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Title:

Cluster analysis of the signal curves in perfusion DCE-MRI datasets

Description:

Pathological studies show that tumors consist of different sub-regions with more homogeneous vascular properties during their growth. In addition, destroying tumor's blood supply is the target of most cancer therapies. Finding the sub-regions in the tissue of interest with similar perfusion patterns provides us with valuable information about ti...

Pathological studies show that tumors consist of different sub-regions with more homogeneous vascular properties during their growth. In addition, destroying tumor's blood supply is the target of most cancer therapies. Finding the sub-regions in the tissue of interest with similar perfusion patterns provides us with valuable information about tissue structure and angiogenesis. This information on cancer therapy, for example, can be used in monitoring the response of the cancer treatment to the drug. Cluster analysis of perfusion curves assays to find sub-regions with a similar perfusion pattern. The present work focuses on the cluster analysis of perfusion curves, measured by dynamic contrast enhanced magnetic resonance imaging (DCE-MRI). The study, besides searching for the proper clustering method, follows two other major topics, the choice of an appropriate similarity measure, and determining the number of clusters. These three subjects are connected to each other in such a way that success in one direction will help solving the other problems. This work introduces a new similarity measure, parallelism measure (PM), for comparing the parallelism in the washout phase of the signal curves. Most of the previous works used the Euclidean distance as the measure of dissimilarity. However, the Euclidean distance does not take the patterns of the signal curves into account and therefore for comparing the signal curves is not sufficient. To combine the advantages of both measures a two-steps clustering is developed. The two-steps clustering uses two different similarity measures, the introduced PM measure and Euclidean distance in two consecutive steps. The results of two-steps clustering are compared with the results of other clustering methods. The two-steps clustering besides good performance has some other advantages. The granularity and the number of clusters are controlled by thresholds defined by considering the noise in signal curves. The method is easy to implement and is robust against noise. The focus of the work is mainly the cluster analysis of breast tumors in DCE-MRI datasets. The possibility to adopt the method for liver datasets is studied as well. Minimize

Publisher:

Ludwig-Maximilians-Universität München

Year of Publication:

2012-10-18

Document Type:

Dissertation ; NonPeerReviewed

Subjects:

Fakultät für Mathematik ; Informatik und Statistik

Fakultät für Mathematik ; Informatik und Statistik Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

Relations:

http://edoc.ub.uni-muenchen.de/15042/

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Title:

A comparison of Gap statistic definitions with and without logarithm function

Author:

Description:

The Gap statistic is a standard method for determining the number of clusters in a set of data. The Gap statistic standardizes the graph of $\log(W_{k})$, where $W_{k}$ is the within-cluster dispersion, by comparing it to its expectation under an appropriate null reference distribution of the data. We suggest to use $W_{k}$ instead of $\log(W_{k...

The Gap statistic is a standard method for determining the number of clusters in a set of data. The Gap statistic standardizes the graph of $\log(W_{k})$, where $W_{k}$ is the within-cluster dispersion, by comparing it to its expectation under an appropriate null reference distribution of the data. We suggest to use $W_{k}$ instead of $\log(W_{k})$, and to compare it to the expectation of $W_{k}$ under a null reference distribution. In fact, whenever a number fulfills the original Gap statistic inequality, this number also fulfills the inequality of a Gap statistic using $W_{k}$, but not \textit{vice versa}. The two definitions of the Gap function are evaluated on several simulated data sets and on a real data of DCE-MR images. Minimize

Year of Publication:

2011-03-24

Document Type:

text

Subjects:

Statistics - Methodology ; Computer Science - Computer Vision and Pattern Recognition

Statistics - Methodology ; Computer Science - Computer Vision and Pattern Recognition Minimize

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Title:

A comparison of Gap statistic definitions with and without logarithm function

Author:

Description:

The Gap statistic is a standard method for determining the number of clusters in a set of data. The Gap statistic standardizes the graph of $\log(W_{k})$, where $W_{k}$ is the within-cluster dispersion, by comparing it to its expectation under an appropriate null reference distribution of the data. We suggest to use $W_{k}$ instead of $\log(W_{k...

The Gap statistic is a standard method for determining the number of clusters in a set of data. The Gap statistic standardizes the graph of $\log(W_{k})$, where $W_{k}$ is the within-cluster dispersion, by comparing it to its expectation under an appropriate null reference distribution of the data. We suggest to use $W_{k}$ instead of $\log(W_{k})$, and to compare it to the expectation of $W_{k}$ under a null reference distribution. In fact, whenever a number fulfills the original Gap statistic inequality, this number also fulfills the inequality of a Gap statistic using $W_{k}$, but not \textit{vice versa}. The two definitions of the Gap function are evaluated on several simulated data set and on a real data of DCE-MR images. Minimize

Year of Publication:

2010-12-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Language:

eng

Subjects:

Technische Reports ; ddc:510

Technische Reports ; ddc:510 Minimize

Relations:

http://epub.ub.uni-muenchen.de/11920/1/mojgan_englmeier_schmid.pdf ; Mohajer, Mojgan und Englmeier, Karl-Hans und Schmid, Volker J. (2010): A comparison of Gap statistic definitions with and without logarithm function. Department of Statistics: Technical Reports, Nr. 96

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