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CPS1950 Paolo G. et al.
DREB -0.04 0.35
AST 0.42 0.07
TOV 0.05 0.04
STL 0.17 0.04
BLK 0.43 -0.01
BLKA -0.28 -0.20
PTS 0.58 -0.25
Component 1 was characterized by a large number of points (PTS) due to
a high 3-point field goals percentage (3PP) and to a high number of assists
(AST) and by a large number of blocks (BLK). Component 2 was related to a
high field goal percentage (FGP) and a lot of defensive rebounds (DREB). These
were variables playing the most relevant role in determining the clusters. Some
variables such as TOV, STL and OREB do not seem to contribute to the
description of the clusters.
The two cluster centroids distinguished the teams with respect to low
(Cluster 1) or high (Cluster 2) levels of the two components. Therefore, the
teams assigned to Cluster 1 had a worse performance in comparison with
those belonging to Cluster 2. The membership degree matrix (not reported
here) offered a better insight into the obtained clusters. We found that all the
teams assigned to Cluster 2 reached the playoff stage, whilst Cluster 1 was
composed by all the teams not qualified to the playoff stage and some other
teams which played the next stage. Note that Cluster 2 contained the NBA
champion (Golden State Warriors) and the runner-up of the finals (Cleveland
Cavaliers) and teams ending the regular season within the first four positions.
Hence, the obtained partition was able to identify the best NBA teams for the
regular season 2017/18, i.e., those assigned to Cluster 2, which were extremely
good if compared to the remaining teams, i.e., those assigned to Cluster 1.

4. Discussion and Conclusion
In this paper, a new clustering procedure for detecting a fuzzy partition of
observation units in a reduced subspace is introduced. It is based on the RKM
and FKM methods by considering a linear combination of their loss functions
and by replacing the (hard) allocation matrix by the fuzzy membership degree
matrix. The effectiveness of the proposal is shown by a real-life example.

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