arXiv subjects

William Cappelletti

Publications and source records attributed to William Cappelletti.

5 recordsLinked to original sources

arXiv2026

Geodesics of Dynamic Graphs for Regime Change Detection

Traditional change point detection in dynamic networks assumes abrupt transitions between stationary states, overlooking scenarios of continuous evolution which arise in most real-world applications, such as social networks or physical systems. We address this gap by formally defining regimes as periods of coherent dynamics in temporal graphs, which we characterize as trajectories along geodesics in a suitably defined graph space. This original perspective allows us to define regime changes as significant drifts in dynamics, either toward new trajectories or with pace changes. We leverage graph regression methods to measure the cumulative distance of sequences of observed graphs from the estimated geodesics between their endpoints, in the relevant graph space, which we can combine with change point detection algorithms. We present experiments on dynamic networks, with changing trajectories and varying speeds, in which we outperform state of the art change point detection models. Then, we analyse mobility data during the Covid-19 pandemic, and show that our assumptions on regular network evolution lead to change points that are more aligned to external events compared to the outcomes of baseline methods. Our work is the first to model and detect changes between evolving regimes in graph space, providing a realistic and powerful tool for analyzing complex temporal graph data.

cs.LG↗

arXiv2025

rETF-semiSL: Semi-Supervised Learning for Neural Collapse in Temporal Data

Deep neural networks for time series must capture complex temporal patterns, to effectively represent dynamic data. Self- and semi-supervised learning methods show promising results in pre-training large models, which -- when finetuned for classification -- often outperform their counterparts trained from scratch. Still, the choice of pretext training tasks is often heuristic and their transferability to downstream classification is not granted, thus we propose a novel semi-supervised pre-training strategy to enforce latent representations that satisfy the Neural Collapse phenomenon observed in optimally trained neural classifiers. We use a rotational equiangular tight frame-classifier and pseudo-labeling to pre-train deep encoders with few labeled samples. Furthermore, to effectively capture temporal dynamics while enforcing embedding separability, we integrate generative pretext tasks with our method, and we define a novel sequential augmentation strategy. We show that our method significantly outperforms previous pretext tasks when applied to LSTMs, transformers, and state-space models on three multivariate time series classification datasets. These results highlight the benefit of aligning pre-training objectives with theoretically grounded embedding geometry.

cs.LG↗

arXiv2024

Graph-Dictionary Signal Model for Sparse Representations of Multivariate Data

Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures, but no prior model exists to infer such underlying structure elements from data. We define a novel Graph-Dictionary signal model, where a finite set of graphs characterizes relationships in data distribution as filters on the weighted sum of their Laplacians. We propose a framework to infer the graph dictionary representation from observed node signals, which allows to include a priori knowledge about signal properties, and about underlying graphs and their coefficients. We introduce a bilinear generalization of the primal-dual splitting algorithm to solve the learning problem. We show the capability of our method to reconstruct graphs from signals in multiple synthetic settings, where our model outperforms popular baselines. Then, we exploit graph-dictionary representations in an illustrative motor imagery decoding task on brain activity data, where we classify imagined motion better than standard methods relying on many more features. Our graph-dictionary model bridges a gap between sparse representations of multivariate data and a structured decomposition of sample-varying relationships into a sparse combination of elementary graph atoms.

cs.LG↗

arXiv2024

SzCORE: A Seizure Community Open-source Research Evaluation framework for the validation of EEG-based automated seizure detection algorithms

The need for high-quality automated seizure detection algorithms based on electroencephalography (EEG) becomes ever more pressing with the increasing use of ambulatory and long-term EEG monitoring. Heterogeneity in validation methods of these algorithms influences the reported results and makes comprehensive evaluation and comparison challenging. This heterogeneity concerns in particular the choice of datasets, evaluation methodologies, and performance metrics. In this paper, we propose a unified framework designed to establish standardization in the validation of EEG-based seizure detection algorithms. Based on existing guidelines and recommendations, the framework introduces a set of recommendations and standards related to datasets, file formats, EEG data input content, seizure annotation input and output, cross-validation strategies, and performance metrics. We also propose the 10-20 seizure detection benchmark, a machine-learning benchmark based on public datasets converted to a standardized format. This benchmark defines the machine-learning task as well as reporting metrics. We illustrate the use of the benchmark by evaluating a set of existing seizure detection algorithms. The SzCORE (Seizure Community Open-source Research Evaluation) framework and benchmark are made publicly available along with an open-source software library to facilitate research use, while enabling rigorous evaluation of the clinical significance of the algorithms, fostering a collective effort to more optimally detect seizures to improve the lives of people with epilepsy.

eess.SP↗

arXiv2020

Polyadic Quantum Classifier

We introduce here a supervised quantum machine learning algorithm for multi-class classification on NISQ architectures. A parametric quantum circuit is trained to output a specific bit string corresponding to the class of the input datapoint. We train and test it on an IBMq 5-qubit quantum computer and the algorithm shows good accuracy --compared to a classical machine learning model-- for ternary classification of the Iris dataset and an extension of the XOR problem. Furthermore, we evaluate with simulations how the algorithm fares for a binary and a quaternary classification on resp. a known binary dataset and a synthetic dataset.

quant-ph↗