Address Clustering Powered by DeFi Mathematics

Address clustering is the backbone of any meaningful on‑chain analysis, as explored in Decoding On‑Chain Data, Metrics, Whale Movements, and Clustering Insights.

When combined with the rich mathematical framework that underlies decentralized finance (DeFi), it becomes a powerful lens for identifying whale activity, tracking liquidity movements, and revealing hidden relationships between seemingly unrelated addresses.

Below is an in‑depth exploration of how DeFi mathematics drives address clustering, presented as a clear, step‑by‑step guide for analysts, developers, and researchers alike.

The Basics of Address Clustering

At its core, address clustering seeks to group together blockchain addresses that are controlled by the same entity.
Because each transaction is a link between inputs and outputs, a graph naturally emerges:

• Vertices represent addresses.
• Edges represent transactions that consume inputs and produce outputs.

The simplest rule is that any address that appears as an input in the same transaction as another address must belong to the same cluster.
This “common‑input” heuristic can be expanded in many ways, but it sets the stage for the more sophisticated techniques that follow.

DeFi Mathematics: The Engine Behind Clustering

DeFi introduces a suite of financial instruments—liquidity pools, automated market makers, flash loans, and more—that generate complex on‑chain behavior.
To untangle this behavior, we apply mathematical tools from the field of Blockchain Pattern Decoding Through Mathematical Models, including:

• Graph theory – to capture the network structure.
• Probability and statistics – to model uncertainty.
• Linear algebra – for dimensionality reduction and feature extraction.
• Optimization – to find the best clustering configuration.

These disciplines converge to produce algorithms that can distinguish between benign multi‑output transactions and malicious mixing techniques.

Building the Transaction Graph

1. Collect raw data
   Pull all transactions from a block explorer API or a full node.
   Store each transaction’s inputs, outputs, timestamp, and fee.

2. Normalize addresses
   Convert addresses to a canonical form to avoid duplicate entries due to checksum variations.

3. Create edges
   For every transaction, add an edge from each input address to each output address.
   Optionally weight the edge by transaction value or gas fee.

4. Add temporal information
   Store the block height or timestamp to enable time‑window analysis.

The result is a directed, weighted graph that reflects every transfer of value across the network.

Feature Engineering: From Raw Edges to Meaningful Signals

Graph‑based clustering requires features that capture the essence of address behavior.
Common features include:

These features are typically normalized and then assembled into a feature matrix for each address.

Similarity Metrics

Once features are extracted, we need a way to quantify how similar two addresses are.
Popular similarity measures include:

• Cosine similarity – useful for high‑dimensional feature vectors.
• Jaccard index – compares sets of connected addresses.
• Pearson correlation – captures linear relationships in time‑series features.

In many DeFi scenarios, a composite similarity score that blends multiple metrics yields the best results.
For example:

Sim(A,B) = α * Cosine(A,B) + β * Jaccard(A,B) + γ * Correlation(A,B)

where α, β, and γ are weights tuned to the specific use case.

Clustering Algorithms

1. Hierarchical Agglomerative Clustering

Start with each address as its own cluster and iteratively merge the two most similar clusters until a stopping criterion is met.
A threshold on the similarity score determines when to stop merging, allowing analysts to control cluster granularity.

2. DBSCAN (Density‑Based Spatial Clustering)

DBSCAN groups points that are closely packed together and marks points in low‑density regions as outliers.
It is robust against noise and does not require a preset number of clusters—valuable when dealing with unknown numbers of wallets.

3. Spectral Clustering

Leverages the eigenvectors of a similarity matrix to partition the graph.
Spectral clustering can uncover community structures that are not evident through local similarity alone.

4. Bayesian Inference

Model the probability that two addresses belong to the same entity given observed features.
A Bayesian framework naturally incorporates prior knowledge (e.g., known whale addresses) and updates beliefs as new data arrives.

DeFi‑Specific Adjustments

DeFi protocols introduce patterns that generic clustering misses.
Some adjustments include:

• Liquidity pool detection – addresses that frequently appear as inputs or outputs of the same pool contract can be grouped using a “pool participation” feature.
• Flash loan signatures – rapid, multi‑transaction chains that revert if conditions are not met can be flagged and treated as separate clusters.
• Stablecoin wrapping – addresses that frequently wrap or unwrap tokens often exhibit a distinct signature.
• Router interactions – addresses that send tokens to router contracts before receiving swapped assets can be linked via the router as an intermediary.

Incorporating these DeFi‑specific signals reduces false positives caused by common patterns like “change outputs” that do not imply shared control.

Whale Tracking: A Practical Use Case

Whales are addresses that control significant amounts of value.
Identifying whales is essential for market analysis, regulatory oversight, and risk management.

Step 1: Identify High‑Balance Addresses

Query the blockchain to retrieve balances above a threshold (e.g., $1 million).
Store these as candidate whale addresses.

Step 2: Build Local Graphs

For each candidate, extract a subgraph that includes all transactions within a 30‑day window before and after the high‑balance event.

Step 3: Compute Clustering Metrics

Apply the feature engineering pipeline to the local subgraph.
Use DBSCAN with a distance metric based on transaction volume similarity.

Step 4: Merge Overlapping Clusters

If a whale address shares transactions with multiple clusters, merge them if similarity exceeds a higher threshold.
This step accounts for whales that move funds across multiple wallets.

Step 5: Visualize Activity

Create a Sankey diagram showing the flow of value between clusters over time.
This visual representation helps spot patterns such as “pump and dump” or strategic liquidity provision.

This practical use case for whale tracking is illustrated in Whale Movements Revealed Through On‑Chain Metrics.

Dynamic Clustering: Adapting to Market Movements

Static clustering can quickly become outdated in fast‑moving DeFi markets.
Dynamic clustering continuously updates cluster assignments as new transactions arrive.

Key components:

• Incremental feature update – recalculate features for affected addresses after each new transaction.
• Sliding time windows – only consider the last N blocks to keep the model responsive.
• Online learning – retrain the clustering model in real time using streaming algorithms.

Dynamic clustering allows analysts to detect emerging whales before they accumulate large positions, and this approach is discussed in the article on Market Movers in DeFi Discovered via Chain Calculations.

Handling Mixers and Privacy Enhancers

Mixers and privacy tools deliberately obfuscate transaction trails.
While they increase privacy, they also pose a challenge for clustering.

Approaches to mitigate their impact:

• Entropy analysis – high entropy in output addresses indicates potential mixing.
• Suspicious transaction flags – flag transactions that deviate from typical patterns (e.g., many outputs with identical amounts).
• Probabilistic linking – assign a low confidence score to potential cluster merges that involve mixers, and flag them for manual review.

Limitations and Ethical Considerations

Ethical use of clustering data mandates:

• Transparency – disclose methodology and uncertainty levels.
• Anonymization – where possible, share only aggregated statistics rather than raw addresses.
• Consent – avoid profiling users without clear regulatory justification.

Future Directions

1. Multichain clustering – extend models to cross‑chain interactions (e.g., bridges, wrapped tokens).
2. Graph neural networks – learn embeddings directly from transaction graphs, capturing higher‑order relationships, a technique explored in Quantitative DeFi Mapping with Chain Data Models.
3. Explainable AI – provide interpretable explanations for why two addresses are clustered together.
4. Real‑time alerts – integrate clustering outputs into monitoring dashboards for instant whale detection.

As DeFi continues to innovate, the mathematical tools for address clustering must evolve to keep pace with new protocols and privacy mechanisms.

Conclusion

Address clustering powered by DeFi mathematics transforms raw transaction data into actionable insights.
By marrying graph theory with statistical inference, and tailoring algorithms to the unique behaviors of DeFi protocols, analysts can:

• Reveal hidden ownership structures.
• Track whales and liquidity movements.
• Detect anomalous activity in real time.

The field remains dynamic, offering ample opportunities for researchers to push the boundaries of on‑chain analytics.
Whether you’re building a compliance tool, a trading strategy, or a blockchain explorer, mastering these techniques will give you a decisive edge in the decentralized world.