Overview

The Cluster Scatter 2D and Cluster Scatter 3D widgets group optimization trials into clusters to reveal structure in objective or parameter space.

Method Summary

Method	Role	Strength	Limitation
k-means	Partition data into k clusters	Fast, intuitive, WCSS measurable	Assumes spherical clusters
Elbow	Auto-estimate optimal k	No manual k selection needed	Less reliable on smooth WCSS curves

Initialization Strategies for k-means

Both use Lloyd's algorithm (assign → update → converge). Only the initial centroid selection differs.

Strategy	Method	Best for
k-means++	D²-proportional probabilistic sampling	Default — avoids local optima
Deterministic	Same D²-proportional sampling, fixed seed (42)	Fully reproducible results

Workflow

flowchart TD
    start["Run clustering"] --> sel{"k selection"}
    sel -- "Elbow (Auto)" --> elbowStep["Try k=2..max_k with Elbow method<br/>→ auto-pick best k"]
    elbowStep --> runElbow["Run k-means with chosen k"]
    sel -- "Manual" --> runManual["Run k-means with user-specified k"]

    init{"Init strategy<br/>(applies within k-means)"}
    init -- "k-means++" --> initA["Probabilistic D² sampling<br/>(seed derived from n, k)"]
    init -- "Deterministic" --> initB["Same D² sampling,<br/>seed fixed to 42"]

Input Space

Setting	Features used	Best analysis
Objective Space	Objective values only	Find trials with similar performance
Variable Space	Parameter values only	Identify patterns in design variables
Combined	Objectives + parameters	See joint structure across both spaces

Related Methods

• Dendrogram: hierarchical clustering, no upfront $k$
• PCA Biplot: standardized 2D principal-component projection
• SOM Map: Self-Organizing Map, topology-preserving 2D map