6 Search Results for "Landi, Claudia"

Document
DOI: 10.4230/LIPIcs.WABI.2025.11
Mutational Signature Refitting on Sparse Pan-Cancer Data

Authors: Gal Gilad, Teresa M. Przytycka, and Roded Sharan

Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)

Abstract
Mutational processes shape cancer genomes, leaving characteristic marks that are termed signatures. The level of activity of each such process, or its signature exposure, provides important information on the disease, improving patient stratification and the prediction of drug response. Thus, there is growing interest in developing refitting methods that decipher those exposures. Previous work in this domain was unsupervised in nature, employing algebraic decomposition and probabilistic inference methods. Here we provide a supervised approach to the problem of signature refitting and show its superiority over current methods. Our method, SuRe, leverages a neural network model to capture correlations between signature exposures in real data. We show that SuRe outperforms previous methods on sparse mutation data from tumor type specific data sets, as well as pan-cancer data sets, with an increasing advantage as the data become sparser. We further demonstrate its utility in clinical settings.
Cite as

Gal Gilad, Teresa M. Przytycka, and Roded Sharan. Mutational Signature Refitting on Sparse Pan-Cancer Data. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gilad_et_al:LIPIcs.WABI.2025.11,
  author =	{Gilad, Gal and Przytycka, Teresa M. and Sharan, Roded},
  title =	{{Mutational Signature Refitting on Sparse Pan-Cancer Data}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{11:1--11:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.11},
  URN =		{urn:nbn:de:0030-drops-239374},
  doi =		{10.4230/LIPIcs.WABI.2025.11},
  annote =	{Keywords: mutational signatures, signature refitting, cancer genomics, genomic data analysis, somatic mutations}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.29
Sparsification of the Generalized Persistence Diagrams for Scalability Through Gradient Descent

Authors: Mathieu Carrière, Seunghyun Kim, and Woojin Kim

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
The generalized persistence diagram (GPD) is a natural extension of the classical persistence barcode to the setting of multi-parameter persistence and beyond. The GPD is defined as an integer-valued function whose domain is the set of intervals in the indexing poset of a persistence module, and is known to be able to capture richer topological information than its single-parameter counterpart. However, computing the GPD is computationally prohibitive due to the sheer size of the interval set. Restricting the GPD to a subset of intervals provides a way to manage this complexity, compromising discriminating power to some extent. However, identifying and computing an effective restriction of the domain that minimizes the loss of discriminating power remains an open challenge. In this work, we introduce a novel method for optimizing the domain of the GPD through gradient descent optimization. To achieve this, we introduce a loss function tailored to optimize the selection of intervals, balancing computational efficiency and discriminative accuracy. The design of the loss function is based on the known erosion stability property of the GPD. We showcase the efficiency of our sparsification method for dataset classification in supervised machine learning. Experimental results demonstrate that our sparsification method significantly reduces the time required for computing the GPDs associated to several datasets, while maintaining classification accuracies comparable to those achieved using full GPDs. Our method thus opens the way for the use of GPD-based methods to applications at an unprecedented scale.
Cite as

Mathieu Carrière, Seunghyun Kim, and Woojin Kim. Sparsification of the Generalized Persistence Diagrams for Scalability Through Gradient Descent. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carriere_et_al:LIPIcs.SoCG.2025.29,
  author =	{Carri\`{e}re, Mathieu and Kim, Seunghyun and Kim, Woojin},
  title =	{{Sparsification of the Generalized Persistence Diagrams for Scalability Through Gradient Descent}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{29:1--29:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.29},
  URN =		{urn:nbn:de:0030-drops-231810},
  doi =		{10.4230/LIPIcs.SoCG.2025.29},
  annote =	{Keywords: Multi-parameter persistent homology, Generalized persistence diagram, Generalized rank invariant, Non-convex optimization, Gradient descent}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.41
Decomposing Multiparameter Persistence Modules

Authors: Tamal K. Dey, Jan Jendrysiak, and Michael Kerber

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Dey and Xin (J.Appl.Comput.Top., 2022) describe an algorithm to decompose finitely presented multiparameter persistence modules using a matrix reduction algorithm. Their algorithm only works for modules whose generators and relations are distinctly graded. We extend their approach to work on all finitely presented modules and introduce several improvements that lead to significant speed-ups in practice. Our algorithm is fixed-parameter tractable with respect to the maximal number of relations of the same degree and with further optimisation we obtain an O(n³) time algorithm for interval-decomposable modules. In particular, we can decide interval-decomposability in this time. As a by-product to the proofs of correctness we develop a theory of parameter restriction for persistence modules. Our algorithm is implemented as a software library aida, the first to enable the decomposition of large inputs. We show its capabilities via extensive experimental evaluation.
Cite as

Tamal K. Dey, Jan Jendrysiak, and Michael Kerber. Decomposing Multiparameter Persistence Modules. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dey_et_al:LIPIcs.SoCG.2025.41,
  author =	{Dey, Tamal K. and Jendrysiak, Jan and Kerber, Michael},
  title =	{{Decomposing Multiparameter Persistence Modules}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{41:1--41:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.41},
  URN =		{urn:nbn:de:0030-drops-231939},
  doi =		{10.4230/LIPIcs.SoCG.2025.41},
  annote =	{Keywords: Topological Data Analysis, Multiparameter Persistence Modules, Persistence, Decomposition}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.64
Super-Polynomial Growth of the Generalized Persistence Diagram

Authors: Donghan Kim, Woojin Kim, and Wonjun Lee

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
The Generalized Persistence Diagram (GPD) for multi-parameter persistence naturally extends the classical notion of persistence diagram for one-parameter persistence. However, unlike its classical counterpart, computing the GPD remains a significant challenge. The main hurdle is that, while the GPD is defined as the Möbius inversion of the Generalized Rank Invariant (GRI), computing the GRI is intractable due to the formidable size of its domain, i.e., the set of all connected and convex subsets in a finite grid in ℝ^d with d ≥ 2. This computational intractability suggests seeking alternative approaches to computing the GPD. In order to study the complexity associated to computing the GPD, it is useful to consider its classical one-parameter counterpart, where for a filtration of a simplicial complex with n simplices, its persistence diagram contains at most n points. This observation leads to the question: Given a d-parameter simplicial filtration, could the cardinality of its GPD (specifically, the support of the GPD) also be bounded by a polynomial in the number of simplices in the filtration? This is the case for d = 1, where we compute the persistence diagram directly at the simplicial filtration level. If this were also the case for d ≥ 2, it might be possible to compute the GPD directly and much more efficiently without relying on the GRI. We show that the answer to the question above is negative, demonstrating the inherent difficulty of computing the GPD. More specifically, we construct a sequence of d-parameter simplicial filtrations where the cardinalities of their GPDs are not bounded by any polynomial in the number of simplices. Furthermore, we show that several commonly used methods for constructing multi-parameter filtrations can give rise to such "wild" filtrations.
Cite as

Donghan Kim, Woojin Kim, and Wonjun Lee. Super-Polynomial Growth of the Generalized Persistence Diagram. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 64:1-64:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kim_et_al:LIPIcs.SoCG.2025.64,
  author =	{Kim, Donghan and Kim, Woojin and Lee, Wonjun},
  title =	{{Super-Polynomial Growth of the Generalized Persistence Diagram}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{64:1--64:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.64},
  URN =		{urn:nbn:de:0030-drops-232162},
  doi =		{10.4230/LIPIcs.SoCG.2025.64},
  annote =	{Keywords: Persistent homology, M\"{o}bius inversion, Multiparameter persistence, Generalized persistence diagram, Generalized rank invariant}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.69
Computing Betti Tables and Minimal Presentations of Zero-Dimensional Persistent Homology

Authors: Dmitriy Morozov and Luis Scoccola

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
The Betti tables of a multigraded module encode the grades at which there is an algebraic change in the module. Multigraded modules show up in many areas of pure and applied mathematics, and in particular in topological data analysis, where they are known as persistence modules, and where their Betti tables describe the places at which the homology of filtered simplicial complexes changes. Although Betti tables of singly and bigraded modules are already being used in applications of topological data analysis, their computation in the bigraded case (which relies on an algorithm that is cubic in the size of the filtered simplicial complex) is a bottleneck when working with large datasets. We show that, in the special case of 0-dimensional homology (relevant for clustering and graph classification) Betti tables of bigraded modules can be computed in log-linear time. We also consider the problem of computing minimal presentations, and show that minimal presentations of 0-dimensional persistent homology can be computed in quadratic time, regardless of the grading poset.
Cite as

Dmitriy Morozov and Luis Scoccola. Computing Betti Tables and Minimal Presentations of Zero-Dimensional Persistent Homology. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 69:1-69:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{morozov_et_al:LIPIcs.SoCG.2025.69,
  author =	{Morozov, Dmitriy and Scoccola, Luis},
  title =	{{Computing Betti Tables and Minimal Presentations of Zero-Dimensional Persistent Homology}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{69:1--69:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.69},
  URN =		{urn:nbn:de:0030-drops-232219},
  doi =		{10.4230/LIPIcs.SoCG.2025.69},
  annote =	{Keywords: Multiparameter persistence, Zero-dimensional homology, Minimal presentation, Betti table}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.15
The Reeb Graph Edit Distance Is Universal

Authors: Ulrich Bauer, Claudia Landi, and Facundo Mémoli

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specific construction, we show that the interleaving distance and the functional distortion distance on Reeb graphs are not universal.
Cite as

Ulrich Bauer, Claudia Landi, and Facundo Mémoli. The Reeb Graph Edit Distance Is Universal. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bauer_et_al:LIPIcs.SoCG.2020.15,
  author =	{Bauer, Ulrich and Landi, Claudia and M\'{e}moli, Facundo},
  title =	{{The Reeb Graph Edit Distance Is Universal}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.15},
  URN =		{urn:nbn:de:0030-drops-121730},
  doi =		{10.4230/LIPIcs.SoCG.2020.15},
  annote =	{Keywords: Reeb graphs, topological descriptors, edit distance, interleaving distance}
}
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