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| 13. |
- Strandberg, Johan, 1981-
(författare)
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Non-parametric methods for functional data
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we develop and study non-parametric methods within three major areas of functional data analysis: testing, clustering and prediction. The thesis consists of an introduction to the field, a presentation and discussion of the three areas, and six papers.In Paper I, we develop a procedure for testing for group differences in functional data. In case of significant group differences, the test procedure identifies which of the groups that significantly differ, and also the parts of the domain they do so, while controlling the type I error of falsely rejecting the null hypothesis. In Paper II, the methodology introduced in Paper I is applied to knee kinematic curves from a one-leg hop for distance to test for differences within and between three groups of individuals (with and without knee deficits). It was found that two of the groups differed in their knee kinematics. We also found that the individual kinematic patterns differed between the two legs in one of the groups. In Paper III, we test for group differences in three groups with respect to joint kinematics from a vertical one-leg hop using a novel method that allows accounting for multiple joints at the same time. The aim of Paper III, as one of few within the field of biomechanics, is to illustrate how different choices prior to the analysis can result in different contrasting conclusions. Specifically, we show how the conclusions depend on the choice of type of movement curve, the choice of leg for between-group comparisons and the included joints.In Paper IV, we present a new non-parametric clustering method for dependent functional data, the double clustering bagging Voronoi method. The objective of the method is to identify latent group structures that slowly vary over domain and give rise to different frequency patterns of functional data object types. The method uses a bagging strategy based on random Voronoi tessellations in which local representatives are formed and clustered. Combined with the clustering method, we also propose a multiresolution approach which allows identification of latent structures at different scales. A simulated dataset is used to illustrate the method's potential in finding stable clusters at different scales. The method is also applied to varved lake sediment data with the aim of reconstructing the climate over the past 6000 years, at different resolutions. In Paper V, we expand and modify the bagging strategy used in Paper IV, by considering different methods of generating the tessellations and clustering the local representatives of the tessellations. We propose new methods for clustering dependent categorical data (e.g., labelled functional data) along a one-dimensional domain, which we also compare in a simulation study. In Paper VI, two kriging approaches to predict spatial functional processes are compared, namely functional kriging and spatio-temporal kriging. A simulation study is conducted to compare their prediction performance and computational times. The overall results show that prediction performance is about the same for stationary spatio-temporal processes while functional kriging works better for non-stationary spatio-temporal processes. Furthermore, the computational time for (ordinary) kriging for functional data, was considerably lower than spatio-temporal kriging. Conditions are also formulated under which it is proved that the two functional kriging methods: ordinary kriging for functional data and pointwise functional kriging coincide.
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| 15. |
- Vidman, Linda, 1989-
(författare)
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cancer subtype identification using cluster analysis on high-dimensional omics data
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Identification and prediction of cancer subtypes are important parts in the development towards personalized medicine. By tailoring treatments, it is possible to decrease unnecessary suffering and reduce costs. Since the introduction of next generation sequencing techniques, the amount of data available for medical research has increased rapidly. The high dimensional omics data produced by various techniques requires statistical methods to transform data into information and knowledge.All papers in this thesis are related to distinguishing of disease subtypes in patients with cancer using omics data. The high dimension and the complexity of sequencing data from tumor samples makes it necessary to pre—process the data. We carry out comparisons of feature selection methods and clustering methods used for identification of cancer subtypes. In addition, we evaluate the effect that certain characteristics of the data have on the ability to identify cancer subtypes. The results show that no method outperforms the others in all cases and the relative ranking of methods is very dependent on the data. We also show that the benefit of receiving a more homogeneous data by analyzing genders separately can outweigh the possible drawbacks caused by smaller sample sizes. One of the major challenges when dealing with omics data from tumor samples is that the patients are generally a very heterogeneous group. Factors that lead to heterogeneity include age, gender, ethnicity and stage of disease. How big the effect size is for each of these factors might affect the ability to identify the subgroups of interest.In omics data, the feature space is often large and how many of the features that are informative for the factors of interest will also affect the complexity of the problem. We present a novel clustering approach that can identify different clusters in different subsets of the feature space, which is applied on methylation data to create new potential biomarkers. It is shown that by combining clinical data with methylation data for patients with clear cell renal carcinoma, it is possible to improve the currently used prediction model for disease progression. Using unsupervised clustering techniques, we identify three molecular subtypes of prostate cancer bone metastases based on gene expression profiles. The robustness of the identified subtypes is confirmed by applying several clustering algorithms with very similar results.
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| 16. |
- Wang, Jianfeng, 1984-
(författare)
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Enhanced block sparse signal recovery and bayesian hierarchical models with applications
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is carried out within two projects ‘Statistical modelling and intelligentdata sampling in Magnetic resonance imaging (MRI) and positron-emission tomography(PET) measurements for cancer therapy assessment’ and ‘WindCoE -Nordic Wind Energy Center’ during my PhD study. It mainly focuses on applicationsof Bayesian hierarchical models (BHMs) and theoretical developments ofcompressive sensing (CS). Under the first project, Paper I improves the quantityestimation of MRI parametric imaging by utilizing inherent dependent structure inthe image through BHMs; Paper III constructs a theoretically unbiased and asymptoticallynormal estimator of sparsity of a sparsified MR image by using a BHM;Paper IV extends block sparsity estimation from real-valued signal recovery tocomplex-valued signal recovery. It also demonstrates the importance of accuratelyestimating the block sparsity through a sensitivity analysis; Paper V proposes anew measure, i.e. q-ratio block constrained minimal singular value, of measurementmatrix for block sparse signal recovery. An algorithm for computing thisnew measure is also presented. In the second project, Paper II estimates the uncertaintyof Weather Research and Forecasting (WRF) model’s daily-mean 2-metertemperature in a cold region by using a BHM. It is a computationally cheaper andfaster alternative to traditional ensemble approach. In summary, this thesis makessignificant contributions in improving and optimizing the estimation proceduresof parameters of interest in MRI and WRF in practice, and developing the novelestimators and measure under the framework of CS in theory.
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