A polynomial time computable metric between point sets

Ramon, Jan; Bruynooghe, Maurice

doi:10.1007/pl00013304

Cited by 58 publications

(53 citation statements)

References 5 publications

(10 reference statements)

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“…the Hausdorff metric, symmetric difference distances, distances based on relations between sets, etc. For our algorithm, we adopt the distance proposed in [10,11]. The distance between sets of elements is defined in [10] via transport networks (for more information on the concept of transport networks see [7]).…”

Section: Definition 1 (Linked Clause)mentioning

confidence: 99%

Relational IBL in Music with a New Structural Similarity Measure

Tobudic

Widmer

2003

Inductive Logic Programming

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Abstract. It is well known that many hard tasks considered in machine learning and data mining can be solved in an rather simple and robust way with an instance-and distance-based approach. In this paper we present another difficult task: learning, from large numbers of performances by concert pianists, to play music expressively. We model the problem as a multi-level decomposition and prediction task. Motivated by structural characteristics of such a task, we propose a new relational distance measure that is a rather straightforward combination of two existing measures. Empirical evaluation shows that our approach is in general viable and our algorithm, named DISTALL, is indeed able to produce musically interesting results. The experiments also provide evidence of the success of ILP in a complex domain such as music performance: it is shown that our instance-based learner operating on structured, relational data outperforms a propositional k-NN algorithm.

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Section: Definition 1 (Linked Clause)mentioning

confidence: 99%

Relational IBL in Music with a New Structural Similarity Measure

Tobudic

Widmer

2003

Inductive Logic Programming

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“…This is not restricted to tuples of a single relation. Using relational distance measures, it is possible to apply clustering and instance-based learning to multirelational data [13]. Most relational distance measures are based on recursive descent and set distances, i.e., distances between sets of points.…”

Section: Siql and Sindbad: Query Language And Demonstration Overviewmentioning

confidence: 99%

SINDBAD and SiQL: An Inductive Database and Query Language in the Relational Model

Wicker

Richter

Kessler

et al.

Machine Learning and Knowledge Discovery in Databases

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Abstract. In this demonstration, we will present the concepts and an implementation of an inductive database -as proposed by Imielinski and Mannila -in the relational model. The goal is to support all steps of the knowledge discovery process on the basis of queries to a database system. The query language SiQL (structured inductive query language), an SQL extension, offers query primitives for feature selection, discretization, pattern mining, clustering, instance-based learning and rule induction. A prototype system processing such queries was implemented as part of the SINDBAD (structured inductive database development) project. To support the analysis of multi-relational data, we incorporated multi-relational distance measures based on set distances and recursive descent. The inclusion of rule-based classification models made it necessary to extend the data model and software architecture significantly. The prototype is applied to three different data sets: gene expression analysis, gene regulation prediction and structure-activity relationships (SARs) of small molecules.

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“…For clustering multi-instance objects, it is possible to use distance functions for sets of objects like [6,7]. Having such a distance measure, it is possible to cluster multi-instance objects with k-medoid methods like PAM and CLARANS [11] or employ density-based clustering approaches like DBSCAN [9].…”

Section: Related Workmentioning

confidence: 99%

“…Another problem of this approach is that the selection of a meaningful distance measure has an important impact of the resulting clustering. For example, netflow-distance [7] demands that all instances within two compared objects are somehow similar, whereas for the minimal Hausdorff [12] distance the indication of similarity is only dependent on the closest pair.…”

Section: Related Workmentioning

confidence: 99%

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An EM-Approach for Clustering Multi-Instance Objects

Kriegel¹,

Pryakhin²,

Schubert³

2006

Advances in Knowledge Discovery and Data Mining

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Abstract. In many data mining applications the data objects are modeled as sets of feature vectors or multi-instance objects. In this paper, we present an expectation maximization approach for clustering multiinstance objects. We therefore present a statistical process that models multi-instance objects. Furthermore, we present M-steps and E-steps for EM clustering and a method for finding a good initial model. In our experimental evaluation, we demonstrate that the new EM algorithm is capable to increase the cluster quality for three real world data sets compared to a k-medoid clustering.

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A polynomial time computable metric between point sets

Cited by 58 publications

References 5 publications

Relational IBL in Music with a New Structural Similarity Measure

Relational IBL in Music with a New Structural Similarity Measure

SINDBAD and SiQL: An Inductive Database and Query Language in the Relational Model

An EM-Approach for Clustering Multi-Instance Objects

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