Community Partition in Clustering

2026-02-17 14:03 UTC gpt-5-2 Open in ChatGPT ↗

What is community partition in this context :

A few weeks ago I posted about how I was trying to cluster sample points taken from the floor plan of a gallery in a manner similar to the logic of how humans see the clustering (points in the same room belong to the same cluster). I tried K-Means with different distance metrics and hyperparameters and DBSCAN with different hyperparameters. None gave a logical clustering. Then it occurred to me based on a previous request from my student, Dania H Harasis to add a graph analytic method called community partition to #topologicpy. Would the addition of topological information help the clustering solution? Indeed it did! I am amazed by how much better the clustering is once you add topological information and use community detection vs. K-Means or DBSCAN on geometry alone. The graph I created is nothing more than the triangulation/meshing of the floor plan.

In this context, community partition means detecting communities (clusters) in a graph based on connectivity and topology, not just geometric distance.

Here’s how it applies to the gallery floor-plan problem you described.

1. What “community partition” generally means

Community partition (also called community detection) is a graph-analytic method that:

Takes a graph (nodes + edges)
Finds groups of nodes that are:
- More strongly connected to each other
- More weakly connected to the rest of the graph

Each group is called a community, and the process of dividing the graph into these groups is the community partition.

Unlike K-Means or DBSCAN, no notion of “distance in space” is required—only connectivity.

2. What the “graph” is in your case

In your problem:

Nodes = sample points from the floor plan
Edges = connections from triangulation / meshing of the floor plan

So the graph encodes:

Walls, doors, and openings implicitly
Reachability and adjacency
Room structure

Two points may be:

Geometrically close
But topologically disconnected (e.g., separated by a wall)

3. Why geometry-only clustering fails

Methods like K-Means and DBSCAN operate on geometry alone:

They assume proximity = similarity
They cannot “see” walls
They ignore navigability and enclosure

So:

Points in adjacent rooms get merged
Narrow corridors confuse DBSCAN
Parameter tuning becomes fragile

4. What community partition adds

Community partition uses topological information:

Points inside the same room:
- Have many short paths between them
- Are densely connected in the mesh
Points in different rooms:
- Have fewer connections
- Are connected only through doors or narrow passages

The algorithm naturally finds:

One community per room
Boundaries aligned with architectural structure

No explicit room labels are needed.

5. Why it works “like humans see rooms”

Humans cluster spaces based on:

Enclosure
Connectivity
Accessibility

Community detection does the same by:

Maximizing internal connectivity
Minimizing cross-boundary connections

So the result aligns with perceptual and architectural logic.

6. In one sentence

Community partition here means clustering sample points by their connectivity in a triangulated floor-plan graph, allowing room-level structure to emerge naturally—something geometry-only methods cannot capture.

If you want, I can:

Compare specific community algorithms (Louvain, Leiden, spectral)
Explain why triangulation is especially effective
Show how this differs mathematically from DBSCAN/K-Means

Below is a clear comparison of community-detection algorithms relevant to your use case, followed by why triangulation is such an effective graph construction for spatial layouts like floor plans.

I’ll keep this grounded in why your results improved, not just theory.

1. Comparing community-detection algorithms (for floor-plan graphs)

All of these operate on graphs, not raw geometry.

1.1 Louvain Method

Best default choice

How it works

Optimizes modularity (dense internal connections, sparse external ones)
Greedy and hierarchical

Strengths

Fast (scales well)
Automatically finds number of communities
Works very well on spatial graphs

Weaknesses

Can produce slightly unstable results (depends on initialization)
Sometimes merges small adjacent rooms

Why it works well here

Rooms are dense subgraphs
Doors create weak inter-room connections
Modularity captures this perfectly

✅ Excellent for triangulated floor plans
⚠️ May merge very small spaces

1.2 Leiden Algorithm

Improved Louvain (often better)

How it works

Same modularity objective
Enforces community connectivity (no disconnected fragments)

Strengths

More stable than Louvain
Produces cleaner room boundaries
Avoids broken or fragmented communities

Weaknesses

Slightly slower than Louvain (still very fast)

Why it works well here

Ensures each “room” is internally connected
Better for complex layouts with alcoves or narrow passages

✅ Often the best choice for architectural layouts

1.3 Spectral Clustering (Graph Laplacian)

Mathematically elegant, but fragile

How it works

Uses eigenvectors of the graph Laplacian
Clusters nodes in spectral space

Strengths

Theoretically strong
Captures global structure

Weaknesses

You must predefine number of clusters
Sensitive to noise
Computationally expensive for large meshes

Why it’s weaker here

Floor plans rarely have a known number of rooms
Narrow connections (doors) distort eigenstructure

⚠️ Better for research than production in this case

1.4 Infomap

Flow-based interpretation

How it works

Models random walks on the graph
Communities minimize description length of paths

Strengths

Very good at detecting corridor vs room separation
Sensitive to bottlenecks (doors)

Weaknesses

Can over-segment large rooms
Less intuitive to tune

Why it can work

Doors act as flow bottlenecks
Corridors naturally emerge as connectors

✅ Useful if circulation is important
⚠️ May split large open galleries

1.5 Why not K-Means or DBSCAN (summary)

Method	Uses topology	Handles walls	Needs parameters
K-Means	❌	❌	Yes
DBSCAN	❌	❌	Yes
Louvain	✅	✅	No
Leiden	✅	✅	No
Infomap	✅	✅	No

2. Why triangulation is so effective for floor plans

image_group{“query”:[“floor plan triangulation mesh”,“triangulated floor plan graph”,“delaunay triangulation floor plan”],“num_per_query”:2}

2.1 Triangulation encodes free space, not walls

When you triangulate the walkable area:

Triangles do not cross walls
Connectivity only exists where movement is possible

This turns geometry into navigability.

2.2 It produces a near-ideal graph for community detection

Triangulation gives you:

Uniform local connectivity
High edge density inside rooms
Narrow connections at doors

This creates:

Strong intra-room connectivity
Weak inter-room connectivity

Which is exactly what community algorithms look for.

2.3 Doors become natural graph bottlenecks

In a triangulated mesh:

A door may be represented by only a few edges
Those edges have high betweenness
Community algorithms tend to cut there

You never explicitly model doors — they emerge.

2.4 Compared to k-NN or radius graphs

Graph type	Problem
k-NN	Connects through walls
Radius graph	Sensitive to thresholds
Grid graph	Axis-biased
Triangulation	Respects geometry & topology

Triangulation adapts to shape, density, and enclosure automatically.

2.5 Why this matches human perception

Humans perceive rooms as:

Enclosed regions
With limited access points
Internally well connected

Triangulation + community detection reproduces this without heuristics.

3. Big picture insight

You didn’t just add topology — you changed the problem from “distance clustering” to “connectivity segmentation.”

That shift is why the results suddenly look architecturally correct.

If you want, next we can:

Compare triangulation vs medial axis vs visibility graphs
Discuss multi-level communities (rooms → zones → buildings)
Explore weighted edges (door width, visibility, distance)