New approaches for analysing functional data - a focus on shape

Sami Helander

New approaches for analysing functional data - a focus on shape

Julkaisun otsikon käännös: New approaches for analysing functional data - a focus on shape

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Funktionaalinen data - joukko jatkuvasta lähteestä kerättyjä mittaussarjoja - on yleistynyt useissa sovelluksissa, monilla eri tutkimuksen aloilla. Tällaista dataa tutkittaessa havaittuja yksikköjä käsitellään usein funktioina, joilla on jatkuva funktionaalinen rakenne. Tämä ilmenee lähes loputtomana skaalana uusia rakenteen ja muodon vaihteluja, joita esiintyy ainoastaan tällaisilla aineistoilla. Siispä, funktionaalisten aineistojen rakenteellisia vaihteluja huomioivat menetelmät ovat saaneet osakseen paljon huomiota funktionaalisen datan tutkimuksessa. Tämä väitöskirja tarkastelee funktionaalisten aineistojen muoto-ominaisuuksia kolmella eri lähestymistavalla, hyödyntäen funktionaalista tilastollista syvyyttä sekä rakenteellisille vaihteluille herkkiä metriikoita. Ensimmäinen lähestymistapa havainnollistaa data-lähtöisen metodiikan hyötyjä, joissa asiantuntija voi hyödyntää aineistoon liittyvää kontekstuaalista tietämystään. Tarjoamme tilastolliseen syvyyteen pohjautuvan johdonmukaisen viitekehyksen tilastolliselle analyysille, joka mahdollistaa ad hoc tietämyksen hyödyntämisen. Toisessa lähestymistavassamme tarkastelemme muoto-yksityiskohtia hyödyntävää metodiikkaa yleisemmästä näkökulmasta. Esittelemme uuden funktionaalisen tilastollisen syvyyden menetelmän, joka hyödyntää aivan hiljattain löydettyä muoto-poikkeavuuden käsitettä. Kolmas lähestymistapa ottaa askeleen kohti vieläkin yleisempää viitekehystä, ja tarkastelee muotoon sekä rakenteeseen liittyviä käsitteitä funktionaalisten metriikoiden kautta. Täsmällisemmin, esittelemme uuden integroitujen metriikoiden perheen, joka tarjoaa mittarin funktioiden kokonaisvaltaiselle paikalliselle samankaltaisuudelle.

Julkaisun otsikon käännös	New approaches for analysing functional data - a focus on shape
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Ilmonen, Pauliina, Vastuuprofessori Viitasaari, Lauri, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-64-0881-1
Sähköinen ISBN	978-952-64-0882-8
Tila	Julkaistu - 2022
OKM-julkaisutyyppi	G5 Artikkeliväitöskirja

Tutkimusalat

funktionaalinen data
muoto-herkkyys
tilastollinen syvyys
funktionaalinen syvyys
integroitu metriikka

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-64-0882-8

Science-IT
Hakala, M. (Manager)
Perustieteiden korkeakoulu
Laitteistot/tilat: Facility

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@phdthesis{040331606cc144cb8c3843ce0fe24f3b,

title = "New approaches for analysing functional data - a focus on shape",

abstract = "Functional data - sets of measurement sequences arising from a generating source of continuous nature - has become pervasive in many applications, across many fields of research. The commonly adopted methodology for exploring such data treats the observed units as functions, with continuous functional structure. This introduces a nigh boundless range of new modes of variability in shape and structure, unique to only this type of data. Thus, methodology encompassing the structural variability of functional data has risen to the attention in functional data literature. In this thesis, we approach the shape features of functional data from three different angles, utilizing functional notions of statistical depth as well as metrics, sensitive to variations in structure. Our first approach demonstrates the advantages of data-driven methodology, that allows for the expert to utilize their contextual knowledge of the data. Thus, we provide a consistent framework, through statistical depth, for applying this ad hoc understanding to the analysis. In our second approach, we take a more universal outlook towards shape-encompassing methodology and introduce a new functional depth definition that utilizes some very recently discovered general notions of shape outlyingness. The third approach takes a step back from the context of depth and focuses on the more general concept of shape-sensitive metrics in functional spaces. We, in particular, introduce and study the properties of a new family of integrated metrics, that provide a notion of the overall local likeness (based on any pilot metric) of two curves.",

keywords = "functional data, shape-sensitivity, statistical depth, functional depth, integrated metric, funktionaalinen data, muoto-herkkyys, tilastollinen syvyys, funktionaalinen syvyys, integroitu metriikka, functional data, shape-sensitivity, statistical depth, functional depth, integrated metric",

author = "Sami Helander",

year = "2022",

language = "English",

isbn = "978-952-64-0881-1",

series = "Aalto University publication series DOCTORAL THESES",

publisher = "Aalto University",

number = "102",

address = "Finland",

school = "Aalto University",

}

TY - BOOK

T1 - New approaches for analysing functional data - a focus on shape

AU - Helander, Sami

PY - 2022

Y1 - 2022

N2 - Functional data - sets of measurement sequences arising from a generating source of continuous nature - has become pervasive in many applications, across many fields of research. The commonly adopted methodology for exploring such data treats the observed units as functions, with continuous functional structure. This introduces a nigh boundless range of new modes of variability in shape and structure, unique to only this type of data. Thus, methodology encompassing the structural variability of functional data has risen to the attention in functional data literature. In this thesis, we approach the shape features of functional data from three different angles, utilizing functional notions of statistical depth as well as metrics, sensitive to variations in structure. Our first approach demonstrates the advantages of data-driven methodology, that allows for the expert to utilize their contextual knowledge of the data. Thus, we provide a consistent framework, through statistical depth, for applying this ad hoc understanding to the analysis. In our second approach, we take a more universal outlook towards shape-encompassing methodology and introduce a new functional depth definition that utilizes some very recently discovered general notions of shape outlyingness. The third approach takes a step back from the context of depth and focuses on the more general concept of shape-sensitive metrics in functional spaces. We, in particular, introduce and study the properties of a new family of integrated metrics, that provide a notion of the overall local likeness (based on any pilot metric) of two curves.

AB - Functional data - sets of measurement sequences arising from a generating source of continuous nature - has become pervasive in many applications, across many fields of research. The commonly adopted methodology for exploring such data treats the observed units as functions, with continuous functional structure. This introduces a nigh boundless range of new modes of variability in shape and structure, unique to only this type of data. Thus, methodology encompassing the structural variability of functional data has risen to the attention in functional data literature. In this thesis, we approach the shape features of functional data from three different angles, utilizing functional notions of statistical depth as well as metrics, sensitive to variations in structure. Our first approach demonstrates the advantages of data-driven methodology, that allows for the expert to utilize their contextual knowledge of the data. Thus, we provide a consistent framework, through statistical depth, for applying this ad hoc understanding to the analysis. In our second approach, we take a more universal outlook towards shape-encompassing methodology and introduce a new functional depth definition that utilizes some very recently discovered general notions of shape outlyingness. The third approach takes a step back from the context of depth and focuses on the more general concept of shape-sensitive metrics in functional spaces. We, in particular, introduce and study the properties of a new family of integrated metrics, that provide a notion of the overall local likeness (based on any pilot metric) of two curves.

KW - functional data

KW - shape-sensitivity

KW - statistical depth

KW - functional depth

KW - integrated metric

KW - funktionaalinen data

KW - muoto-herkkyys

KW - tilastollinen syvyys

KW - funktionaalinen syvyys

KW - integroitu metriikka

KW - functional data

KW - shape-sensitivity

KW - statistical depth

KW - functional depth

KW - integrated metric

M3 - Doctoral Thesis

SN - 978-952-64-0881-1

T3 - Aalto University publication series DOCTORAL THESES

PB - Aalto University

ER -

New approaches for analysing functional data - a focus on shape

Abstrakti

Tutkimusalat

Pääsy asiakirjaan

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Science-IT

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