Hands-On Unsupervised Learning with Python

Adjusted Rand score

The adjusted Rand score is a measure of discrepancy between the true label distribution and the predicted one. In order to compute it, it's necessary to define quantities as follows:

• a: Representing the number of sample pairs (x_i, x_j) with the same true labels (y_i, y_j) : y_i = y_j and assigned to the same cluster K_c
• b: Representing the number of sample pairs (x_i, x_j) with different true labels (y_i, y_j) : y_i ≠ y_j and assigned to different clusters K_c and K_d with c ≠ d

If there are M values, the total number of binary combinations is obtained using the binomial coefficient with k=2, therefore, an initial measure of discrepancy is:

Obviously, this value can be dominated either by a or b. In both cases, a higher score indicates ...