3,378 research outputs found
An MBO scheme for clustering and semi-supervised clustering of signed networks
We introduce a principled method for the signed clustering problem, where the goal is to partition a weighted undirected graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are
mostly negative. Our method relies on a graph-based diffuse interface model formulation utilizing the GinzburgâLandau functional, based on an adaptation of the classic numerical MerrimanâBenceâOsher (MBO) scheme for minimizing such graph-based functionals. The proposed objective function aims to minimize the total weight of inter-cluster positively-weighted edges, while maximizing the total weight of the inter-cluster negatively-weighted edges. Our method scales to large sparse networks, and can be easily adjusted to incorporate labelled data information, as is often the case in the context of semisupervised learning. We tested our method on a number of both synthetic stochastic block models and real-world data sets (including financial correlation matrices), and obtained promising results that compare favourably against a number of state-of-the-art approaches from the recent literature
Content-based Propagation of User Markings for Interactive Segmentation of Patterned Images
Efficient and easy segmentation of images and volumes is of great practical
importance. Segmentation problems that motivate our approach originate from
microscopy imaging commonly used in materials science, medicine, and biology.
We formulate image segmentation as a probabilistic pixel classification
problem, and we apply segmentation as a step towards characterising image
content. Our method allows the user to define structures of interest by
interactively marking a subset of pixels. Thanks to the real-time feedback, the
user can place new markings strategically, depending on the current outcome.
The final pixel classification may be obtained from a very modest user input.
An important ingredient of our method is a graph that encodes image content.
This graph is built in an unsupervised manner during initialisation and is
based on clustering of image features. Since we combine a limited amount of
user-labelled data with the clustering information obtained from the unlabelled
parts of the image, our method fits in the general framework of semi-supervised
learning. We demonstrate how this can be a very efficient approach to
segmentation through pixel classification.Comment: 9 pages, 7 figures, PDFLaTe
Emerging Developments in Interfaces and Free Boundaries
The field of the mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a well established and flourishing area of research. This workshop focused on recent developments and emerging new themes. By bringing together experts in these fields we achieved progress in open questions and developed novel research directions in mathematics related to interfaces and free boundaries. This interdisciplinary workshop brought together researchers from distinct mathematical fields such as analysis, computation, optimisation and modelling to discuss emerging challenges
Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates
The study of cerebral anatomy in developing neonates is of great importance for
the understanding of brain development during the early period of life. This
dissertation therefore focuses on three challenges in the modelling of cerebral
anatomy in neonates during brain development. The methods that have been
developed all use Magnetic Resonance Images (MRI) as source data.
To facilitate study of vascular development in the neonatal period, a set of image
analysis algorithms are developed to automatically extract and model cerebral
vessel trees. The whole process consists of cerebral vessel tracking from
automatically placed seed points, vessel tree generation, and vasculature
registration and matching. These algorithms have been tested on clinical Time-of-
Flight (TOF) MR angiographic datasets.
To facilitate study of the neonatal cortex a complete cerebral cortex segmentation
and reconstruction pipeline has been developed. Segmentation of the neonatal
cortex is not effectively done by existing algorithms designed for the adult brain
because the contrast between grey and white matter is reversed. This causes pixels
containing tissue mixtures to be incorrectly labelled by conventional methods. The
neonatal cortical segmentation method that has been developed is based on a novel
expectation-maximization (EM) method with explicit correction for mislabelled
partial volume voxels. Based on the resulting cortical segmentation, an implicit
surface evolution technique is adopted for the reconstruction of the cortex in
neonates. The performance of the method is investigated by performing a detailed
landmark study.
To facilitate study of cortical development, a cortical surface registration algorithm
for aligning the cortical surface is developed. The method first inflates extracted
cortical surfaces and then performs a non-rigid surface registration using free-form
deformations (FFDs) to remove residual alignment. Validation experiments using
data labelled by an expert observer demonstrate that the method can capture local
changes and follow the growth of specific sulcus
Understanding the spreading power of all nodes in a network: a continuous-time perspective
Centrality measures such as the degree, k-shell, or eigenvalue centrality can
identify a network's most influential nodes, but are rarely usefully accurate
in quantifying the spreading power of the vast majority of nodes which are not
highly influential. The spreading power of all network nodes is better
explained by considering, from a continuous-time epidemiological perspective,
the distribution of the force of infection each node generates. The resulting
metric, the \textit{expected force}, accurately quantifies node spreading power
under all primary epidemiological models across a wide range of archetypical
human contact networks. When node power is low, influence is a function of
neighbor degree. As power increases, a node's own degree becomes more
important. The strength of this relationship is modulated by network structure,
being more pronounced in narrow, dense networks typical of social networking
and weakening in broader, looser association networks such as the Internet. The
expected force can be computed independently for individual nodes, making it
applicable for networks whose adjacency matrix is dynamic, not well specified,
or overwhelmingly large
AutoSOME: a clustering method for identifying gene expression modules without prior knowledge of cluster number
<p>Abstract</p> <p>Background</p> <p>Clustering the information content of large high-dimensional gene expression datasets has widespread application in "omics" biology. Unfortunately, the underlying structure of these natural datasets is often fuzzy, and the computational identification of data clusters generally requires knowledge about cluster number and geometry.</p> <p>Results</p> <p>We integrated strategies from machine learning, cartography, and graph theory into a new informatics method for automatically clustering self-organizing map ensembles of high-dimensional data. Our new method, called AutoSOME, readily identifies discrete and fuzzy data clusters without prior knowledge of cluster number or structure in diverse datasets including whole genome microarray data. Visualization of AutoSOME output using network diagrams and differential heat maps reveals unexpected variation among well-characterized cancer cell lines. Co-expression analysis of data from human embryonic and induced pluripotent stem cells using AutoSOME identifies >3400 up-regulated genes associated with pluripotency, and indicates that a recently identified protein-protein interaction network characterizing pluripotency was underestimated by a factor of four.</p> <p>Conclusions</p> <p>By effectively extracting important information from high-dimensional microarray data without prior knowledge or the need for data filtration, AutoSOME can yield systems-level insights from whole genome microarray expression studies. Due to its generality, this new method should also have practical utility for a variety of data-intensive applications, including the results of deep sequencing experiments. AutoSOME is available for download at <url>http://jimcooperlab.mcdb.ucsb.edu/autosome</url>.</p
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