Mastering Machine Learning Algorithms

Adjusted Rand Index

This score is useful to compare the original label distribution with the clustering prediction. Ideally, we'd like to reproduce the exact ground truth distribution, but in general, this is very difficult in real-life scenarios. A way to measure the discrepancy is provided by the Adjusted Rand Index. In order to compute this score, we need to define the auxiliary variables:

• a: Number of sample pairs (y_i, y_j) that have the same true label and that are assigned to the same cluster
• b: Number of sample pairs (y_i, y_j) that have a different true label and that are assigned to different clusters

The Rand Index is defined as:

The Adjusted Rand Index is the Rand Index corrected for chance and it's defined as:

The R_A measure  ...