the SSE. In the next section, we will demonstrate that using Otsu’s threshold instead of the mean point often leads to significantly better initial clusterings on a variety of data sets.

![\[fig\_histo\] Comparison of mean point and Otsu’s thresholds](otsupca_shuttle_histo){width="0.8\columnwidth"}

Experimental Results {#sec_exp}
====================

The experiments were performed on $24$ commonly used data sets from the UCI Machine Learning Repository [@Frank12]. Table \[tab\_data\_set\] gives the data set descriptions. For each data set, the number of clusters ($K$) was set equal to the number of classes ($K'$), as commonly seen in the related literature [@He04; @Arthur07; @Su07; @Redmond07; @AlHasan09; @Cao09; @Kang09; @Onoda12].

In clustering applications, normalization is a common preprocessing step that is necessary to prevent attributes with large ranges from dominating the distance calculations and also to avoid numerical instabilities in the computations. Two commonly used normalization schemes are linear scaling to unit range (min-max normalization) and linear scaling to unit variance (z-score normalization). Several studies revealed that the former scheme is preferable to the latter since the latter is likely to eliminate valuable between-cluster variation [@Milligan88; @Su07]. As a result, we used min-max normalization to map the attributes of each data set to the $[0,1]$ interval.

  ID   Data Set                                  $N$   