Hotz, Thomas

[["dc.bibliographiccitation.firstpage","593"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","IEEE Transactions on Pattern Analysis and Machine Intelligence"],["dc.bibliographiccitation.lastpage","603"],["dc.bibliographiccitation.volume","32"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:46:05Z"],["dc.date.available","2017-09-07T11:46:05Z"],["dc.date.issued","2010"],["dc.description.abstract","We propose an intrinsic multifactorial model for data on Riemannian manifolds that typically occur in the statistical analysis of shape. Due to the lack of a linear structure, linear models cannot be defined in general; to date only one-way MANOVA is available. For a general multifactorial model, we assume that variation not explained by the model is concentrated near elements defining the effects. By determining the asymptotic distributions of respective sample covariances under parallel transport, we show that they can be compared by standard MANOVA. Often in applications manifolds are only implicitly given as quotients, where the bottom space parallel transport can be expressed through a differential equation. For Kendall's space of planar shapes, we provide an explicit solution. We illustrate our method by an intrinsic two-way MANOVA for a set of leaf shapes. While biologists can identify genotype effects by sight, we can detect height effects that are otherwise not identifiable."],["dc.identifier.doi","10.1109/TPAMI.2009.117"],["dc.identifier.gro","3142944"],["dc.identifier.isi","000274548800003"],["dc.identifier.pmid","20224117"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/404"],["dc.language.iso","en"],["dc.notes.intern","WoS Import 2017-03-10"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.relation.issn","0162-8828"],["dc.title","Intrinsic MANOVA for Riemannian Manifolds with an Application to Kendall's Space of Planar Shapes"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","177"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Annals of the Institute of Statistical Mathematics"],["dc.bibliographiccitation.lastpage","193"],["dc.bibliographiccitation.volume","67"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Huckemann, Stephan"],["dc.date.accessioned","2017-09-07T11:50:30Z"],["dc.date.available","2017-09-07T11:50:30Z"],["dc.date.issued","2015"],["dc.description.abstract","This paper gives a comprehensive treatment of local uniqueness, asymptotics and numerics for intrinsic sample means on the circle. It turns out that local uniqueness as well as rates of convergence are governed by the distribution near the antipode. If the distribution is locally less than uniform there, we have local uniqueness and asymptotic normality with a square-root rate. With increased proximity to the uniform distribution the rate can be arbitrarily slow, and in the limit, local uniqueness is lost. Further, we give general distributional conditions, e.g., unimodality, that ensure global uniqueness. Along the way, we discover that sample means can occur only at the vertices of a regular polygon which allows to compute intrinsic sample means in linear time from sorted data. This algorithm is finally applied in a simulation study demonstrating the dependence of the convergence rates on the behavior of the density at the antipode."],["dc.identifier.doi","10.1007/s10463-013-0444-7"],["dc.identifier.gro","3147630"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5093"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0020-3157"],["dc.title","Intrinsic means on the circle: uniqueness, locus and asymptotics"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","699"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Journal of Multivariate Analysis"],["dc.bibliographiccitation.lastpage","714"],["dc.bibliographiccitation.volume","100"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.date.accessioned","2017-09-07T11:50:32Z"],["dc.date.available","2017-09-07T11:50:32Z"],["dc.date.issued","2008"],["dc.identifier.doi","10.1016/j.jmva.2008.08.008"],["dc.identifier.gro","3147646"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5101"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Elsevier BV"],["dc.relation.issn","0047-259X"],["dc.title","Principal component geodesics for planar shape spaces"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","98"],["dc.bibliographiccitation.issue","1-2"],["dc.bibliographiccitation.journal","Journal of Mathematical Imaging and Vision"],["dc.bibliographiccitation.lastpage","106"],["dc.bibliographiccitation.volume","50"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.date.accessioned","2017-09-07T11:48:38Z"],["dc.date.available","2017-09-07T11:48:38Z"],["dc.date.issued","2013"],["dc.description.abstract","We survey some effects that singular strata may have in the positive curvature context of circles and shape spaces when conducting (semi-)intrinsic statistical analyses. Here, the analysis of data on a stratified space is based on statistical descriptors defined in a possibly different stratified space. E.g. in geodesic principal component analysis for shape spaces, shape data are described by generalized geodesics which naturally form a shape space of their own, different from the original one. In a general context, if the descriptors are obtained as generalized Fréchet means, under rather general circumstances, a strong law of large numbers is valid. If furthermore the descriptors are sufficiently well behaved, a classical central limit theorem can be adopted. One of the crucial conditions is that hitting of singular strata as well as of cut loci, if present, must be controlled. We review the statistical role of the cut locus of intrinsic means for circles as well as that of singular strata for shape spaces (occurring where the group action is degenerate) and conclude with an identification of potential research directions."],["dc.identifier.doi","10.1007/s10851-013-0462-3"],["dc.identifier.gro","3146940"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4719"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0924-9907"],["dc.title","On Means and Their Asymptotics: Circles and Shape Spaces"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","39"],["dc.bibliographiccitation.lastpage","43"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.editor","Gusnanto, A."],["dc.contributor.editor","Mardia, K. V."],["dc.contributor.editor","Fallaize, C. J."],["dc.contributor.editor","Voss, J."],["dc.date.accessioned","2017-09-07T11:47:59Z"],["dc.date.available","2017-09-07T11:47:59Z"],["dc.date.issued","2010"],["dc.identifier.gro","3146825"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4629"],["dc.language.iso","en"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Department of Statistics, University of Leeds"],["dc.publisher.place","Leeds"],["dc.relation.conference","The 29th Leeds Annual Statistical Research (LASR) Workshop"],["dc.relation.eventend","2010-07-08"],["dc.relation.eventlocation","Leeds"],["dc.relation.eventstart","2010-07-06"],["dc.relation.isbn","978-0-85316-293-3"],["dc.relation.ispartof","High-throughput Sequencing, Proteins and Statistics"],["dc.title","Geodesic and parallel models for leaf shape"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","2238"],["dc.bibliographiccitation.issue","6"],["dc.bibliographiccitation.journal","The Annals of Applied Probability"],["dc.bibliographiccitation.lastpage","2258"],["dc.bibliographiccitation.volume","23"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Le, Huiling"],["dc.contributor.author","Marron, J. S."],["dc.contributor.author","Mattingly, Jonathan C."],["dc.contributor.author","Miller, Ezra"],["dc.contributor.author","Nolen, James"],["dc.contributor.author","Owen, Megan"],["dc.contributor.author","Patrangenaru, Vic"],["dc.contributor.author","Skwerer, Sean"],["dc.date.accessioned","2017-09-07T11:50:34Z"],["dc.date.available","2017-09-07T11:50:34Z"],["dc.date.issued","2013"],["dc.identifier.doi","10.1214/12-aap899"],["dc.identifier.gro","3147638"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/5096"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","Institute of Mathematical Statistics"],["dc.relation.issn","1050-5164"],["dc.title","Sticky central limit theorems on open books"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["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","1507"],["dc.bibliographiccitation.issue","9"],["dc.bibliographiccitation.journal","IEEE Transactions on Pattern Analysis and Machine Intelligence"],["dc.bibliographiccitation.lastpage","1519"],["dc.bibliographiccitation.volume","30"],["dc.contributor.author","Huckemann, Stephan"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.date.accessioned","2017-09-07T11:48:14Z"],["dc.date.available","2017-09-07T11:48:14Z"],["dc.date.issued","2008"],["dc.description.abstract","Quadratic differentials naturally define analytic orientation fields on planar surfaces. We propose to model orientation fields of fingerprints by specifying quadratic differentials. Models for all fingerprint classes such as arches, loops, and whorls are laid out. These models are parameterized by a few geometrically interpretable parameters that are invariant under euclidean motions. We demonstrate their ability in adapting to given observed orientation fields, and we compare them to existing models using the fingerprint images of the NIST Special Database 4. We also illustrate that these models allow for extrapolation into unobserved regions. This goes beyond the scope of earlier models for the orientation field as those are restricted to the observed planar fingerprint region. Within the framework of quadratic differentials, we are able to analytically verify Penrose's formula for the singularities on a palm [19]. Potential applications of these models are the use of their parameters as indexes of large fingerprint databases, as well as the definition of intrinsic coordinates for single fingerprint images."],["dc.identifier.doi","10.1109/TPAMI.2007.70826"],["dc.identifier.gro","3143245"],["dc.identifier.isi","000257504400001"],["dc.identifier.pmid","18617711"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/738"],["dc.notes.intern","WoS Import 2017-03-10"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.publisher","Ieee Computer Soc"],["dc.relation.issn","0162-8828"],["dc.title","Global models for the orientation field of fingerprints: An approach based on quadratic differentials"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","2255"],["dc.bibliographiccitation.issue","16"],["dc.bibliographiccitation.journal","Bioinformatics"],["dc.bibliographiccitation.lastpage","2262"],["dc.bibliographiccitation.volume","30"],["dc.contributor.author","Futschik, Andreas"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Munk, Axel"],["dc.contributor.author","Sieling, Hannes"],["dc.date.accessioned","2017-09-07T11:45:36Z"],["dc.date.available","2017-09-07T11:45:36Z"],["dc.date.issued","2014"],["dc.description.abstract","Motivation: DNA segmentation, i.e. the partitioning of DNA in compositionally homogeneous segments, is a basic task in bioinformatics. Different algorithms have been proposed for various partitioning criteria such as Guanine/Cytosine (GC) content, local ancestry in population genetics or copy number variation. A critical component of any such method is the choice of an appropriate number of segments. Some methods use model selection criteria and do not provide a suitable error control. Other methods that are based on simulating a statistic under a null model provide suitable error control only if the correct null model is chosen. Results: Here, we focus on partitioning with respect to GC content and propose a new approach that provides statistical error control: as in statistical hypothesis testing, it guarantees with a user-specified probability 1 - alpha that the number of identified segments does not exceed the number of actually present segments. The method is based on a statistical multiscale criterion, rendering this as a segmentation method that searches segments of any length (on all scales) simultaneously. It is also accurate in localizing segments: under benchmark scenarios, our approach leads to a segmentation that is more accurate than the approaches discussed in the comparative review of Elhaik et al. In our real data examples, we find segments that often correspond well to features taken from standard University of California at Santa Cruz (UCSC) genome annotation tracks."],["dc.identifier.doi","10.1093/bioinformatics/btu180"],["dc.identifier.gro","3142071"],["dc.identifier.isi","000342746000003"],["dc.identifier.pmid","24753487"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4222"],["dc.language.iso","en"],["dc.notes.intern","WoS Import 2017-03-10"],["dc.notes.status","final"],["dc.notes.submitter","PUB_WoS_Import"],["dc.relation.eissn","1460-2059"],["dc.relation.issn","1367-4803"],["dc.title","Multiscale DNA partitioning: statistical evidence for segments"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.subtype","original"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","11"],["dc.bibliographiccitation.lastpage","20"],["dc.contributor.author","Hotz, Thomas"],["dc.contributor.author","Gottschlich, Carsten"],["dc.contributor.author","Lorenz, Robert"],["dc.contributor.author","Bernhardt, Stefanie"],["dc.contributor.author","Hantschel, Michael"],["dc.contributor.author","Munk, Axel"],["dc.contributor.editor","Brömme, Arslan"],["dc.contributor.editor","Busch, Christoph"],["dc.date.accessioned","2018-02-05T09:43:18Z"],["dc.date.available","2018-02-05T09:43:18Z"],["dc.date.issued","2011"],["dc.description.abstract","We study the effect of growth on the fingerprints of adolescents, based on which we suggest a simple method to adjust for growth when trying to retrieve an adolescent's fingerprint in a database years later. Here, we focus on the statistical analyses used to determine how fingerprints grow: Procrustes analysis allows us to establish that fingerprints grow isotropically, an appropriate mixed effects model shows that fingerprints essentially grow proportionally to body height. The resulting growth model is validated by showing that it brings points of interest as close as if both fingerprints were taken from an adult. Further details on this study, in particular results when applying our growth model in verification and identification tests, can be found in C. Gottschlich, T. Hotz, R. Lorenz, S. Bernhardt, M. Hantschel and A. Munk: Modeling the Growth of Fingerprints Improves Matching for Adolescents, IEEE Transations on Information Forensics and Security, 2011"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/11949"],["dc.language.iso","en"],["dc.notes.status","fcwi-famis"],["dc.publisher","Gesellschaft für Informatik"],["dc.publisher.place","Bonn"],["dc.relation.eventend","09.09.2011"],["dc.relation.eventlocation","Darmstadt"],["dc.relation.eventstart","08.09.2011"],["dc.relation.ispartof","BIOSIG 2011 Proceedings - international conference of the biometrics special interest group"],["dc.title","Statistical analyses of fingerprint growth"],["dc.type","conference_paper"],["dc.type.internalPublication","unknown"],["dspace.entity.type","Publication"]]