
Sara ScaramucciaUniversity of Rome Tor Vergata | UNIROMA2 · Dipartimento di Matematica
Sara Scaramuccia
PhD in Computer Science
Computational Topology, Computational Geometry, Topological Data Analysis, Visual Information, Machine Learning
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13
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Introduction
Additional affiliations
Education
November 2014 - May 2018
September 2011 - December 2013
September 2007 - November 2011
Publications
Publications (13)
The aim of this chapter is to give a handy but thorough introduction to persistent homology and its applications. The chapter’s path is made by the following steps. First, we deal with the constructions from data to simplicial complexes according to the kind of data: filtrations of data, point clouds, networks, and topological spaces. For each cons...
We introduce an algorithm to decompose any finite-type persistence module with coefficients in a field into what we call an {\em interval basis}. This construction yields both the standard persistence pairs of Topological Data Analysis (TDA), as well as a special set of generators inducing the interval decomposition of the Structure theorem. The co...
We introduce an algorithm to decompose any finite-type persistence module with coefficients in a field into what we call an {\em interval basis}. This construction yields both the standard persistence pairs of Topological Data Analysis (TDA), as well as a special set of generators inducing the interval decomposition of the Structure theorem. The co...
The combination of persistent homology and discrete Morse theory has proven very effective in visualizing and analyzing big and heterogeneous data. Indeed, topology provides computable and coarse summaries of data independently from specific coordinate systems and does so robustly to noise. Moreover, the geometric content of a discrete gradient vec...
Understanding choices performed by online customers is a growing need in the travel industry. In many practical situations, the only available information is the flight search query performed by the customer with no additional profile knowledge. In general, customer flight bookings are driven by prices, duration, number of connections, and so on. H...
Persistent homology allows for tracking topological features, like loops, holes and their higher-dimensional analogues, along a single-parameter family of nested shapes. Computing descriptors for complex data characterized by multiple parameters is becoming a major challenging task in several applications, including physics, chemistry, medicine, an...
The main objective of this paper is to introduce and study a notion of perfectness for discrete gradient vector fields with respect to (multi-parameter) persistent homology. As a natural generalization of usual perfectness in Morse theory for homology, persistence-perfectness entails having the least number of critical cells relevant for persistent...
Persistent Homology (PH) allows tracking homology features like loops, holes and their higher-dimensional analogs, along with a single-parameter family of nested spaces. Currently, computing descriptors for complex data characterized by multiple functions is becoming an important task in several applications, including physics, chemistry, medicine,...
Multivariate data are becoming more and more popular in several applications, including physics, chemistry, medicine, geography, etc. A multivariate dataset is represented by a cell complex and a vector-valued function defined on the complex vertices. The major challenge arising when dealing with multivariate data is to obtain concise and effective...
Persistent homology is a powerful notion rooted in topological data analysis which allows for retrieving the essential topological features of an object. The attention on persistent homology is constantly growing in a large number of application domains, such as biology and chemistry, astrophysics, automatic classification of images, sensor and soc...
We present a new algorithm for computing a discrete gradient field on multivariate data. For multivariate data, we consider a shape with a vector-valued function f defined on it. The proposed algorithm is well suited for parallel and distribute implementations. The discrete gradient field V we obtain is a reduced representation of the original shap...
A new persistence module-preserving algorithm for a single Morse-based reduction for cubical and simplicial complexes