Have you ever tried to cluster data with additional constraints? Like, what if you have a set of templates or recipes that need to be respected while grouping your data points? That’s exactly what I’m going to talk about today.
Imagine you have a dataset with xy-coordinates and labels, along with a set of templates that define how many points of each label should be in a cluster. For instance, Template 1 might require 3 A labels and 2 B labels, while Template 2 needs 1 A label, 5 B labels, and 3 C labels. The goal is to perform clustering while respecting these template constraints.
## The Problem with Traditional Clustering
Traditional clustering algorithms don’t take into account these kinds of constraints. They’re designed to group similar data points together based on their features, but they don’t care about the underlying structure or rules that govern the data.
## Searching for a Solution
I’ve searched far and wide for guidance on this problem, looking into template-based clustering, multi-modal clustering, and even constraint-based clustering. But the constraints in these methods seem to be limited to whether pairs of points can be in the same cluster or not.
## A Bayesian Approach
I’m interested in solving this problem in a Bayesian setting, using Stan to model the clustering process. But I’m not even sure how to approach this problem in a non-Bayesian way, so any help or pointers would be appreciated.
## What Does ‘Good’ Clustering Mean?
When it comes to evaluating the quality of clustering, there are several factors to consider. Do we want to minimize cluster overlap, cluster size, or distance from all data to their cluster centers? These are just a few possible definitions of ‘good’ clustering, and the right approach will depend on the specific problem at hand.
## Conclusion
Template-based clustering is a challenging problem that requires a deep understanding of clustering algorithms and Bayesian modeling. If you have any experience with this type of problem or know of any relevant resources, I’d love to hear from you.