Python Programming for Biology: Bioinformatics and Beyond

Figure 23.6.  Finding the optimum number of clusters for the k-means method. For a

given data set, the k-means clustering method can be applied to partition the data into

different numbers of clusters. If the number of clusters (k) is not known different numbers

can be tried so that an optimum can be found. A simple way to evaluate the optimum

number of clusters is to measure the relative improvement of the separations of the data

points from their nearest cluster centre. Having more clusters will always give smaller

separations but there will be the most significant change near the optimum number. For

the illustrated example, going from two to three clusters has a bigger jump in minimising

separations than going from three to four clusters. Using four clusters only improves

separations to the centres mildly.

We  can  test  the  jump  method  on  a  simple  normal  data  set  as  before.  The  underlying

clusters are stacked and shuffled randomly and passed in to the function.

data = [random.normal(( 0.0, 0.0), spread, sizeDims),

random.normal(( 1.0, 1.0), spread, sizeDims),

random.normal(( 1.0, 0.0), spread, sizeDims)]

---

data = vstack(data)

random.shuffle(data)

k = jumpMethodCluster(data, (2, 10), 20)

print('Number of clusters:', k)