Dimosthenis Pasadakis

Dimosthenis Pasadakis, Olaf Schenk, Verner Vlacic et al.

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. However, the estimation of the multiple nonlinear eigenvectors is associated with an increased computational cost. We present an implementation of a direct multiway spectral clustering algorithm in the $p$-norm, for $p\in(1,2]$, using a novel C++ GraphBLAS API. The key operations are expressed in linear algebraic terms and are executed over the resulting sparse matrices and dense vectors, parameterized in the algebra pertinent to the computation. We demonstrate the effectiveness and accuracy of our shared-memory algorithm on several artificial test cases. Our numerical examples and comparative results against competitive methods indicate that the proposed implementation attains high quality clusters in terms of the balanced graph cut metric. The strong scaling capabilities of our algorithm are showcased on a range of datasets with up to $8$ million nodes and $48$ million edges.

Lidia Losavio, Luca Persia, Madan Sathe et al.

Technological advancements in cryptocurrency markets have increased accessibility for investors, but concurrently exposed them to the risks of market manipulations. Existing fraud detection mechanisms typically rely on machine learning methods that treat each financial asset (i.e., token) and its related transactions independently. However, market manipulation strategies are rarely isolated events, but are rather characterized by coordination, repetition, and frequent transfers among related assets. This suggests that relational structure constitutes an integral component of the signal and can be effectively represented through graphical means. In this paper, we propose three graph construction methods that rely on aggregated hourly market data. The proposed graphs are processed by a unified spatio-temporal Graph Neural Network (GNN) architecture that combines attention-based spatial aggregation with temporal Transformer encoding. We evaluate our methodology on a real-world dataset comprised of pump-and-dump schemes in cryptocurrency markets, spanning a period of over three years. Our comparative results showcase that our graph-based models achieve significant improvements over standard machine learning baselines in detecting anomalous events. Our work highlights that learned market connectivity provides substantial gains for detecting coordinated market manipulation schemes.

Dimosthenis Pasadakis, Christie Louis Alappat, Olaf Schenk et al.

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering algorithm in the $p$-norm, for $p \in (1, 2]$. The problem of computing multiple eigenvectors of the graph $p$-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of $p$ is reduced in a pseudocontinuous manner, promoting sparser solution vectors that correspond to optimal graph cuts as $p$ approaches one. Monitoring the monotonic decrease of the balanced graph cuts guarantees that we obtain the best available solution from the $p$-levels considered. We demonstrate the effectiveness and accuracy of our algorithm in various artificial test-cases. Our numerical examples and comparative results with various state-of-the-art clustering methods indicate that the proposed method obtains high quality clusters both in terms of balanced graph cut metrics and in terms of the accuracy of the labelling assignment. Furthermore, we conduct studies for the classification of facial images and handwritten characters to demonstrate the applicability in real-world datasets.