🧠 K-means Clustering Metric

🔬 Definition

K-means minimizes the distance between data points and their cluster centers.

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🧠 Objective Function

K-means minimizes:

J = Σ ||xi - μk||²

Where:

• xi = data point
• μk = centroid of cluster k

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⚠️ Important Adaptation (This Project)

In classical K-means:

• data = vectors
• distance = Euclidean

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In this project:

• data = phylogenetic trees
• distance = RF distance

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📐 Modified Objective

Instead of Euclidean distance:

Minimize sum of RF distances within clusters

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🔁 Iterative Process

1. Assign trees to nearest cluster (RF distance)
2. Update cluster representatives
3. Repeat until convergence

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📊 Interpretation

• Low intra-cluster RF → trees are similar
• High inter-cluster RF → clusters are distinct

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📌 Example (Conceptual)

Given 3 trees:

• T1 close to T2 → same cluster
• T3 very different → separate cluster

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🌳 Biological Meaning

Each cluster represents:

• a group of trees with similar topology
• a consistent evolutionary hypothesis

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🔗 Relationship with RF

• RF defines similarity
• K-means uses this similarity to group trees

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