Huckemann, Stephan F.

[["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.journal","Statistica Sinica"],["dc.bibliographiccitation.lastpage","100"],["dc.bibliographiccitation.volume","20"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2019-07-10T08:13:39Z"],["dc.date.available","2019-07-10T08:13:39Z"],["dc.date.issued","2010"],["dc.description.abstract","In this paper, we illustrate a new approach for applying classical statistical methods to multivariate non-linear data. In two examples occurring in the statistical study of shape of three dimensional geometrical objects, we illustrate that the current methods of PCA by linear Euclidean approximation are unsuitable if such data in non-linear spaces fall into regions of high curvature, or if they have a large spread. In the following we give an overview of the background of relevant previous work, and an introduction to the building blocks of our work."],["dc.identifier.fs","582259"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/7238"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/61303"],["dc.language.iso","en"],["dc.notes.intern","Merged from goescholar"],["dc.relation.orgunit","Fakultät für Mathematik und Informatik"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.subject.ddc","510"],["dc.title","Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric lie group actions"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","84"],["dc.bibliographiccitation.journal","Statistica Sinica"],["dc.bibliographiccitation.lastpage","100"],["dc.bibliographiccitation.volume","20"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:48:02Z"],["dc.date.available","2017-09-07T11:48:02Z"],["dc.date.issued","2010"],["dc.description.abstract","A general framework is laid out for principal component analysis (PCA) on quotient spaces that result from an isometric Lie group action on a complete Riemannian manifold. If the quotient is a manifold, geodesics on the quotient can be lifted to horizontal geodesics on the original manifold. Thus, PCA on a manifold quotient can be pulled back to the original manifold. In general, however, the quotient space may no longer carry a manifold structure. Still, horizontal geodesics can be well-defined in the general case. This allows for the concept of generalized geodesics and orthogonal projection on the quotient space as the key ingredients for PCA. Generalizing a result of Bhattacharya and Patrangenaru (2003), geodesic scores can be defined outside a null set. Building on that, an algorithmic method to perform PCA on quotient spaces based on generalized geodesics is developed. As a typical example where non-manifold quotients appear, this framework is applied to Kendall’s shape spaces. In fact, this work has been motivated by an application occurring in forest biometry where the current method of Euclidean linear approximation is unsuitable for performing PCA. This is illustrated by a data example of individual tree stems whose Kendall shapes fall into regions of high curvature of shape space: PCs obtained by Euclidean approximation fail to reflect between-data distances and thus cannot correctly explain data variation. Similarly, for a classical archeological data set with a large spread in shape space, geodesic PCA allows new insights that have not been available under PCA by Euclidean approximation. We conclude by reporting challenges, outlooks, and possible perspectives of intrinsic shape analysis."],["dc.identifier.fs","582260"],["dc.identifier.gro","3146828"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/7496"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4632"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.rights.access","openAccess"],["dc.subject","Extrinsic mean; forest biometry; geodesics; intrinsic mean; Lie group actions; non-linear multivariate statistics; orbifolds; orbit spaces; principal component analysis; Riemannian manifolds; shape analysis"],["dc.subject.ddc","510"],["dc.title","Rejoinder - Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric lie group actions"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.journal","Journal of Mathematical Biology"],["dc.contributor.author","Düring, Bertram"],["dc.contributor.author","Gottschlich, Carsten"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Kreusser, Lisa Maria"],["dc.contributor.author","Schönlieb, Carola-Bibiane"],["dc.date.accessioned","2019-07-09T11:51:04Z"],["dc.date.available","2019-07-09T11:51:04Z"],["dc.date.issued","2019"],["dc.description.abstract","Evidence suggests that both the interaction of so-called Merkel cells and the epidermal stress distribution play an important role in the formation of fingerprint patterns during pregnancy. To model the formation of fingerprint patterns in a biologically meaningful way these patterns have to become stationary. For the creation of synthetic fingerprints it is also very desirable that rescaling the model parameters leads to rescaled distances between the stationary fingerprint ridges. Based on these observations, as well as the model introduced by Kücken and Champod we propose a new model for the formation of fingerprint patterns during pregnancy. In this anisotropic interaction model the interaction forces not only depend on the distance vector between the cells and the model parameters, but additionally on an underlying tensor field, representing a stress field. This dependence on the tensor field leads to complex, anisotropic patterns. We study the resulting stationary patterns both analytically and numerically. In particular, we show that fingerprint patterns can be modeled as stationary solutions by choosing the underlying tensor field appropriately."],["dc.identifier.doi","10.1007/s00285-019-01338-3"],["dc.identifier.pmid","30830268"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/16041"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/59868"],["dc.language.iso","en"],["dc.notes.intern","Merged from goescholar"],["dc.relation.issn","1432-1416"],["dc.rights","CC BY 4.0"],["dc.rights.uri","https://creativecommons.org/licenses/by/4.0"],["dc.subject.ddc","510"],["dc.title","An anisotropic interaction model for simulating fingerprints"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]