Efficient Bitcoin Address Classification Using Quantum-Inspired Feature Selection

Large blockchain datasets often contain redundant information, leading to increased computational costs. Feature selection aims to distill essential information for efficient analysis. Our QIFS method identifies the most relevant features for Bitcoin mixer activity from transaction data, optimizing feature influence and independence through a QUBO model[14].

The cleaned blockchain transaction data is represented as a feature matrix $\mathscr{D}_{m\times n}$, where each of the $n$ columns corresponds to a feature, and each of the $m$ rows represents transaction data associated with a Bitcoin address:

We also define an outcome vector $\mathscr{O}$, which records the classification results for Bitcoin addresses:

Here, $O_{i}$ is a binary variable that takes on values 0 (rejection in Bitcoin classification) or 1 (acceptance).

We aim to select a subset of $K$ features from the original $n$ features to classify Bitcoin addresses. The QUBO model, adapted from Milne et al. [14], balances feature influence and dependence, using the Spearman rank correlation coefficient to evaluate the relevance and distinctiveness of each feature.

The objective function is:

where $x_{j}$ is a binary variable indicating if feature $j$ is selected, and $\alpha$ (where $0\leq\alpha\leq 1$) weights the influence term. The negative sign in the first term aims to maximize influence, while the second term seeks to minimize dependence.

This cost function is optimized using a quantum-inspired machine to determine the feature subset that best balances the influence-dependence trade-off:

where $\mathbf{Q}$ is a matrix encoding both influence and independence factors.

Figure 2 illustrates our proposed Quantum-Inspired Feature Selection pipeline.

Quantum-inspired algorithms employ heuristic methods that approximate quantum behaviors, such as tunneling, to enhance optimization processes [15]. These methods leverage an expanded search space, allowing for more efficient exploration compared to classical methods, and can potentially escape local minima to improve identification of the global optimum.

Simulated Annealing (SA) [16] is another technique to optimize the QUBO formulation during feature selection. SA mimics slowly cooling a material to reach its lowest energy state. By gradually reducing the temperature, SA probabilistically explores the solution space, reducing the likelihood of becoming trapped in local minima and increasing the probability of finding a global optimum. In our methodology, we employ simulated annealing to enhance feature selection, particularly when dealing with large and complex feature spaces.

Quantum annealing (QA) leverages quantum hardware to solve QUBO formulations directly. By formulating our feature selection problem as a QUBO model and utilizing quantum annealing for optimization, we benefit from faster convergence to optimal solutions compared to classical optimization methods.

Quantum-inspired machines, SA, and QA are all applied to further optimize QUBO to identify the global minimum energy cost during feature selection, thereby accelerating the supervised classification process. In our approach, we implement all three techniques to determine the most effective feature selection strategy for our specific task.

In this study, we evaluate the effectiveness of features selected using QIFS, implemented via SA and quantum methods such as D-Wave’s QA and Binary Quadratic Model (BQM). The feature sets are validated on Bitcoin address classification tasks using 10-fold cross-validation, focusing on identifying mixer classes. Metrics such as precision and AUC are used to demonstrate the robustness and utility of features selected by these methods.

Figure 3 provides an overview of our quantum-inspired approaches to feature selection, highlighting similarities and differences between the optimization techniques.

By leveraging quantum-inspired optimization, we aim to achieve high accuracy while minimizing computational overhead. These approaches significantly enhance processing efficiency, enabling effective classification even with large and complex datasets.

We set up a full Bitcoin node leveraging 64GB of RAM, a 12th Gen Intel® Core™ i9-12900K CPU, GeForce GTX 1060 6 GB GPU, and 4 TB of SSD storage, granting us access to the complete raw transaction history of the network. This history contains detailed information about each transaction, including its hash, inputs, outputs, block height, and timestamp. The retrieval process took four months, covering 544,283 blocks and 345,882,038 transactions. Due to computational limitations, we focused on analyzing the first 1,000 transactions associated with each Bitcoin address.

We used WalletExplorer.com³³3walletexplorer.com to acquire a dataset of 694,676 labeled Bitcoin addresses, interacting with 3,459,773 transactions. These addresses were categorized into six classes: exchange, faucet, gambling, market, mixer, and mining pool. Table 1 summarizes the distribution of addresses and corresponding transactions across these categories.

We processed the transaction history for each address by aggregating all relevant transactions into a single sheet record. Then these records were sorted chronologically prior to feature extraction. Table 2 details the selected features, which are categorized into five groups: basic statistics features, extra statistics features, moment features and transaction patterns features. Calculating each feature requires access to the complete transaction history for an address. This requires retrieving all transactions involving the address before computing any statistical measures. By iterating through the sorted transaction history only once, we can efficiently extract all 69 features.

The four transaction types, coinbase, spent, received, and payback, are mutually exclusive. A transaction is categorized as a coinbase transaction if it has a coinbase input, representing a block reward. If it lacks a coinbase input and the sender’s address appears in any of its inputs, it’s identified as a spent transaction. Conversely, if the address appears only in the outputs, it’s classified as a received transaction. Finally, transactions with the address in both inputs and outputs are categorized as payback transactions. To understand the behavior of the address, we analyze the distribution moments of various types of transactions. These include total transactions, spent transactions, received transactions, coinbase transactions, payback transactions, and multiple input and output transactions. We believe that the frequency of transactions for each category helps identify address types. Beyond frequency, moments of these distributions and transaction intervals reveal further insight. For example, they can indicate an address that was initially active but has become dormant, or even exhibit periodic transaction patterns. In addition, distinguishing between spending, receiving, and payback transactions is crucial. Provides valuable clues on how addresses are being used within the Bitcoin transaction history.

Before the QISF process, each class is binarized as 0 or 1, transforming the data into a QUBO structure suitable for decision-making. Subsequently, the Spearman method is employed to compute correlations between each feature and the mixer class. The results of this correlation analysis are visualized in Figure 5. Table 3 evaluates the time efficiency of various QISF methods for the mixer class. SA, which selected 23 features, exhibited the lowest computational time at 0.0055 seconds. In comparison, QA with 9 features and QA BQM with 7 features required considerably more time, measuring 6.644 seconds and 6.0041 seconds, respectively. These results highlight that SA offers a significant computational speed advantage over other quantum-inspired algorithms in feature selection tasks.

The QISF methodology is specifically tailored for the mixer class. For implementation, we utilized the Python library dwave-neal [17], which progressively converges toward the equilibrium distribution of the Ising model by iteratively updating spins in a sequence of increasing beta values. For quantum processing, the D-Wave Quantum Machine Advantage system 6.4, equipped with 5,612 working qubits, was employed. The D-Wave Hybrid solver (version 2.2) was used to solve general BQM problems. Tables 4,  5 provide details on the features selected by SA, QA, and QA BQM for the mixer class.

We training of seven common classification algorithms include Logistic Regression[18], Adaptive Boosting with Decision Tree (AdaBoost-SAMME)[19, 20], Random Forest[11], Extreme Gradient Boosting (XGBoost)[12], LightGBM[21], SVM[22] and Neural Network. These algorithms serve as a baseline for comparison with the quantum approach. We leverage the Python machine learning library Scikit-learn[23] to employ seven different classifiers. To optimize each classifier and identify a suitable set of parameters, we utilize a 10-fold cross-validation. Notably, decision tree-based methods are unaffected by data normalization. Therefore, for these methods, we retain the original data. However, for classifiers like logistic regression and SVM, which rely on distance metrics, we normalize the features by dividing each dimension by its maximum absolute value.

Among the mixer classes, both Random Forest and SA Random Forest achieve the best F1 score, reaching 92% and 91%. SA Random Forest exhibits a faster 30.3% training time 212 minutes and 23.2 seconds compared to Quantum Random Forest 305 minutes and 5.7 seconds. Table 6 details the results of both all features and SA feature selection of mixer in supervised classifiers. Our experiments revealed that most classifiers performed consistently on the mixer category. However, Logistic Regression showed poor performance on this category. This suggests that tree-based classifiers might be better suited for this task compared to linear models.

We evaluate recall scores for each class within Bitcoin labeled Bitcoin addresses using several supervised machine learning classifiers, alongside SA, QA, and QA BQM quantum algorithms. These classifiers are assessed based on transaction history summaries of labeled addresses. Recall serves as a metric to quantify each model’s effectiveness in accurately identifying positive cases, where a positive case indicates the correct classification of a transaction history as belonging to the mixer class. Figures 11, Figure 11, Figure 13, Figure 13 illustrate the recall scores for each classifier across distinct classes. Notably, within the mixer class, both the Random Forest and SA Random Forest classifiers achieve the highest recall score of 97%, indicating their superior effectiveness in identifying mixer transactions. In contrast, QA and QA BQM Random Forest classifiers demonstrate lower recall performances, achieving scores of 0.62% and 0.76%, respectively.

AUC reflects the probability of a classifier ranking a positive instance higher than a negative one. In Table 7, a higher AUC for the mixer class indicates a stronger ability to distinguish between mixer and othres Bitcoin labeled addresses. Notably, Random Forest, XGBoost, and SA Random Forest all achieve outstanding AUC scores of 0.99, rivaling those of exchange, market, and mining pool classes. This suggests these Bitcoin class modules exhibit stability and effectiveness.

Strikingly, among all classifiers evaluated, SA Random Forest and Random Forest emerged alongside XGBoost as the top performers, exceeding an AUC score of 0.99 for the mixer class. This exceptional performance suggests their remarkable ability to identify a high stable models of genuine mixer transactions. Particularly noteworthy, Random Forest and SA Random Forest demonstrates exceptional performance within the mixer class, achieving the best results among all models with a F1-score of 91% and an AUC of 0.99.

We examine the most important features in different machine learning models, ranked based on their importance of information gain as described by Louppe et al.[24]. The random forest model shown in Table 8, the top 10 most important features of the random forest model are dominated by those related to transaction balances, including USD and BTC, and the transaction volume includes the number spent and received. This suggests that the model heavily relies on financial activity for classification. Features related to transaction patterns and moments like average and standard deviation of balances also appear within the top 20, indicating their influence on the model’s predictions.

SA Random Forest model shown in Table 9, the top 9 most important features show some overlap with the Random Forest model, with features related to transaction balances including USD and BTC, spending include USD and BTC appearing again. However, the SA Random Forest model seems to place less emphasis on transaction volume include number spent and received compared to the classical model. Interestingly, a new feature, lifetime, emerges as important in the SA Random Forest model, suggesting that the model might benefit from understanding the overall duration of user activity.

QA Random Forest model shown in Table 10, the top 6 most important features highlight the significance of received transactions and various statistical moments. In particular, the feature related to the USD received reappears, indicating its importance across models. Basic statistics such as transaction frequency also emerge, alongside higher moments that may provide deeper insights into the distribution of transaction amounts. Additionally, transaction patterns are emphasized through features that capture output behavior and overall transaction trends, suggesting that a holistic view of user activity is essential in this model.

In the QA BQM Random Forest model, the top 5 important features reveal a continued emphasis on balance statistics and lifetime as significant factors. The average balance in BTC demonstrates its relevance, along with the transaction frequency as a basic statistic. The inclusion of the lifetime feature further aligns with the trend observed in other models, indicating its potential impact on predicting user behavior. Moments related to payback and overall transaction patterns are also included, reinforcing the model’s focus on understanding transactional dynamics over time.

The current classification methodology is affected by data imbalance, as highlighted in Table 1. This imbalance often leads to increased false negatives and reduced sensitivity for minority classes, ultimately degrading the model’s overall reliability and robustness. To mitigate this limitation, we plan to integrate the Synthetic Minority Oversampling Technique (SMOTE) [27] prior to feature summarization. This technique is anticipated to enhance the recall for underrepresented classes, resulting in a more balanced and robust classification model. Additionally, incorporating cost-sensitive learning during the training phase of Random Forest and other decision tree-based algorithms could further improve model performance, as indicated by Seliya et al. [28].

We also propose conducting an ablation study to evaluate the contribution of each feature set to the overall model performance. Understanding the impact of individual feature sets will inform future improvements by identifying which features are most crucial for classification accuracy and which are redundant, allowing for a more efficient and streamlined model. This study will involve systematically removing different feature groups—such as Transaction Patterns—and assessing the resultant impact on classification accuracy. By quantifying the influence of individual feature sets and examining the effectiveness of quantum-inspired SA in feature selection, we aim to gain a deeper understanding of the factors driving performance improvements.

Moreover, the QIFS methodology demonstrates substantial potential beyond its current scope, which is currently focused on Bitcoin mixer address classification. By optimizing feature selection, QIFS can significantly reduce computational overhead for classical machine learning models, thereby facilitating efficient processing across a variety of domains where feature selection plays a critical role. This positions QIFS as a viable approach for broader applications in fields such as cybersecurity, healthcare, and predictive maintenance, where effective feature selection is pivotal for improving model efficiency and overall performance. For instance, in cybersecurity, QIFS can be used to identify key features for detecting network intrusions, enhancing the precision and speed of intrusion detection systems. In healthcare, QIFS could optimize the selection of biomarkers from high-dimensional genomic data, thus improving the accuracy of diagnostic models. In predictive maintenance, QIFS can help identify critical indicators of machinery health, allowing for proactive interventions and minimizing downtime.

Acknowledgements We acknowledge support from the National Science and Technology Council, Taiwan, under Grants NSTC 112-2119-M-033-001, by the research project Applications of quantum computing in optimization and finances.