A cluster analysis of basketball players for each of the five traditionally defined positions

Determining the players’ playing styles and bringing the right players together are very important for winning in basketball. This study aimed to group basketball players into similar clusters according to their playing styles for each of the traditionally defined five positions (point guard (PG), shooting guard (SG), small forward (SF), power forward (PF), and center (C)). This way, teams would be able to identify their type of players to help them determine what type of players they should recruit to build a better team. The 17 game-related statistics from 15 seasons of the National Basketball Association (NBA) were analyzed using a hierarchical clustering method. The cluster validity indices (CVIs) were used to determine the optimum number of groups. Based on this analysis, four clusters were identified for PG, SG, and SF positions, while five clusters for PF position and six clusters for C position were established. In addition to the definition of the created clusters, their individual achievements were examined based on three performance indicators: adjusted plus-minus (APM), average points differential, and the percentage of clusters on winning teams. This study contributes to the evaluation of team compatibility, which is a significant part of winning, as it allows one to determine the playing styles for each position, while examining the success of position pair combinations.

Towards Expert-Inspired Automatic Criterion to Cut a Dendrogram for Real-Industrial Applications

Hierarchical clustering is one of the most preferred choices to understand the underlying structure of a dataset and defining typologies, with multiple applications in real life. Among the existing clustering algorithms, the hierarchical family is one of the most popular, as it permits to understand the inner structure of the dataset and find the number of clusters as an output, unlike popular methods, like k-means. One can adjust the granularity of final clustering to the goals of the analysis themselves. The number of clusters in a hierarchical method relies on the analysis of the resulting dendrogram itself. Experts have criteria to visually inspect the dendrogram and determine the number of clusters. Finding automatic criteria to imitate experts in this task is still an open problem. But, dependence on the expert to cut the tree represents a limitation in real applications like the fields industry 4.0 and additive manufacturing. This paper analyses several cluster validity indexes in the context of determining the suitable number of clusters in hierarchical clustering. A new Cluster Validity Index (CVI) is proposed such that it properly catches the implicit criteria used by experts when analyzing dendrograms. The proposal has been applied on a range of datasets and validated against experts ground-truth overcoming the results obtained by the State of the Art and also significantly reduces the computational cost.

Automatic Domain Decomposition in Finite Element Method – A Comparative Study

In this paper, an automatic data clustering approach is presented using some concepts of the graph theory. Some Cluster Validity Index (CVI) is mentioned, and DB Index is defined as the objective function of meta-heuristic algorithms. Six Finite Element meshes are decomposed containing two- and three- dimensional types that comprise simple and complex meshes. Six meta-heuristic algorithms are utilized to determine the optimal number of clusters and minimize the decomposition problem. Finally, corresponding statistical results are compared.

Clustering refinement

Advanced validation of cluster analysis is expected to increase confidence and allow reliable implementations. In this work, we describe and test CluReAL, an algorithm for refining clustering irrespective of the method used in the first place. Moreover, we present ideograms that enable summarizing and properly interpreting problem spaces that have been clustered. The presented techniques are built on absolute cluster validity indices. Experiments cover a wide variety of scenarios and six of the most popular clustering techniques. Results show the potential of CluReAL for enhancing clustering and the suitability of ideograms to understand the context of the data through the lens of the cluster analysis. Refinement and interpretability are both crucial to reduce failure and increase performance control and operational awareness in unsupervised analysis.