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CPS2182 Lynne Billard et al.
= {(, )|(, ) ≤ ∀ ≠ ′}. The updated partition is now
̂

(+1)
(+1) = ( 1 (+1) , … , ).
(iv) Stop: Repeat (ii) and (iii) until the improvement of SSR. is smaller than a
predetermined criterion, or the number of iterations reaches a predetermined
maximum number.
2.2 Comparison of k-means and k-regressions algorithms
To compare the -means algorithm with the -regressions algorithm,
consider the data set
(I) which is composed of three clusters that follow the equations:
(1) : = 142 + 5 +
1
(2) : = 53 − 3 +
2
(3) : = −43 + 0.6 +
3
These data are displayed in Figure 1.

Data I with 3 underlying clusters

Figure 1
The -means algorithm produced the partitions of Figures 2(a) and 2(b);
Figure 2(a) used the city block distance and Figure 2(b) used the Hausdorff
distance. In contrast, Figure 2(c) is the partition obtained by the -regressions
algorithm (after 10 iterations); clearly, this is closer to the original data sect
than were those obtained by the -means method.

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