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Margareta Ackerman

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8 papers

1 author row

JMLR Journal 2016 Journal Article

A Characterization of Linkage-Based Hierarchical Clustering

Margareta Ackerman
Shai Ben-David

The class of linkage-based algorithms is perhaps the most popular class of hierarchical algorithms. We identify two properties of hierarchical algorithms, and prove that linkage- based algorithms are the only ones that satisfy both of these properties. Our characterization clearly delineates the difference between linkage-based algorithms and other hierarchical methods. We formulate an intuitive notion of locality of a hierarchical algorithm that distinguishes between linkage-based and global hierarchical algorithms like bisecting $k$-means, and prove that popular divisive hierarchical algorithms produce clusterings that cannot be produced by any linkage-based algorithm. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

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JAAMAS Journal 2016 Journal Article

The authorship dilemma: alphabetical or contribution?

Margareta Ackerman
Simina Brânzei

Abstract Scientific communities have adopted different conventions for ordering authors on publications. Are these choices inconsequential, or do they have significant influence on individual authors, the quality of the projects completed, and research communities at large? What are the trade-offs of using one convention over another? In order to investigate these questions, we formulate a basic two-player game theoretic model, which already illustrates interesting phenomena that can occur in more realistic settings. We find that contribution-based ordering leads to a denser collaboration network and a greater number of publications, while alphabetical ordering can improve research quality. Contrary to the assumption that free riding is a weakness of the alphabetical ordering scheme, when there are only two authors, this phenomenon can occur under any contribution scheme, and the worst case occurs under contribution-based ordering. Finally, we show how authors working on multiple projects can cooperate to attain optimal research quality and eliminate free riding given either contribution scheme.

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NeurIPS Conference 2014 Conference Paper

Incremental Clustering: The Case for Extra Clusters

Margareta Ackerman
Sanjoy Dasgupta

The explosion in the amount of data available for analysis often necessitates a transition from batch to incremental clustering methods, which process one element at a time and typically store only a small subset of the data. In this paper, we initiate the formal analysis of incremental clustering methods focusing on the types of cluster structure that they are able to detect. We find that the incremental setting is strictly weaker than the batch model, proving that a fundamental class of cluster structures that can readily be detected in the batch setting is impossible to identify using any incremental method. Furthermore, we show how the limitations of incremental clustering can be overcome by allowing additional clusters.

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AAAI Conference 2012 Conference Paper

Weighted Clustering

Margareta Ackerman
Shai Ben-David
Simina Brânzei
David Loker

We investigate a natural generalization of the classical clustering problem, considering clustering tasks in which different instances may have different weights. We conduct the first extensive theoretical analysis on the influence of weighted data on standard clustering algorithms in both the partitional and hierarchical settings, characterizing the conditions under which algorithms react to weights. Extending a recent framework for clustering algorithm selection, we propose intuitive properties that would allow users to choose between clustering algorithms in the weighted setting and classify algorithms accordingly.

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IJCAI Conference 2011 Conference Paper

Discerning Linkage-Based Algorithms among Hierarchical Clustering Methods

Margareta Ackerman
Shai Ben-David

Selecting a clustering algorithm is a perplexing task. Yet since different algorithms may yield dramatically different outputs on the same data, the choice of algorithm is crucial. When selecting a clustering algorithm, users tend to focus on cost-related considerations (software purchasing costs, running times, etc). Differences concerning the output of the algorithms are not usually considered. Recently, a formal approach for selecting a clustering algorithm has been proposed (Ackerman, Ben-David, and Loker, NIPS 2010). The approach involves distilling abstract properties of the input-output behavior of different clustering paradigms and classifying algorithms based on these properties. In this paper, we extend this approach into the hierarchical setting. The class of linkage-based algorithms is perhaps the most popular class of hierarchical algorithms. We identify two properties of hierarchical algorithms, and prove that linkage-based algorithms are the only ones that satisfy both of these properties. Our characterization clearly delineates the difference between linkage-based algorithms and other hierarchical algorithms. We formulate an intuitive notion of locality of a hierarchical algorithm that distinguishes between linkage-based and "global" hierarchical algorithms like bisecting k-means, and prove that popular divisive hierarchical algorithms produce clusterings that cannot be produced by any linkage-based algorithm.

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NeurIPS Conference 2010 Conference Paper

Towards Property-Based Classification of Clustering Paradigms

Margareta Ackerman
Shai Ben-David
David Loker

Clustering is a basic data mining task with a wide variety of applications. Not surprisingly, there exist many clustering algorithms. However, clustering is an ill defined problem - given a data set, it is not clear what a “correct” clustering for that set is. Indeed, different algorithms may yield dramatically different outputs for the same input sets. Faced with a concrete clustering task, a user needs to choose an appropriate clustering algorithm. Currently, such decisions are often made in a very ad hoc, if not completely random, manner. Given the crucial effect of the choice of a clustering algorithm on the resulting clustering, this state of affairs is truly regrettable. In this paper we address the major research challenge of developing tools for helping users make more informed decisions when they come to pick a clustering tool for their data. This is, of course, a very ambitious endeavor, and in this paper, we make some first steps towards this goal. We propose to address this problem by distilling abstract properties of the input-output behavior of different clustering paradigms. In this paper, we demonstrate how abstract, intuitive properties of clustering functions can be used to taxonomize a set of popular clustering algorithmic paradigms. On top of addressing deterministic clustering algorithms, we also propose similar properties for randomized algorithms and use them to highlight functional differences between different common implementations of k-means clustering. We also study relationships between the properties, independent of any particular algorithm. In particular, we strengthen Kleinbergs famous impossibility result, while providing a simpler proof.

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TCS Journal 2009 Journal Article

Efficient enumeration of words in regular languages

Margareta Ackerman
Jeffrey Shallit

The cross-section enumeration problem is to list all words of length n in a regular language L in lexicographical order. The enumeration problem is to list the first m words in L according to radix order. We present an algorithm for the cross-section enumeration problem that is linear in n + t, where t is the output size. We provide a detailed analysis of the asymptotic running time of our algorithm and that of known algorithms for both enumeration problems. We discuss some shortcomings of the enumeration algorithm found in the Grail computation package. In the practical domain, we modify Mäkinen’s enumeration algorithm to get an algorithm that is usually the most efficient in practice. We performed an extensive performance analysis of the new and previously known enumeration and cross-section enumeration algorithms and found when each algorithm is preferable.

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NeurIPS Conference 2008 Conference Paper

Measures of Clustering Quality: A Working Set of Axioms for Clustering

Shai Ben-David
Margareta Ackerman

Aiming towards the development of a general clustering theory, we discuss abstract axiomatization for clustering. In this respect, we follow up on the work of Kelinberg, (Kleinberg) that showed an impossibility result for such axiomatization. We argue that an impossibility result is not an inherent feature of clustering, but rather, to a large extent, it is an artifact of the specific formalism used in Kleinberg. As opposed to previous work focusing on clustering functions, we propose to address clustering quality measures as the primitive object to be axiomatized. We show that principles like those formulated in Kleinberg's axioms can be readily expressed in the latter framework without leading to inconsistency. A clustering-quality measure is a function that, given a data set and its partition into clusters, returns a non-negative real number representing how strong' or conclusive' the clustering is. We analyze what clustering-quality measures should look like and introduce a set of requirements (`axioms') that express these requirement and extend the translation of Kleinberg's axioms to our framework. We propose several natural clustering quality measures, all satisfying the proposed axioms. In addition, we show that the proposed clustering quality can be computed in polynomial time.

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