<p>I have a set of rectangles, which I want to cluster (group) as shown <a href="https://i.sstatic.net/V5vOs.png" rel="nofollow noreferrer">here</a>(I can not post images yet, so please bear with me).</p>

<p>The approach I took was to consider central points of each rectangle as a data point in $R^2$ and cluster them using Euclidean distance (K-means, K-mediods approach or any other method). Traditional clustering approaches help you to discover shapes in data, but I am <strong>not</strong> trying to discover such shapes, as I know the best shape would be rectangles. I do not know the number of clusters (number of bounding rectangles) beforehand. However, given a clustering solution, an objective measure (BIC) can be calculated to measure clustering accuracy. </p>

<p>Given this situation, my question is, is there any algorithmic formulation of this or a similar problem? </p>

CC BY-SA 3.0
2013-05-22T17:27:42.993Z
Are the rectangles in your set assumed to be disjoint?
Antoine Amarilli 'a3nm'
CC BY-SA 3.0
2013-05-22T18:30:07.007Z
yes.the original rectangles are disjoint, as well as the bigger rectangles where I want to combine them.
rivu
<cg.comp-geom><clustering>
Grouping a set of rectangles in larger rectangular regions
rivu
# Grouping a set of rectangles in larger rectangular regions

(Asked by: username_0 on 2013-05-22)

I have a set of rectangles, which I want to cluster (group) as shown [here](https://i.sstatic.net/V5vOs.png)(I can not post images yet, so please bear with me).

The approach I took was to consider central points of each rectangle as a data point in $R^2$ and cluster them using Euclidean distance (K-means, K-mediods approach or any other method). Traditional clustering approaches help you to discover shapes in data, but I am **not** trying to discover such shapes, as I know the best shape would be rectangles. I do not know the number of clusters (number of bounding rectangles) beforehand. However, given a clustering solution, an objective measure (BIC) can be calculated to measure clustering accuracy.

Given this situation, my question is, is there any algorithmic formulation of this or a similar problem?

**Tags:** cg.comp-geom, clustering

> **Comments:**
> **username_1**: Are the rectangles in your set assumed to be disjoint?  
> **username_0**: yes.the original rectangles are disjoint, as well as the bigger rectangles where I want to combine them.  

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## 0 answers

