As new facilities come online, the astronomical community will be provided with extremely large data. sets of well-sampled light curves (LCs) of transients. This motivates systematic studies of the LCs of supernovae (SNe) of all types, including the early rising phase. We performed unsupervised k-means clustering on a sample of 59 R-band SN II LCs and find that the rise to peak plays an important role in classifying LCs. Our sample can be divided into three classes: slowly rising (II-S), fast rise/slow decline (II-FS), and fast rise/fast decline (II-FF). We also identify three outliers based on the algorithm. The II-FF and II-FS classes are disjoint. in their decline rates, while the II-S class is intermediate and "bridges the gap." This may explain recent conflicting results regarding II-P/II-L populations. The II-FS class is also significantly less luminous than the other two classes. Performing clustering on the first two principal component analysis components gives equivalent results to using the full LC morphologies. This indicates that Type II LCs could possibly be reduced to two parameters. We present several important caveats to the technique, and find that the division into. these classes is not fully robust. Moreover, these classes have some overlap, and are defined in the R. band only. It is currently unclear if they represent distinct physical classes, and more data is needed to study these issues. However, we show that the outliers are actually composed of slowly evolving SN IIb, demonstrating the potential of such methods. The slowly evolving SNe IIb may arise from single massive progenitors.