Departure from Regularity: Degree Heterogeneity and Eigengap as the Structural Drivers of ASE-LSE Latent Subspace Disagreement

Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same network. Yet the structural reasons behind this disagreement remain incompletely understood. This paper provides a structural account. We show that regularity is a sufficient condition for perfect agreement: when every node has the same number of connections, the two methods produce identical latent subspaces. Any departure from this regularity introduces disagreement, and we prove an explicit bound whose two terms suggest the structural ingredients controlling it: degree heterogeneity, which pushes the methods apart, and community structure strength, which pulls them back together. We validate both drivers empirically across thousands of simulated networks, confirming that heterogeneity drives disagreement up, community strength suppresses it, and their ratio provides a strong predictor of when the two embeddings can be treated as interchangeable and when they cannot.

Deep Attention-based Sequential Ensemble Learning for BLE-Based Indoor Localization in Care Facilities

Indoor localization systems in care facilities enable optimization of staff allocation, workload management, and quality of care delivery. Traditional machine learning approaches to Bluetooth Low Energy (BLE)-based localization treat each temporal measurement as an independent observation, fundamentally limiting their performance. To address this limitation, this paper introduces Deep Attention-based Sequential Ensemble Learning (DASEL), a novel framework that reconceptualizes indoor localization as a sequential learning problem. The framework integrates frequency-based feature engineering, bidirectional GRU networks with attention mechanisms, multi-directional sliding windows, and confidence-weighted temporal smoothing to capture human movement trajectories. Evaluated on real-world data from a care facility using 4-fold temporal cross-validation, DASEL achieves a macro F1 score of 0.4438, representing a 53.1% improvement over the best traditional baseline (0.2898).