Kannao et al. allowed nonlinear boundary between clusters of the space [27].
Our model uncovered an interesting, novel spatial patterning for producers and nonproducers, wherein nonproducers the equivalent of cheats in our simulations were almost always found on the boundary between clusters of producers and empty (unoccupied) slots.
As illustrated in Fig. 5, a positive immunofluorescent signal corresponding to MMP-2 was found at the ill-defined boundary between clusters of normal transplanted hepatocytes and the surrounding host liver (Fig. 5a c), in agreement with previous findings (Koenig et al. 2005).
As stated by Sankar and Cho [ 41]: " the appearance of clustering is a function of how populations are sampled, of how criteria for boundaries between clusters are set, and of the level of resolution used.
It is worth mentioned that the spectral clustering used here is different from the spectral reordering method (Johansen-Berg et al. 2004), which requires a manual definition of the boundaries between clusters.
Table 3 Mapping between clusters of ToBI labels and prosodic categories for detection Annotation tier ToBI labels Four-way pitch accent Two-way pitch accent Boundary Tone tier H*, L+H*, *, *?, X*? High Accent - L*, L*+!H, L*+H Low !H*, H+!H*, L+!H* Downstepped Others Unaccent Boundary tier 3, 4 - Boundary presence Others - Boundary absence.
Meanwhile, these data have often no sharp boundary between clusters.
In the crisp clustering method, the boundary between clusters is fully defined.
Ideally, a clustering algorithm should identify the natural boundaries between the clusters without utilizing more clusters than necessary to account for the entire dataset.
