arXiv subjects

Maria Giulia Preti

Publications and source records attributed to Maria Giulia Preti.

6 recordsLinked to original sources

arXiv2026

Topological Signal Processing: An Application-Oriented Tutorial

Many modern datasets are large and carry complex structural relationships. Graph-based methods have traditionally been used to represent networked data, modeling individual elements as nodes and pairwise interactions as edges. Furthermore, Graph Signal Processing (GSP) has been developed to analyze signals on graph nodes, such as temperature measurements (node signals) across different regions of a country represented as a graph. Topological Signal Processing (TSP) is an emerging field that generalizes GSP, enabling the analysis of signals defined not only on nodes but also on edges, triangles, and higher-dimensional network elements, modeled as simplicial complexes and related topological structures. This makes TSP naturally well-suited for studying higher-order interactions in complex systems by extending classical signal processing concepts, such as filtering and Fourier transforms, to the topological level. Despite its versatility, TSP remains challenging for many practitioners. Therefore, we present an accessible overview of TSP foundations while drawing connections with application-oriented settings. We focus on processing techniques based on the combinatorial Hodge Laplacian, which generalizes the graph Laplacian to simplicial complexes. In particular, we review key TSP concepts, relate them to real-world examples, and discuss how higher-order structures and signals can be derived from datasets. For instance, we introduce an edge-level signal capturing lagged interactions between nodal signals, and demonstrate its use in a case study on TSP-based analysis of brain imaging data, revealing nontrivial interactions between sets of brain regions. Overall, we aim to promote a broader adoption of TSP by bridging methodological developments with applications, fostering its use among a wide community of theoretical and applied researchers.

eess.SP↗

arXiv2019

Decoupling of brain function from structure reveals regional behavioral specialization in humans

The brain is an assembly of neuronal populations interconnected by structural pathways. Brain activity is expressed on and constrained by this substrate. Therefore, statistical dependencies between functional signals in directly connected areas can be expected higher. However, the degree to which brain function is bound by the underlying wiring diagram remains a complex question that has been only partially answered. Here, we introduce the structural-decoupling index to quantify the coupling strength between structure and function, and we reveal a macroscale gradient from brain regions more strongly coupled, to regions more strongly decoupled, than expected by realistic surrogate data. This gradient spans behavioral domains from lower-level sensory function to high-level cognitive ones and shows for the first time that the strength of structure-function coupling is spatially varying in line with evidence derived from other modalities, such as functional connectivity, gene expression, microstructural properties and temporal hierarchy.

q-bio.NC↗

arXiv2019

Guided Graph Spectral Embedding: Application to the C. elegans Connectome

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based on wavelets and Slepians-that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion and its linear approximation, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode's neural network in terms of functionality and importance of cells. Compared to Laplacian embedding, the guided approach, focused on a certain class of cells (sensory, inter- and motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low or high order processing functions.

cs.LG↗

arXiv2018

Augmented Slepians: Bandlimited Functions that Counterbalance Energy in Selected Intervals

Slepian functions provide a solution to the optimization problem of joint time-frequency localization. Here, this concept is extended by using a generalized optimization criterion that favors energy concentration in one interval while penalizing energy in another interval, leading to the "augmented" Slepian functions. Mathematical foundations together with examples are presented in order to illustrate the most interesting properties that these generalized Slepian functions show. Also the relevance of this novel energy-concentration criterion is discussed along with some of its applications.

eess.SP↗

arXiv2017

Guiding Network Analysis using Graph Slepians: An Illustration for the C. Elegans Connectome

Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier transform and then transpose signal processing operations to graphs by implementing them in the spectral domain. Here, we build on recent work that generalized Slepian functions to the graph setting. In particular, graph Slepians are band-limited graph signals with maximal energy concentration in a given subgraph. We show how this approach can be used to guide network analysis; i.e., we propose a visualization that reveals network organization of a subgraph, but while striking a balance with global network structure. These developments are illustrated for the structural connectome of the C. Elegans.

cs.LG↗

arXiv2017

When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum

The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smallest non-zero eigenvalue and plays a key role for graph clustering. Graph signal processing focusses on the analysis of signals that are attributed to the graph nodes. The eigendecomposition of the graph Laplacian allows to define the graph Fourier transform and extend conventional signal-processing operations to graphs. Here, we introduce the design of Slepian graph signals, by maximizing energy concentration in a predefined subgraph for a graph spectral bandlimit. We establish a novel link with classical Laplacian embedding and graph clustering, which provides a meaning to localized graph frequencies.

cs.LG↗