i have a list of points which are the inertia values of a kmeans algorithm.
To determine the optimum amount of clusters i need to find the point, where this curve starts to flatten.
Data example
Here is how my list of values is created and filled:
sum_squared_dist = []
K = range(1,50)
for k in K:
km = KMeans(n_clusters=k, random_state=0)
km = km.fit(normalized_modeling_data)
sum_squared_dist.append(km.inertia_)
print(sum_squared_dist)
How can i find a point, where the pitch of this curve increases (the curve is falling, so the first derivation is negative)?
My approach
derivates = []
for i in range(len(sum_squared_dist)):
derivates.append(sum_squared_dist[i] - sum_squared_dist[i-1])
I want to find the optimum number of clusters any given data using the elbow method. Could someone help me how i can find the point where the list of the inertia values starts to flatten?
Edit
Datapoints:
[7342.1301373073857, 6881.7109460930769, 6531.1657905495022,
6356.2255554679778, 6209.8382535595829, 6094.9052166741121,
5980.0191582610196, 5880.1869867848218, 5779.8957906367368,
5691.1879324562778, 5617.5153566271356, 5532.2613232619951,
5467.352265375117, 5395.4493783888756, 5345.3459908298091,
5290.6769823693812, 5243.5271656371888, 5207.2501206569532,
5164.9617535255456]
I worked on a Python package modeled after the Kneedle algorithm. It finds x=5
as the point where the curve starts to flatten. The documentation and the paper discuss the algorithm for choosing the knee point in more detail.
y = [7342.1301373073857, 6881.7109460930769, 6531.1657905495022,
6356.2255554679778, 6209.8382535595829, 6094.9052166741121,
5980.0191582610196, 5880.1869867848218, 5779.8957906367368,
5691.1879324562778, 5617.5153566271356, 5532.2613232619951,
5467.352265375117, 5395.4493783888756, 5345.3459908298091,
5290.6769823693812, 5243.5271656371888, 5207.2501206569532,
5164.9617535255456]
x = range(1, len(y)+1)
from kneed import KneeLocator
kn = KneeLocator(x, y, curve='convex', direction='decreasing')
print(kn.knee)
5
import matplotlib.pyplot as plt
plt.xlabel('number of clusters k')
plt.ylabel('Sum of squared distances')
plt.plot(x, y, 'bx-')
plt.vlines(kn.knee, plt.ylim()[0], plt.ylim()[1], linestyles='dashed')