There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

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Data clustering: a review

We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging.

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Normalized cuts and image segmentation

We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images and found results very encouraging.

/pdf/normalized-cuts-and-image-segmentation-1q390dk21h.pdf

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Previous work has demonstrated that Fourier imaging data will often possess multifold linear shift-invariant autoregression relationships. This autoregressive structure is useful because it enables missing data samples to be imputed as a linear combination of neighboring samples, and also implies that certain structured matrices formed from the data will have low rank characteristics. The latter observation has enabled a range of powerful structured low-rank matrix recovery techniques for reconstructing sparsely-sampled and/or low-quality data in Fourier imaging modalities like magnetic resonance imaging. In this work, we demonstrate theoretically and empirically that similar modeling principles also apply to sinogram data, and demonstrate how this can be leveraged to restore missing information from real high-resolution X-ray imaging data from an integrated circuit.

Low-Rank Modeling of Local Sinogram Neighborhoods with Tomographic Applications

Neural activity in the brain produces weak dynamic electromagnetic fields that can be measured by an array of sensors Using a spatiotemporal modeling framework, a novel approach to localization of multiple neural sources has been developed This approach is based on the MUSIC algorithm originally developed for estimating the direction of arrival of signals impinging on a sensor array The authors present applications of this technique to magnetic field measurements of a phantom and of a human evoked somatosensory response The results of the somatosensory localization are mapped onto the brain anatomy obtained from magnetic resonance images >

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Electromagnetic imaging of dynamic brain activity

Optimized MAP Reconstruction of H2-weighted Fourier Rebinned TOF PET

Obesity is a global health problem, particularly in the U.S. where one third of adults are obese. A reliable and accurate method of quantifying obesity is necessary. Visceral adipose tissue (VAT) and subcutaneous adipose tissue (SAT) are two measures of obesity that reflect different associated health risks, but accurate measurements in humans or rodent models are difficult. In this paper we present an automatic, registration-based segmentation method for mouse adiposity studies using microCT images. We co-register the subject CT image and a mouse CT atlas. Our method is based on surface matching of the microCT image and an atlas. Surface-based elastic volume warping is used to match the internal anatomy. We acquired a whole body scan of a C57BL6/J mouse injected with contrast agent using microCT and created a whole body mouse atlas by manually delineate the boundaries of the mouse and major organs. For method verification we scanned a C57BL6/J mouse from the base of the skull to the distal tibia. We registered the obtained mouse CT image to our atlas. Preliminary results show that we can warp the atlas image to match the posture and shape of the subject CT image, which has significant differences from the atlas. We plan to use this software tool in longitudinal obesity studies using mouse models.

A registration-based segmentation method with application to adiposity analysis of mice microCT images

The human brain exhibits dynamic interactions among brain regions when responding to stimuli and executing tasks, which can be recorded using functional magnetic resonance imaging (fMRI). Functional MRI signals collected in response to specific tasks consist of a combination of task-related and spontaneous (task-independent) activity. By exploiting the highly structured spatiotemporal patterns of resting state networks, this paper presents a matched-filter approach to decomposing fMRI signals into task and resting-state components. To perform the decomposition, we first use a temporal alignment procedure that is a windowed version of the brainsync transform to synchronize a resting template to the brain’s response to tasks. The resulting ‘matched filter’ removes the components of the fMRI signal that can be described by resting connectivity, leaving the portion of brain activity directly related to tasks. We present a closed-form expression for the windowed synchronization transform that is used by the matched filter. We demonstrate performance of this procedure in application to motor task and language task fMRI data. We show qualitatively and quantitatively that by removing the resting activity, we are able to identify task activated regions in the brain more clearly. Additionally, we show improved prediction accuracy in multivariate pattern analysis when using the matched filtered fMRI data.

/pdf/a-matched-filter-decomposition-of-fmri-into-resting-and-task-52kfb4j7u0.pdf

Richard M. Leahy

Papers

Low-Rank Modeling of Local Sinogram Neighborhoods with Tomographic Applications

Electromagnetic imaging of dynamic brain activity

Optimized MAP Reconstruction of H2-weighted Fourier Rebinned TOF PET

A registration-based segmentation method with application to adiposity analysis of mice microCT images

A Matched Filter Decomposition of fMRI into Resting and Task Components.