GIORGIA ZACCARIA

Dottoressa di ricerca

ciclo: XXXIV



Titolo della tesi: Ultrametric models for hierarchical dimensionality reduction

Many relevant multidimensional phenomena, such as well-being, climate change, sustainable development, poverty and so on, are defined by nested latent concepts, which can be represented by a tree-shape structure supposing hierarchical relationships among observed variables. In literature, several methodologies have been proposed to both model the relationships among observed variables which reflect unobserved ones, and assess the existence of unobserved variables of "higher-order''. Nonetheless, these methodologies are usually developed with sequential procedures which do not optimize a unique objective function, and/or a confirmatory approach, i.e., by setting the relationships between observed and unobserved variables a priori. This dissertation discusses some new simultaneous, exploratory and parsimonious models for hierarchical dimensionality reduction, which overcome the limitations of the existing methodologies. The proposals introduced herein are based, "directly'' or "indirectly'', upon the definition of an ultrametric matrix, which differs from the well-known definition of an ultrametric distance matrix, and is one-to-one associated with a hierarchy of latent concepts. The first proposal allows to model a nonnegative correlation matrix via an ultrametric correlation one by detecting reliable concepts, associated with disjoint groups of variables, and hierarchical relationships among them. The second work compares the first proposal with the traditional agglomerative hierarchical clustering algorithms applied on variables, after a transformation of correlations into distances, by highlighting the need of specific models to inspect the hierarchical relationships among variables. The third proposal extends the definition of an ultrametric matrix to a generic one by relaxing the non-negativity assumption and applying it to a covariance matrix. The extended ultrametric covariance matrix is then used to model the covariance structures of a Gaussian mixture model by both defining a new parsimonious parameterization of a covariance matrix and inspecting the hierarchical structure underlying multidimensional phenomena in heterogeneous populations. The fourth proposal introduces a quantification of latent concepts via a hierarchical extension of Principal Component Analysis. Even if not directly based on the definition of an ultrametric matrix, this proposal aims in turn at pinpointing nested partitions of variables into groups, each one associated with a component. The proposed models are illustrated both via simulation studies and real data applications in order to study their performances and abilities.

Produzione scientifica

11573/1619687 - 2022 - An ultrametric model to build a Composite Indicators system
Cavicchia, Carlo; Sarnacchiaro, Pasquale; Vichi, Maurizio; Zaccaria, Giorgia - 04b Atto di convegno in volume
congresso: 10th International conference IES 2022 innovation and society 5.0: statistical and economic methodologies for quality assessment (Capua, Italia)
libro: Book of short papers. IES 2022 Innovation & society 5.0: statistical and economic methodologies for quality assessment - (978-88-94593-35-8; 978-88-94593-36-5)

11573/1615269 - 2022 - Gaussian mixture model with an extended ultrametric covariance structure
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 01a Articolo in rivista
rivista: ADVANCES IN DATA ANALYSIS AND CLASSIFICATION (Springer Berlin Heidelberg) pp. 399-427 - issn: 1862-5347 - wos: WOS:000761878300001 (0) - scopus: 2-s2.0-85125274026 (0)

11573/1652360 - 2022 - Hierarchical disjoint principal component analysis
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 01a Articolo in rivista
rivista: ASTA. ADVANCES IN STATISTICAL ANALYSIS (Heidelberg ; Berlin : Springer) pp. 1-38 - issn: 1863-818X - wos: WOS:000843962200001 (0) - scopus: 2-s2.0-85137218706 (0)

11573/1652648 - 2022 - Complex Dimensionality Reduction: Ultrametric Models for Mixed-Type Data
Mingione, Marco; Vichi, Maurizio; Zaccaria, Giorgia - 02a Capitolo o Articolo
libro: SMPS 2022: Building Bridges between Soft and Statistical Methodologies for Data Science - (978-3-031-15509-3)

11573/1656384 - 2022 - An ultrametric model for building a composite indicator system to study climate change in European countries
Zaccaria, Giorgia; Sarnacchiaro, Pasquale - 04b Atto di convegno in volume
congresso: 51st scientific meeting of the Italian statistical society, SIS 2022 (Caserta)
libro: Book of the short papers. SIS 2022 51st scientific meeting of the Italian statistical society - (9788891932310)

11573/1554267 - 2021 - The ultrametric covariance model for modelling teachers’ job satisfaction
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 04b Atto di convegno in volume
congresso: 50th Edition of the Scientific Meeting of the Italian Statistical Society (Pisa; Italy)
libro: Book of short papers SIS 2021 - (9788891927361)

11573/1567032 - 2021 - Model-based clustering with parsimonious covariance structure
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 04b Atto di convegno in volume
congresso: 13th scientific meeting of the classification and data analysis group, CLADAG 2021 (Florence; Italy (telematico))
libro: CLADAG 2021 book of abstracts and short papers. 13th scientific meeting of the classification and data analysis group - Firenze, September 9-11, 2021 - (978-88-5518-340-6)

11573/1586634 - 2021 - A parsimonious parameterization of a nonnegative correlation matrix
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 04b Atto di convegno in volume
congresso: 5th international workshop on models and learning for clustering and classification, MBC2 2020 (Catania)
libro: Book of short papers of the 5th international workshop on models and learning for clustering and classification MBC2 2020, Catania, Italy - (9788855265393)

11573/1391004 - 2020 - Exploring hierarchical concepts: theoretical and application comparisons
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 02a Capitolo o Articolo
libro: Advanced studies in behaviormetrics and data science. Essays in honor of Akinori Okada - (978-981-15-2699-2)

11573/1403712 - 2020 - The ultrametric correlation matrix for modelling hierarchical latent concepts
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 01a Articolo in rivista
rivista: ADVANCES IN DATA ANALYSIS AND CLASSIFICATION (Springer Berlin Heidelberg) pp. 837-853 - issn: 1862-5347 - wos: WOS:000536067100001 (6) - scopus: 2-s2.0-85085703483 (6)

11573/1448295 - 2020 - Exploring drug consumption via an ultrametric correlation matrix
Zaccaria, Giorgia; Vichi, Maurizio - 04b Atto di convegno in volume
congresso: 50th Meeting of the Italian Statistical Society (Canceled)
libro: Book of short papers SIS 2020 - (9788891910776)

11573/1292036 - 2019 - Hierarchical clustering and dimensionality reduction for big data
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 04b Atto di convegno in volume
congresso: SIS 2019 (Milano, Italia)
libro: Smart statistics for smart applications. Book of short paper SIS2019 - (9788891915108)

11573/1302650 - 2019 - A new hierarchical model-based composite indicator on climate change
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 04b Atto di convegno in volume
congresso: 9th International conference IES 2019 - Innovation & Society - Statistical evaluation systems at 360°: techniques, technologies and new frontiers (Rome; Italy)
libro: Statistical methods for service quality evaluation. Book of short papers of IES 2019, Rome, Italy, July 4-5 - (9788886638654)

11573/1341564 - 2019 - Dimensionality reduction via hierarchical factorial structure
Cavicchia, Carlo; Vichi, Maurizio; Zaccaria, Giorgia - 04b Atto di convegno in volume
congresso: CLADAG 2019, the 12th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS). (Cassino; Italy)
libro: CLADAG 2019 Book of Short Papers - (978-88-8317-108-6)

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