Clustering

An overview of the methods used in Tunny Dashboard's Cluster Scatter 2D / 3D widgets. For detailed theory, refer to the individual method documents.

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Clustering Methods

Method	Role	Strengths	Limitations	Details
k-means (Lloyd's algorithm)	Partition data into $k$ clusters	Fast, intuitive, quality measurable via WCSS	Assumes spherical clusters; risk of local optima	kmeans.md

k-means Initialization Strategies (Init)

The initial centroid selection method for k-means. Both are internal settings of k-means, not separate clustering methods — the Lloyd's algorithm itself (assign → update → converge) is shared.

Init strategy	Description	Best for
k-means++	D²-proportional probability sampling (Xoshiro256Plus, fixed seed derived from n · k)	Avoid local optima; quality-first
Deterministic	Same k-means++ D²-proportional sampling (delegated to linfa), but with a fixed seed (42)	Fully reproducible results required

Choosing the Number of Clusters (k)

The Elbow method is an auxiliary tool for k-means, not a clustering method itself. It is used to decide "how many clusters to split into" before running k-means.

Method	Role	Strengths	Limitations	Details
Elbow method	Auto-estimate optimal $k$ from the rate of change in WCSS (within-cluster sum of squares)	No need for user to specify $k$	Estimation accuracy decreases when WCSS is smooth	elbow.md

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Workflow

flowchart TD
    start["Run clustering"] --> sel{"k selection"}
    sel -- "Elbow (Auto)" --> elbowStep["Elbow method exhaustively tries k=2..max_k<br/>and auto-estimates optimal k"]
    elbowStep --> runElbow["Run k-means with estimated k<br/>(applying Init strategy)"]
    sel -- "Manual" --> runManual["Run k-means directly with user-specified k<br/>(applying Init strategy)"]

    init{"Init strategy<br/>(differs only in k-means initialization)"}
    init -- "k-means++" --> initA["D²-proportional probability sampling<br/>(seed derived from n, k)"]
    init -- "Deterministic" --> initB["Same D²-proportional sampling,<br/>seed fixed to 42"]

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Choosing the 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

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Related Methods

Other structure-revealing tools, available as separate widgets:

• Dendrogram: hierarchical clustering that builds a full merge tree instead of committing to a single $k$ upfront
• PCA Biplot: projects trials and variables onto a standardized 2D principal-component plane
• SOM Map: a Self-Organizing Map, topology-preserving 2D map complementary to a fixed $k$-cluster partition