# How to measure the consistency of clustering results

I'm clustering data on a daily basis and would like to measure the consistency of the clustering method.

Let's say following clusters result in method A:

On day 1: {a,b,c} {d,f} {g}
On day 2: {a,b,c} {d,f} {g}
On day 3: {a,b,c} {d,f} {g}


With method B:

On day 1: {a,b,c} {d,f} {g}
On day 2: {a,b} {c,d,f} {g}
On day 3: {a,b} {c,d} {f} {g}


With method C:

On day 1: {a,b,c} {d,f} {g}
On day 2: {a} {b} {c,g} {f}
On day 3: {a,g,d} {b} {c} {e,f}


The amount of variables stays the same, but the cluster sizes and count varies.

Obviously the grouping is less consistent in the latter examples than in the first one. Ideally I'd like to have a measure that assigns a value of 1.0 to a completely consistent method and 0.0 where the clustering seems random. I'm struggling to find any literature and pointers to how this can be achieved. How could it be done?

### Background

In my case the clusters are on correlation matrices of financial instruments.