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.

/pdf/data-clustering-a-review-4c452f5cab.pdf

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.

/pdf/normalized-cuts-and-image-segmentation-2ru3ikxuj5.pdf

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

Localization error bounds are presented for both electroencephalograms (EEGs) and magnetoencephalograms (MEGs) as graphical error contours for a 37-sensor arrangement. Both one and two dipole cases were examined for all possible dipole orientations and locations within a head quadrant. The results show a strong dependence on absolute dipole location and orientation. The results also show that fusion of the EEG and MEG measurements into a combined model reduces the lower bound. A Monte Carlo simulation was performed to check the tightness of the bounds for a selected case. The simple head model, the white and relatively low power noise, and the few relatively strong dipoles were all selected in this study as optimistic conditions to establish possibly fundamental resolution limits for any localization effort. >

Error bounds for MEG and EEG source localization

A technique for processing of data from time-of-flight (TOF) PET scanners. The size of TOF PET data may be reduced without significant loss of information through a process called rebinning. The rebinning may use the Fourier transform properties of the measured PET data, taken with respect to the time-of-flight variable, to perform data reduction. Through this rebinning process, TOF PET data may be converted to any of the following reduced representations: 2D TOF PET data, 3D non-TOF PET data, and 2D non-TOF PET data. Mappings may be exact or approximate. Approximate mappings may not require a Fourier transform in the axial direction which may have advantages when used with PET scanners of limited axial extent. Once TOF PET data is reduced in size using this rebinning, PET images may be reconstructed with hardware and/or software that is substantially less complex and that may run substantially faster in comparison to reconstruction from the original non-rebinned data.

Exact and approximate rebinning of time-of-flight pet positron emission tomography data

Three-dimensional reconstruction studies were performed using simulated data from an electronically collimated camera for single photon emitters. An adaptation of the algebraic reconstruction technique (ART) was used to reconstruct a spherical phantom using pin-hole images from multiple angular views. Configurations corresponding to several geometrical arrangements of the first detector of the electronically collimated system were compared, and it was concluded that the configuration where at least two planes of the first detector were arranged in an orthogonal geometry was needed to produce uniform resolution.

Computer Simulated Studies of Tomographic Reconstruction with an Electronically Collimated Camera for SPECT

Canonical Granger causality between regions of interest.

Characterizing functional brain connectivity using resting fMRI is challenging due to the relatively small BOLD signal contrast and low SNR. Gaussian filtering tends to undermine the individual differences detected by analysis of BOLD signal by smoothing signals across boundaries of different functional areas. Temporal non-local means (tNLM) filtering denoises fMRI data while preserving spatial structures but the kernel and parameters for tNLM filter need to be chosen carefully in order to achieve optimal results. Global PDF-based tNLM filtering (GPDF) is a new, data-dependent optimized kernel function for tNLM filtering which enables us to perform global filtering with improved noise reduction effects without blurring adjacent functional regions.

Richard M. Leahy

Papers

Error bounds for MEG and EEG source localization

Exact and approximate rebinning of time-of-flight pet positron emission tomography data

Computer Simulated Studies of Tomographic Reconstruction with an Electronically Collimated Camera for SPECT

Canonical Granger causality between regions of interest.

Global PDF-based temporal non-local means filtering reveals individual differences in brain connectivity