Page 340 - Contributed Paper Session (CPS) - Volume 6

CPS1950 Paolo G. et al.
the interval [0, 1], e.g., {0, 0.05, …, 0.95, 1}. The optimal triplet can then be
determined by means of, for instance, the Calinski Harabasz index (Caliński, &
Harabasz, 1974) or the Silhouette one (Kaufman and Rousseeuw, 1990), widely
used in the standard (non-fuzzy) clustering framework. Other indexes for fuzzy
clustering, such as the Fuzzy Silhouette index (Campello & Hruschka, 2006) or
the Xie & Beni one (Xie & Beni, 1991), can also be adopted. An alternative
strategy can be based on cross-validation techniques.

3. Result
We analyzed the NBA data (Ferraro et al., 2018) referring to I = 30 NBA
teams on which J = 11 statistics (see Table 1) for the regular season 2017/18
were collected. The data also contained two additional variables concerning
the conference (Western or Eastern) and the playoff appearance (Yes or No).
By means of FRFKM we aimed at studying whether a partition of the NBA
teams can be discovered and whether the team statistics can be summarized
through a limited number of components. The data were standardized before
running FRFKM. We decided to vary K and Q in the set {2, 3, 4, 5} and  in the
set reported in Section 2.4.1.
Table 1. Variables
Acronym Statistic
FGP field goal percentage
3PP 3-point field goals percentage
FTP free throw percentage
OREB offensive rebounds
DREB defensive rebounds
AST assists
TOV turnovers
STL steals
BLK blocks
BLKA blocked field goal attempts
PTS points
The optimal values of K, Q and  were found by maximizing the Fuzzy
Silhouette index. The maximum value (equal to 0.82) was registered when K =
2, Q = 2 and  = 0.95, hence, the FRFKM solution was mainly based on the
FKM one. The obtained components were simplified by exploiting the
rotational freedom of FRFKM. Varimax-rotated component weights reported
in Table 2 were found.
Table 2. Component weights (weights higher than 0.30 in absolute value are in bold)
Variable Component 1 Component 2
FGP 0.01 0.86
3PP 0.33 0.04
FTP 0.21 0.18
OREB -0.18 -0.01

329 | I S I W S C 2 0 1 9