Aristides Gionis

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.

XTRACT: a system for extracting document type descriptors from XML documents

XML is rapidly emerging as the new standard for data representation and exchange on the Web. An XML document can be accompanied by a Document Type Descriptor (DTD) which plays the role of a schema for an XML data collection. DTDs contain valuable information on the structure of documents and thus have a crucial role in the efficient storage of XML data, as well as the effective formulation and optimization of XML queries. In this paper, we propose XTRACT, a novel system for inferring a DTD schema for a database of XML documents. Since the DTD syntax incorporates the full expressive power of regular expressions, naive approaches typically fail to produce concise and intuitive DTDs. Instead, the XTRACT inference algorithms employ a sequence of sophisticated steps that involve: (1) finding patterns in the input sequences and replacing them with regular expressions to generate “general” candidate DTDs, (2) factoring candidate DTDs using adaptations of algorithms from the logic optimization literature, and (3) applying the Minimum Description Length (MDL) principle to find the best DTD among the candidates. The results of our experiments with real-life and synthetic DTDs demonstrate the effectiveness of XTRACTs approach in inferring concise and semantically meaningful DTD schemas for XML databases.

Evaluating strategies for similarity search on the web

Finding pages on the Web that are similar to a query page (Related Pages) is an important component of modern search engines. A variety of strategies have been proposed for answering Related Pages queries, but comparative evaluation by user studies is expensive, especially when large strategy spaces must be searched (e.g., when tuning parameters). We present a technique for automatically evaluating strategies using Web hierarchies, such as Open Directory, in place of user feedback. We apply this evaluation methodology to a mix of document representation strategies, including the use of text, anchor-text, and links. We discuss the relative advantages and disadvantages of the various approaches examined. Finally, we describe how to efficiently construct a similarity index out of our chosen strategies, and provide sample results from our index.

Approximating a collection of frequent sets

One of the most well-studied problems in data mining is computing the collection of frequent item sets in large transactional databases. One obstacle for the applicability of frequent-set mining is that the size of the output collection can be far too large to be carefully examined and understood by the users. Even restricting the output to the border of the frequent item-set collection does not help much in alleviating the problem.In this paper we address the issue of overwhelmingly large output size by introducing and studying the following problem: What are the k sets that best approximate a collection of frequent item sets? Our measure of approximating a collection of sets by k sets is defined to be the size of the collection covered by the the k sets, i.e., the part of the collection that is included in one of the k sets. We also specify a bound on the number of extra sets that are allowed to be covered. We examine different problem variants for which we demonstrate the hardness of the corresponding problems and we provide simple polynomial-time approximation algorithms. We give empirical evidence showing that the approximation methods work well in practice.

The price of validity in dynamic networks

Massive-scale self-administered networks like Peer-to-Peer and Sensor Networks have data distributed across thousands of participant hosts. These networks are highly dynamic with short-lived hosts being the norm rather than an exception. In recent years, researchers have investigated best-effort algorithms to efficiently process aggregate queries (e.g., sum, count, average, minimum and maximum) [6, 13, 21, 34, 35, 37] on these networks. Unfortunately, query semantics for best-effort algorithms are ill-defined, making it hard to reason about guarantees associated with the result returned. In this paper, we specify a correctness condition, single-site validity, with respect to which the above algorithms are best-effort. We present a class of algorithms that guarantee validity in dynamic networks. Experiments on real-life and synthetic network topologies validate performance of our algorithms, revealing the hitherto unknown price of validity.

XTRACT: Learning Document Type Descriptors from XML Document Collections

XML is rapidly emerging as the new standard for data representation and exchange on the Web. Unlike HTML, tags in XML documents describe the semantics of the data and not how it is to be displayed. In addition, an XML document can be accompanied by a Document Type Descriptor (DTD) which plays the role of a schema for an XML data collection. DTDs contain valuable information on the structure of documents and thus have a crucial role in the efficient storage of XML data, as well as the effective formulation and optimization of XML queries. Despite their importance, however, DTDs are not mandatory, and it is frequently possible that documents in XML databases will not have accompanying DTDs. In this paper, we propose XTRACT, a novel system for inferring a DTD schema for a database of XML documents. Since the DTD syntax incorporates the full expressive power of regular expressions, naive approaches typically fail to produce concise and intuitive DTDs. Instead, the XTRACT inference algorithms employ a sequence of sophisticated steps that involve: (1) finding patterns in the input sequences and replacing them with regular expressions to generate “general” candidate DTDs, (2) factoring candidate DTDs using adaptations of algorithms from the logic optimization literature, and (3) applying the Minimum Description Length (MDL) principle to find the best DTD among the candidates. The results of our experiments with real-life and synthetic DTDs demonstrate the effectiveness of XTRACTs approach in inferring concise and semantically meaningful DTD schemas for XML databases.

Finding recurrent sources in sequences

Many genomic sequences and, more generally, (multivariate) time series display tremendous variability. However, often it is reasonable to assume that the sequence is actually generated by or assembled from a small number of sources, each of which might contribute several segments to the sequence. That is, there are h hidden sources such that the sequence can be written as a concatenation of k > h pieces, each of which stems from one of the h sources. We define this (k,h)-segmentation problem and show that it is NP-hard in the general case. We give approximation algorithms achieving approximation ratios of 3 for the L1 error measure and √5 for the L2 error measure, and generalize the results to higher dimensions. We give empirical results on real (chromosome 22) and artificial data showing that the methods work well in practice.

Dimension induced clustering

It is commonly assumed that high-dimensional datasets contain points most of which are located in low-dimensional manifolds. Detection of low-dimensional clusters is an extremely useful task for performing operations such as clustering and classification, however, it is a challenging computational problem. In this paper we study the problem of finding subsets of points with low intrinsic dimensionality. Our main contribution is to extend the definition of fractal correlation dimension, which measures average volume growth rate, in order to estimate the intrinsic dimensionality of the data in local neighborhoods. We provide a careful analysis of several key examples in order to demonstrate the properties of our measure. Based on our proposed measure, we introduce a novel approach to discover clusters with low dimensionality. The resulting algorithms extend previous density based measures, which have been successfully used for clustering. We demonstrate the effectiveness of our algorithms for discovering low-dimensional m-flats embedded in high dimensional spaces, and for detecting low-rank sub-matrices.

Spectral ordering and biochronology of European fossil mammals

Abstract Spectral algorithms have been shown to work well in a wide range of situations that involve the task of ordering. When applied to the localities of a set of European Neogene land mammal taxa, spectral ordering relies almost entirely on the most common genera, depends on connectivity more than on length of taxon lists, and is robust to noise from rarer and less connected taxa. The spectral coefficients for localities are highly correlated with known geochronological ages. Although elementary compared with more sophisticated biochronological tools, spectral ordering allows a fast and standardized way to generate biochronological ordering of localities when other information than faunal lists is lacking. Compared with the conventional mammal Neogene (MN) units, spectral ordering of localities appears to lack distinct temporal boundaries in taxon content and render a much lower count of Lazarus events. If, as seems to be the case, biochronology depends mainly on the most common taxa and if evolutionary change is also most clearly reflected in them, then the main evolutionary patterns should be detectable at a modest level of sampling.

The discrete basis problem

Matrix decomposition methods represent a data matrix as a product of two factor matrices: one containing basis vectors that represent meaningful concepts in the data, and another describing how the observed data can be expressed as combinations of the basis vectors. Decomposition methods have been studied extensively, but many methods return real-valued matrices. Interpreting real-valued factor matrices is hard if the original data is Boolean. In this paper, we describe a matrix decomposition formulation for Boolean data, the Discrete Basis Problem. The problem seeks for a Boolean decomposition of a binary matrix, thus allowing the user to easily interpret the basis vectors. We also describe a variation of the problem, the Discrete Basis Partitioning Problem. We show that both problems are NP-hard. For the Discrete Basis Problem, we give a simple greedy algorithm for solving it; for the Discrete Basis Partitioning Problem we show how it can be solved using existing methods. We present experimental results for the greedy algorithm and compare it against other, well known methods. Our algorithm gives intuitive basis vectors, but its reconstruction error is usually larger than with the real-valued methods. We discuss about the reasons for this behavior.