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Adjusted mutual information

YG Yitian Gao
HF Hongwei Fang
KN Ke Ni
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Adjusted mutual information (AMI)64 is introduced to measure discrepancies in clustering results between neighboring configurations.

One assumes that Ut is the clustering result at time step t and Ut+1 at time step t + 1. Their entropy is the amount of uncertainty for a partition set, as defined by:

where P(i) is the probability that an object picked at random from U falls into class Ui.

The probability is defined as

The mutual information (MI) between Ut and Ut+1 is calculated using

Normalized against chance, AMI can then be calculated:

AMI ranges from 0 to 1. If the value of AMI is close to zero, it indicates that two clustering results are largely independent. An AMI of exactly 1 indicates that two clustering results are equal.

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