
M. Soriano-TriguerosUniversity of Seville | US · Computer Science and Artificial Intelligence
M. Soriano-Trigueros
MS Mathematics
Postdoc at Institute of Science and Technology Austria
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14
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February 2020 - July 2020
October 2019 - February 2020
June 2017 - July 2018
Publications
Publications (14)
Given a morphism of persistence modules (a.k.a. persistence morphism) ∶ → , we introduce a novel operator that determines a partial matching between the barcodes of and induced by. We show that the proposed operator is additive with respect to the direct sum of persistence morphisms, and that it contains more information than and the rank invariant...
Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known cla...
We study how to obtain partial matchings using the block function Mf, induced by a morphism f between persistence modules. Mf is defined algebraically and is linear with respect to direct sums of morphisms. We study some interesting properties of Mf, and provide a way of obtaining using matrix operations.
Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known cla...
Recently, trans- S -manifolds have been defined as a wide class of metric f -manifolds which includes, for instance, f -Kenmotsu manifolds, S -manifolds and C -manifolds and generalize well-studied trans-Sasakian manifolds. The definition of trans- S -manifolds is formulated using the covariant derivative of the tensor f and although this formulati...
We use topological data analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify the lifetime of homology classes (persistent homology) along different filtrations (increasing nested sequences of simplic...
We study how to obtain partial matchings using the block function $\mathcal{M}_f$, a novel concept obtained from a morphism f between persistence modules. $\mathcal{M}_f$ is defined algebraically and is linear with respect to direct sums of morphisms. We study some interesting properties of $\mathcal{M}_f$, and provide a way to obtain $\mathcal{M}_...
We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of homology classes (persistent homology) along different filtrations (increasing nested sequences of simplicial...
In this paper, we study how basis-independent partial matchings induced by morphisms between persistence modules (also called ladder modules) can be defined. Besides, we extend the notion of basis-independent partial matchings to the situation of a pair of morphisms with same target persistence module. The relation with the state-of-the-art methods...
Persistent homology and persistent entropy have recently become useful tools for patter recognition. In this paper, we find requirements under which persistent entropy is stable to small perturbations in the input data and scale invariant. In addition, we describe two new stable summary functions combining persistent entropy and the Betti curve. Fi...
In this paper, we apply persistent entropy, a novel topological statistic, for characterization of images of epithelial tissues. We have found out that persistent entropy is able to summarize topological and geometric information encoded by \alpha-complexes and persistent homology. After using some statistical tests, we can guarantee the existence...
In this paper, we apply persistent entropy, a novel topological statistic, for characterization of images of epithelial tissues. We have found out that persistent entropy is able to summarize topological and geometric information encoded by \alpha-complexes and persistent homology. After using some statistical tests, we can guarantee the existence...
Topological data analysis (TDA) aims to obtain useful information from data sets using topological concepts. In particular, it may help to infer from finite sample when a configuration space is a manifold. So far, there is no automatic process to decide the main topological features of a given sampled manifold. In this article, we present an entrop...
Persistent homology and persistent entropy have recently become useful tools for patter recognition. In this paper, we find requirements under which persistent entropy is stable to small perturbations in the input data and scale invariant. In addition, we describe two new stable summary functions combining persistent entropy and the Betti curve. Fi...