The central limit theorem

As shown in by the LLN applied to this business case, the k-means clustering project must provide a reasonable set of centroids and clusters (regions of locations for long-duration phone calls).

This approach can now be extended to the CLT, which states, in machine learning parlance, that when training a large dataset, a subset of mini-batch samples is sufficient. The following two conditions define the main properties of the central limit theorem:

• The variance between the data points of the subset (mini-batch) remains reasonable. In this case, filtering only long-duration calls solves the problem.
• The normal distribution pattern with mini-batch variances close to the variance of the whole dataset.