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Nikolaos Nakis

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Machine Learning Social and Information Networks

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preprint2026arXiv

Aitchison Embeddings for Learning Compositional Graph Representations

Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to graph structure. Many networks naturally admit a role-mixture view, where nodes are best described as mixtures over latent archetypal factors. Motivated by this structure, we propose a compositional graph embedding framework grounded in Aitchison geometry, the canonical geometry for comparing mixtures. Nodes are represented as simplex-valued compositions and embedded via isometric log-ratio (ILR) coordinates, which preserve Aitchison distances while enabling unconstrained optimization in Euclidean space. This yields intrinsically interpretable embeddings whose geometry reflects relative trade-offs among archetypes and supports coherent behavior under component restriction; we consider both fixed and learnable ILR bases. Across node classification and link prediction, our method achieves competitive performance with strong baselines while providing explainability by construction rather than post-hoc. Finally, subcompositional coherence enables principled component restriction: removing and renormalizing subsets preserves a well-defined geometry, which we exploit via subcompositional dimensionality removal to probe how archetype groups influence representations and predictions.

preprint2026arXiv

Rank Is Not Capacity: Spectral Occupancy for Latent Graph Models

Graph representation learning has become a standard approach for analyzing networked data, with latent embeddings widely used for link prediction, community detection, and related tasks. Yet a basic design choice, the latent dimension, is still treated as a brittle hyperparameter, fixed before training and tuned by held-out performance. Learned factors are also identifiable only up to rotation and rescaling, so the nominal rank rarely coincides with the quantity that governs model behavior. We propose Spectral Prefix Extraction and Capacity-Targeted Representation Analysis (Spectra), which replaces rank as the unit of analysis with the spectrum of a learned positive semidefinite kernel, trace-normalized so that spectra are comparable across fits. The normalized eigenvalues form a distribution on the simplex, and their Shannon effective rank acts both as a summary of learned capacity and as a controllable training-time coordinate: a single scalar shapes this realized dimension during training, and bisection targets any desired value within the rank cap. To theoretically support that, we show local regularity and monotonicity of the realized-dimension profile. Across collaboration, social, biological, and infrastructure networks, Spectra traces performance--capacity frontiers that make the trade-off between predictive accuracy and realized dimension visible. It performs competitively with strong link-prediction baselines, yields aligned lower-capacity views of the same fitted model through spectral prefixes, and provides a principled handle on capacity in the overparameterized regime. Capacity thus becomes a property of the fitted model rather than a hyperparameter of the training.

preprint2022arXiv

HM-LDM: A Hybrid-Membership Latent Distance Model

A central aim of modeling complex networks is to accurately embed networks in order to detect structures and predict link and node properties. The latent space models (LSM) have become prominent frameworks for embedding networks and include the latent distance (LDM) and eigenmodel (LEM) as the most widely used LSM specifications. For latent community detection, the embedding space in LDMs has been endowed with a clustering model whereas LEMs have been constrained to part-based non-negative matrix factorization (NMF) inspired representations promoting community discovery. We presently reconcile LSMs with latent community detection by constraining the LDM representation to the D-simplex forming the hybrid-membership latent distance model (HM-LDM). We show that for sufficiently large simplex volumes this can be achieved without loss of expressive power whereas by extending the model to squared Euclidean distances, we recover the LEM formulation with constraints promoting part-based representations akin to NMF. Importantly, by systematically reducing the volume of the simplex, the model becomes unique and ultimately leads to hard assignments of nodes to simplex corners. We demonstrate experimentally how the proposed HM-LDM admits accurate node representations in regimes ensuring identifiability and valid community extraction. Importantly, HM-LDM naturally reconciles soft and hard community detection with network embeddings exploring a simple continuous optimization procedure on a volume constrained simplex that admits the systematic investigation of trade-offs between hard and mixed membership community detection.

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