Dataset Information

Clustering algorithm for formations in football games.

ABSTRACT: In competitive team sports, players maintain a certain formation during a game to achieve effective attacks and defenses. For the quantitative game analysis and assessment of team styles, we need a general framework that can characterize such formation structures dynamically. This paper develops a clustering algorithm for formations of multiple football (soccer) games based on the Delaunay method, which defines the formation of a team as an adjacency matrix of Delaunay triangulation. We first show that heat maps of entire football games can be clustered into several average formations: "442", "4141", "433", "541", and "343". Then, using hierarchical clustering, each average formation is further divided into more specific patterns (clusters) in which the configurations of players are different. Our method enables the visualization, quantitative comparison, and time-series analysis for formations in different time scales by focusing on transitions between clusters at each hierarchy. In particular, we can extract team styles from multiple games regarding the positional exchange of players within the formations. Applying our algorithm to the datasets comprising football games, we extract typical transition patterns of the formation for a particular team.

SUBMITTER: Narizuka T

PROVIDER: S-EPMC6739367 | biostudies-literature | 2019 Sep

REPOSITORIES: biostudies-literature

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Publications

Clustering algorithm for formations in football games.

Narizuka Takuma T Yamazaki Yoshihiro Y

Scientific reports 20190911 1

In competitive team sports, players maintain a certain formation during a game to achieve effective attacks and defenses. For the quantitative game analysis and assessment of team styles, we need a general framework that can characterize such formation structures dynamically. This paper develops a clustering algorithm for formations of multiple football (soccer) games based on the Delaunay method, which defines the formation of a team as an adjacency matrix of Delaunay triangulation. We first sh ...[more]

PMID: 31511542

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Project description:BackgroundWe present the algorithm PFClust (Parameter Free Clustering), which is able automatically to cluster data and identify a suitable number of clusters to group them into without requiring any parameters to be specified by the user. The algorithm partitions a dataset into a number of clusters that share some common attributes, such as their minimum expectation value and variance of intra-cluster similarity. A set of n objects can be clustered into any number of clusters from one to n, and there are many different hierarchical and partitional, agglomerative and divisive, clustering methodologies available that can be used to do this. Nonetheless, automatically determining the number of clusters present in a dataset constitutes a significant challenge for clustering algorithms. Identifying a putative optimum number of clusters to group the objects into involves computing and evaluating a range of clusterings with different numbers of clusters. However, there is no agreed or unique definition of optimum in this context. Thus, we test PFClust on datasets for which an external gold standard of 'correct' cluster definitions exists, noting that this division into clusters may be suboptimal according to other reasonable criteria. PFClust is heuristic in the sense that it cannot be described in terms of optimising any single simply-expressed metric over the space of possible clusterings.ResultsWe validate PFClust firstly with reference to a number of synthetic datasets consisting of 2D vectors, showing that its clustering performance is at least equal to that of six other leading methodologies - even though five of the other methods are told in advance how many clusters to use. We also demonstrate the ability of PFClust to classify the three dimensional structures of protein domains, using a set of folds taken from the structural bioinformatics database CATH.ConclusionsWe show that PFClust is able to cluster the test datasets a little better, on average, than any of the other algorithms, and furthermore is able to do this without the need to specify any external parameters. Results on the synthetic datasets demonstrate that PFClust generates meaningful clusters, while our algorithm also shows excellent agreement with the correct assignments for a dataset extracted from the CATH part-manually curated classification of protein domain structures.

Dataset Information

Clustering algorithm for formations in football games.

Publications

Clustering algorithm for formations in football games.

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