The formula to calculate the optimal cluster size (CS) is:
\[ CS = \left(N^{\frac{1}{D + 2}}\right) \]
Where:
Cluster size refers to the number of clusters into which a dataset can be partitioned. It is a crucial parameter in cluster analysis and machine learning, particularly in unsupervised learning algorithms like k-means clustering. The optimal cluster size depends on the number of data points and the dimensionality of the dataset. A well-chosen cluster size can lead to more meaningful and interpretable results in data analysis.
Let's consider an example:
Using the formula to calculate Optimal Cluster Size:
\[ CS = \left(1000^{\frac{1}{3 + 2}}\right) = \left(1000^{\frac{1}{5}}\right) \approx 3.98 \approx 4 \]
This means that the optimal cluster size would be approximately 4.