed gene pair relationships are conserved between the two species. A series of controls for experimental and biological variance show that most of this divergence does not result from experimental noise. We further show that, while the expression divergence between species is genuinely rapid, expression does not evolve free from selective (functional) constraint. Indeed, the coexpression networks analyzed here are demonstrably functionally coherent as indicated by the functional similarity of coexpressed gene pairs, and this pattern is most pronounced in the conserved human-mouse intersection network. Numerous dense network clusters show evidence of dedicated functions, such as spermatogenesis and immune response, that are clearly consistent with the coherence of the expression patterns of their constituent gene members.ConclusionThe dissonance between global versus local network divergence suggests that the interspecies similarity of the global network properties is of limited biological significance, at best, and that the biologically relevant aspects of the architectures of gene coexpression are specific and particular, rather than universal. Nevertheless, there is substantial evolutionary conservation of the local network structure which is compatible with the notion that gene coexpression networks are subject to purifying selection.

Mining the inner structure of the Web graph

Despite being the sum of decentralized and uncoordinated efforts by heterogeneous groups and individuals, the World Wide Web exhibits a well-defined structure, characterized by several interesting properties. This structure was clearly revealed by Broder et al (2000 Graph structure in the web Comput. Netw. 33 309) who presented the evocative bow-tie picture of the Web. Although, the bow-tie structure is a relatively clear abstraction of the macroscopic picture of the Web, it is quite uninformative with respect to the finer details of the Web graph. In this paper, we mine the inner structure of the Web graph. We present a series of measurements on the Web, which offer a better understanding of the individual components of the bow-tie. In the process, we develop algorithmic techniques for performing these measurements. We discover that the scale-free properties permeate all the components of the bow-tie which exhibit the same macroscopic properties as the Web graph itself. However, close inspection reveals that their inner structure is quite distinct. We show that the Web graph does not exhibit self similarity within its components, and we propose a possible alternative picture for the Web graph, as it emerges from our experiments.