The Incremental Multiresolution Matrix Factorization Algorithm

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric matrices -- an important aspect in the success of many vision problems. Our new algorithm, the incremental multiresolution matrix factorization, uncovers such structure one feature at a time, and hence scales well to large matrices. We describe how this multiscale analysis goes much farther than what a direct global factorization of the data can identify. We evaluate the efficacy of the resulting factorizations for relative leveraging within regression tasks using medical imaging data. We also use the factorization on representations learned by popular deep networks, providing evidence of their ability to infer semantic relationships even when they are not explicitly trained to do so. We show that this algorithm can be used as an exploratory tool to improve the network architecture, and within numerous other settings in vision.Comment: Computer Vision and Pattern Recognition (CVPR) 2017, 10 page

Speeding up Permutation Testing in Neuroimaging

Multiple hypothesis testing is a significant problem in nearly all neuroimaging studies. In order to correct for this phenomena, we require a reliable estimate of the Family-Wise Error Rate (FWER). The well known Bonferroni correction method, while simple to implement, is quite conservative, and can substantially under-power a study because it ignores dependencies between test statistics. Permutation testing, on the other hand, is an exact, non-parametric method of estimating the FWER for a given $\alpha$-threshold, but for acceptably low thresholds the computational burden can be prohibitive. In this paper, we show that permutation testing in fact amounts to populating the columns of a very large matrix ${\bf P}$. By analyzing the spectrum of this matrix, under certain conditions, we see that ${\bf P}$ has a low-rank plus a low-variance residual decomposition which makes it suitable for highly sub--sampled --- on the order of $0.5\%$ --- matrix completion methods. Based on this observation, we propose a novel permutation testing methodology which offers a large speedup, without sacrificing the fidelity of the estimated FWER. Our evaluations on four different neuroimaging datasets show that a computational speedup factor of roughly $50\times$ can be achieved while recovering the FWER distribution up to very high accuracy. Further, we show that the estimated $\alpha$-threshold is also recovered faithfully, and is stable.Comment: NIPS 1

Self-appraisal decisions evoke dissociated dorsal-ventral aMPFC networks

The anterior medial prefrontal cortex (aMPFC) is consistently active during personally salient decisions, yet the differential contributory processes of this region along the dorsal-ventral axis are less understood. Using a self-appraisal decision-making task and functional magnetic resonance imaging, we demonstrated task-dependent connectivity of ventral aMPFC with amygdala, insula, and nucleus accumbens, and dorsal aMPFC connectivity with dorsolateral PFC and bilateral hippocampus. These aMPFC networks appear to subserve distinct contributory processes inherent to self-appraisal decisions, specifically a dorsally mediated cognitive and a ventrally mediated affective/self-relevance network. © 2005 Elsevier Inc. All rights reserved

Relevance to self: A brief review and framework of neural systems underlying appraisal

We argue that many similar findings observed in cognitive, affective, and social neuroimaging research may compose larger processes central to generating self-relevance. In support of this, recent findings from these research domains were reviewed to identify common systemic activation patterns. Superimposition of these patterns revealed evidence for large-scale supramodal processes, which are argued to mediate appraisal of self-relevant content irrespective of specific stimulus types (e.g. words, pictures) and task domains (e.g. induction of reward, fear, pain, etc.). Furthermore, we distinguish between two top-down sub-systems involved in appraisal of self-relevance, one that orients pre-attentive biasing information (e.g. anticipatory or mnemonic) to salient or explicitly self-relevant phenomena, and another that engages introspective processes (e.g. self-reflection, evaluation, recollection) either in conjunction with or independent of the former system. Based on aggregate patterns of activation derived from the reviewed studies, processes in a ventral medial prefrontal cortex (MPFC)-subcortical network appear to track with the former pathway, and processes in a dorsal MPFC-cortical-subcortical network with the latter. As a whole, the purpose of this framework is to re-conceive the functionality of these systems in terms of supramodal processes that more directly reflect the influences of relevance to the self. © 2007 Elsevier Ltd. All rights reserved

Longitudinal diffusion tensor imaging and neuropsychological correlates in traumatic brain injury patients

Traumatic brain injury (TBI) often involves focal cortical injury and white matter (WM) damage that can be measured shortly after injury. Additionally, slowly evolving WM change can be observed but there is a paucity of research on the duration and spatial pattern of long-term changes several years post-injury. The current study utilized diffusion tensor imaging to identify regional WM changes in 12 TBI patients and nine healthy controls at three time points over a four year period. Neuropsychological testing was also administered to each participant at each time point. Results indicate that TBI patients exhibit longitudinal changes to WM indexed by reductions in fractional anisotropy (FA) in the corpus callosum, as well as FA increases in bilateral regions of the superior longitudinal fasciculus (SLF) and portions of the optic radiation (OR). FA changes appear to be driven by changes in radial (not axial) diffusivity, suggesting that observed longitudinal FA changes may be related to changes in myelin rather than to axons. Neuropsychological correlations indicate that regional FA values in the corpus callosum and sagittal stratum (SS) correlate with performance on finger tapping and visuomotor speed tasks (respectively) in TBI patients, and that longitudinal increases in FA in the SS, SLF, and OR correlate with improved performance on the visuomotor speed (SS) task as well as a derived measure of cognitive control (SLF, OR). The results of this study showing progressive WM deterioration for several years post-injury contribute to a growing literature supporting the hypothesis that TBI should be viewed not as an isolated incident but as a prolonged disease state. The observations of long-term neurological and functional improvement provide evidence that some ameliorative change may be occurring concurrently with progressive degeneration

Posterior Cingulate and Lateral Parietal Gray Matter Volume in Older Adults with Depressive Symptoms

Depressive symptoms occurring late in life are an important risk factor for Alzheimer’s disease (AD). The latest research finds that onset of depressive symptoms in late life may herald the development of AD, not only for amnestic Mild Cognitive Impairment (aMCI) patients, but also for cognitively-normal older adults. Neuroimaging of brain structure, blood flow, and glucose metabolism indicates that depressive symptoms in late life are accompanied by structural and functional changes in limbic brain regions vulnerable to AD. The present cross-sectional study was guided by the hypothesis that compared to their non-depressed counterparts, older adults with mild to moderate depressive symptoms have less volume in limbic structures vulnerable to changes in AD—specifically, cortical midline structures such as anterior cingulate and posterior cingulate cortex as well as mesial temporal regions such as bilateral hippocampi and amygdalae. Consistent with our hypothesis, results of a voxel-based morphometry analysis revealed smaller retrosplenial, posterior cingulate, and precuneus gray matter volumes in depressed individuals relative to healthy controls. Right lateral parietal cortex—another region vulnerable to change in AD—was also smaller in the group with depressive symptoms. Contrary to our hypothesis, no volumetric differences were found in the anterior cingulate cortex or mesial temporal lobe. Results of this study show a relationship between geriatric depressive symptoms and brain volume in regions vulnerable to AD. Follow-up of participants over time will tell if brain changes detected here predict development of AD