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

Chronic anemia is commonly observed in patients with hemoglobinopathies, mainly represented by disorders of altered hemoglobin (Hb) structure (sickle cell disease, SCD) and impaired Hb synthesis (e.g. thalassemia syndromes, non-SCD anemia). Both hemoglobinopathies have been associated with white matter (WM) alterations. Novel structural MRI research in our laboratory demonstrated that WM volume was diffusely lower in deep, watershed areas proportional to anemia severity. Furthermore, diffusion tensor imaging analysis has provided evidence that WM microstructure is disrupted proportionally to Hb level and oxygen saturation. SCD patients have been widely studied and demonstrate lower fractional anisotropy (FA) in the corticospinal tract and cerebellum across the internal capsule and corpus callosum. In the present study, we compared 19 SCD and 15 non-SCD anemia patients with a wide range of Hb values allowing the characterization of the effects of chronic anemia in isolation of sickle Hb. We performed a tensor analysis to quantify FA changes in WM connectivity in chronic anemic patients. We calculated the volumetric mean of FA along the pathway of tracks connecting two regions of interest defined by BrainSuite's BCI-DNI atlas. In general, we found lower FA values in anemic patients; indicating the loss of coherence in the main diffusion direction that potentially indicates WM injury. We saw a positive correlation between FA and hemoglobin in these same regions, suggesting that decreased WM microstructural integrity FA is highly driven by chronic hypoxia. The only connection that did not follow this pattern was the connectivity within the left middle-inferior temporal gyrus. Interestingly, more reductions in FA were observed in non-SCD patients (mainly along with intrahemispheric WM bundles and watershed areas) than the SCD patients (mainly interhemispheric).

Chronic anemia: The effects on the connectivity of white matter

https://doi.org/10.1016/j.neuroimage.2023.119944

Identification of overlapping and interacting networks reveals intrinsic spatiotemporal organization of the human brain

There has been a concerted effort by the neuroimaging community to establish standards for computational methods for data analysis that promote reproducibility and portability. In particular, the Brain Imaging Data Structure (BIDS) specifies a standard for storing imaging data, and the related BIDS App methodology provides a standard for implementing containerized processing environments that include all necessary dependencies to process BIDS datasets using image processing workflows. We present the BrainSuite BIDS App, which encapsulates the core MRI processing functionality of BrainSuite within the BIDS App framework. Specifically, the BrainSuite BIDS App implements a participant-level workflow comprising three pipelines and a corresponding set of group-level analysis workflows for processing the participant-level outputs. The BrainSuite Anatomical Pipeline (BAP) extracts cortical surface models from a T1-weighted (T1w) MRI. It then performs surface-constrained volumetric registration to align the T1w MRI to a labeled anatomical atlas, which is used to delineate anatomical regions of interest in the MRI brain volume and on the cortical surface models. The BrainSuite Diffusion Pipeline (BDP) processes diffusion-weighted imaging (DWI) data, with steps that include coregistering the DWI data to the T1w scan, correcting for geometric image distortion, and fitting diffusion models to the DWI data. The BrainSuite Functional Pipeline (BFP) performs fMRI processing using a combination of FSL, AFNI, and BrainSuite tools. BFP coregisters the fMRI data to the T1w image, then transforms the data to the anatomical atlas space and to the Human Connectome Project’s grayordinate space. Each of these outputs can then be processed during group-level analysis. The outputs of BAP and BDP are analyzed using the BrainSuite Statistics in R (bssr) toolbox, which provides functionality for hypothesis testing and statistical modeling. The outputs of BFP can be analyzed using atlas-based or atlas-free statistical methods during group-level processing. These analyses include the application of BrainSync, which synchronizes the time-series data temporally and enables comparison of resting-state or task-based fMRI data across scans. We also present the BrainSuite Dashboard quality control system, which provides a browser-based interface for reviewing the outputs of individual modules of the participant-level pipelines across a study in real-time as they are generated. BrainSuite Dashboard facilitates rapid review of intermediate results, enabling users to identify processing errors and make adjustments to processing parameters if necessary. The comprehensive functionality included in the BrainSuite BIDS App provides a mechanism for rapidly deploying the BrainSuite workflows into new environments to perform large-scale studies. We demonstrate the capabilities of the BrainSuite BIDS App using structural, diffusion, and functional MRI data from the Amsterdam Open MRI Collection’s Population Imaging of Psychology dataset.

/pdf/brainsuite-bids-app-containerized-workflows-for-mri-analysis-2ayebxut.pdf

BrainSuite BIDS App: Containerized Workflows for MRI Analysis

Despite impressive state-of-the-art performance on a wide variety of machine learning tasks in multiple applications, deep learning methods can produce over-confident predictions, particularly with limited training data. Therefore, quantifying uncertainty is particularly important in critical applications such as anomaly or lesion detection and clinical diagnosis, where a realistic assessment of uncertainty is essential in determining surgical margins, disease status and appropriate treatment. In this work, we focus on using quantile regression to estimate aleatoric uncertainty and use it for estimating uncertainty in both supervised and unsupervised lesion detection problems. In the unsupervised settings, we apply quantile regression to a lesion detection task using Variational AutoEncoder (VAE). The VAE models the output as a conditionally independent Gaussian characterized by means and variances for each output dimension. Unfortunately, joint optimization of both mean and variance in the VAE leads to the well-known problem of shrinkage or underestimation of variance. We describe an alternative VAE model, Quantile-Regression VAE (QR-VAE), that avoids this variance shrinkage problem by estimating conditional quantiles for the given input image. Using the estimated quantiles, we compute the conditional mean and variance for input images under the conditionally Gaussian model. We then compute reconstruction probability using this model as a principled approach to outlier or anomaly detection applications. In the supervised setting, we develop binary quantile regression (BQR) for the supervised lesion segmentation task. BQR segmentation can capture uncertainty in label boundaries. We show how quantile regression can be used to characterize expert disagreement in the location of lesion boundaries.

Deep Quantile Regression for Uncertainty Estimation in Unsupervised and Supervised Lesion Detection.

MAP (maximum a posteriori) reconstructions of transmission images produce more accurate ACFs (attenuation correction factors) than smoothed division of blank and transmission scans and analytical methods. Also, for highly specific tracers, transmission images can provide useful anatomical cues for use in localizing structures and image coregistration. The resolution of MAP images reconstructed with a spatially invariant smoothing prior is known to be nonuniform. Spatially variant smoothing parameters are used to achieve uniform resolution throughout the transmission image. We also investigate the relationship between resolution and the global smoothing parameter through computer simulations. The resulting calibration curve can be used to select the smoothing parameter to achieve a desired spatial resolution. The tractability and feasibility of our method is demonstrated through an application to phantom transmission data collected using a Concorde P4 microPET system.

/pdf/fully-3d-uniform-resolution-transmission-micropet-image-35adskfvy4.pdf

Richard M. Leahy

Papers

Chronic anemia: The effects on the connectivity of white matter

Identification of overlapping and interacting networks reveals intrinsic spatiotemporal organization of the human brain

BrainSuite BIDS App: Containerized Workflows for MRI Analysis

Deep Quantile Regression for Uncertainty Estimation in Unsupervised and Supervised Lesion Detection.

Fully 3D uniform resolution transmission microPET image reconstruction