Search arXivSearch

arXiv · 2504.11702

Clustering and analysis of user behaviour in blockchain: A case study of Planet IX

Abstract

Decentralised applications (dApps) that run on public blockchains have the benefit of trustworthiness and transparency as every activity that happens on the blockchain can be publicly traced through the transaction data. However, this introduces a potential privacy problem as this data can be tracked and analysed, which can reveal user-behaviour information. A user behaviour analysis pipeline was proposed to present how this type of information can be extracted and analysed to identify separate behavioural clusters that can describe how users behave in the game. The pipeline starts with the collection of transaction data, involving smart contracts, that is collected from a blockchain-based game called Planet IX. Both the raw transaction information and the transaction events are considered in the data collection. From this data, separate game actions can be formed and those are leveraged to present how and when the users conducted their in-game activities in the form of user flows. An extended version of these user flows also presents how the Non-Fungible Tokens (NFTs) are being leveraged in the user actions. The latter is given as input for a Graph Neural Network (GNN) model to provide graph embeddings for these flows which then can be leveraged by clustering algorithms to cluster user behaviours into separate behavioural clusters. We benchmark and compare well-known clustering algorithms as a part of the proposed method. The user behaviour clusters were analysed and visualised in a graph format. It was found that behavioural information can be extracted regarding the users that belong to these clusters. Such information can be exploited by malicious users to their advantage. To demonstrate this, a privacy threat model was also presented based on the results that correspond to multiple potentially affected areas.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dorottya Zelenyanszki, Zhe Hou, Kamanashis Biswas, Vallipuram Muthukkumarasamy. 2025-04-16. Clustering and analysis of user behaviour in blockchain: A case study of Planet IX. https://arxiv.org/abs/2504.11702

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG

DeepSPoC: A Deep Learning Based Sequential Propagation of Chaos

Classical particle methods based on propagation of chaos (PoC) have been developed for solving mean-field stochastic differential equations and their associated nonlinear Fokker--Planck equations. However, direct PoC implementations are difficult to apply to high-dimensional problems because they require simulating and storing large numbers of interacting particles, often with high particle-particle interaction costs. Motivated by these limitations, we build on the recently proposed sequential propagation of chaos (SPoC) framework, which replaces the fully interacting particle system in PoC with a sequential interaction mechanism. Based on this structure, we present DeepSPoC, a neural particle method that embeds a neural density representation into the sequential particle dynamics. DeepSPoC simulates particles batch by batch, while the neural network represents the evolving empirical law and is substituted into the coefficients of the mean-field SDE, thereby replacing direct particle-particle interactions with particle-network interactions. In DeepSPoC, a recently developed normalizing flow model called KRnet is used to approximate the empirical measure of particles. Compared with direct particle implementations, DeepSPoC substantially reduces memory consumption and evaluates interaction terms more efficiently, thereby improving scalability for high-dimensional problems. We apply DeepSPoC to a wide range of mean-field equations and verify its effectiveness and computational advantages.

cs.LG