Algorithms for discovering bucket orders from data

Gionis, Aristides; Mannila, Heikki; Puolamäki, Kai; Ukkonen, Antti

doi:10.1145/1150402.1150468

Cited by 43 publications

(62 citation statements)

References 28 publications

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“…. , σ (t) are ordered [8], rankings of subsets A of Λ where only labels in A are ordered [22], rankings over a partition of Λ (or bucket orders) [21]. Pairwise preferences are even more general, as most of the previous models cannot model a unique preference λ i λ j [7].…”

Section: Fig 1 Pairwise Decomposition Of Rankingsmentioning

confidence: 99%

A Pairwise Label Ranking Method with Imprecise Scores and Partial Predictions

Destercke

2013

Advanced Information Systems Engineering

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Abstract. In this paper, we are interested in the label ranking problem. We are more specifically interested in the recent trend consisting in predicting partial but more accurate (i.e., making less incorrect statements) orders rather than complete ones. To do so, we propose a ranking method based on pairwise imprecise scores obtained from likelihood functions. We discuss how such imprecise scores can be aggregated to produce interval orders, which are specific types of partial orders. We then analyse the performances of the method as well as its sensitivity to missing data and parameter values.

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Section: Fig 1 Pairwise Decomposition Of Rankingsmentioning

confidence: 99%

A Pairwise Label Ranking Method with Imprecise Scores and Partial Predictions

Destercke

2013

Advanced Information Systems Engineering

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“…For 1 ≤ i ≤ n e + 3, define the i-swap pair to be (3i 1,2,3,4,6,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37). Let x = n e + 1, y = n e + 2, and z = n e + 3.…”

Section: Cubic Vertex Covermentioning

confidence: 99%

“…Ukkonen [33] introduces a scoring function to accurately define a "best-fit" poset or set of posets against the input set of total orders. Gionis et al [14] seek bucket orders (total orders with ties), instead of posets.…”

Section: Introductionmentioning

confidence: 99%

Mining Posets From Linear Orders

Fernandez

Heath

Ramakrishnan

et al. 2013

Discrete Math. Algorithm. Appl.

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There has been much research on the combinatorial problem of generating the linear extensions of a given poset. This paper focuses on the reverse of that problem, where the input is a set of linear orders, and the goal is to construct a poset or set of posets that generates the input. Such a problem finds applications in computational neuroscience, systems biology, paleontology, and physical plant engineering. In this paper, two algorithms are presented for efficiently finding a single poset, if such a poset exists, whose linear extensions are exactly the same as the input set of linear orders. The variation of the problem where a minimum set of posets that cover the input is also explored. This variation is shown to be polynomially solvable for one class of simple posets (kite(2) posets) but NP-complete for a related class (hammock(2,2,2) posets).General Terms: Algorithms.

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“…The order between two entities of different buckets is given by the relative ordering of the buckets they belong to (entities in B i are ranked higher than the entities in B j if i < j). The bucket order problem [11,10,14,12] is, given a set of input rankings, compute a bucket order that best captures the data. The input rankings could be defined on subsets of the universe of entities; they could even be a large collection of pairwise preferences.…”

Section: Introductionmentioning

confidence: 99%

“…We prove an upperbound of O( √ log n) in this setting. When the discrepancies are arbitrary, we model the problem as the traditional bucket order problem studied in [11,10,14,12]. We develop a novel approach which exploits a natural relationship between correlation clustering [5] and the properties satisfied by the buckets in a bucket order.…”

Section: Introductionmentioning

confidence: 99%

On Discovering Bucket Orders from Preference Data

Kenkre¹,

Khan²,

Pandit³

2011

Proceedings of the 2011 SIAM International Conference on Data Mining

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The problem of ordering a set of entities which contain inherent ties among them arises in many applications. Notion of "bucket order" has emerged as a popular mechanism of ranking in such settings. A bucket order is an ordered partition of the set of entities into "buckets". There is a total order on the buckets, but the entities within a bucket are treated as tied.In this paper, we focus on discovering bucket order from data captured in the form of user preferences. We consider two settings: one in which the discrepancies in the input preferences are "local" (when collected from experts) and the other in which discrepancies could be arbitrary (when collected from a large population). We present a formal model to capture the setting of local discrepancies and consider the following question: "how many experts need to be queried to discover the underlying bucket order on n entities?". We prove an upperbound of O( √ log n). In the case of arbitrary discrepancies, we model it as the bucket order problem of discovering a bucket order that best fits the data (captured as pairwise preference statistics). We present a new approach which exploits a connection between the discovery of buckets and the correlation clustering problem. We present empirical evaluation of our algorithms on real and artificially generated datasets.

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Algorithms for discovering bucket orders from data

Cited by 43 publications

References 28 publications

A Pairwise Label Ranking Method with Imprecise Scores and Partial Predictions

A Pairwise Label Ranking Method with Imprecise Scores and Partial Predictions

Mining Posets From Linear Orders

On Discovering Bucket Orders from Preference Data

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