Multi-resolutional shape features via non-Euclidean wavelets: applications to statistical analysis of cortical thickness.

Statistical analysis on arbitrary surface meshes such as the cortical surface is an important approach to understanding brain diseases such as Alzheimer's disease (AD). Surface analysis may be able to identify specific cortical patterns that relate to certain disease characteristics or exhibit differences between groups. Our goal in this paper is to make group analysis of signals on surfaces more sensitive. To do this, we derive multi-scale shape descriptors that characterize the signal around each mesh vertex, i.e., its local context, at varying levels of resolution. In order to define such a shape descriptor, we make use of recent results from harmonic analysis that extend traditional continuous wavelet theory from the Euclidean to a non-Euclidean setting (i.e., a graph, mesh or network). Using this descriptor, we conduct experiments on two different datasets, the Alzheimer's Disease NeuroImaging Initiative (ADNI) data and images acquired at the Wisconsin Alzheimer's Disease Research Center (W-ADRC), focusing on individuals labeled as having Alzheimer's disease (AD), mild cognitive impairment (MCI) and healthy controls. In particular, we contrast traditional univariate methods with our multi-resolution approach which show increased sensitivity and improved statistical power to detect a group-level effects. We also provide an open source implementation.

Comparison of Conventional Methods with Newer Diagnostic Modalities to Detect Genital Tuberculosis in Infertile Women.

Background: Genital tuberculosis is one of the leading causes of female infertility. Paucibacillary nature of the disease in the female genital system often makes its diagnosis difficult. No single test has been able to accurately diagnose genital tuberculosis. In this study we aim to compare conventional diagnostic tests for tuberculosis like Acid Fast Bacilli (AFB) Staining, Lowenstein Jensen (LJ) Culture and Histopathology with newer tests like PCR, MGIT 960, GeneXpert. Methods: This study included 67 infertile women from Vardhman Mahavir Medical College and Safdarjung Hospital, New Delhi. They were subjected to detailed history and routine investigations, namely Haemogram, ESR, Mantoux test, Chest X-ray and pelvic ultrasound to look for the findings of tuberculosis. A premenstrual endometrial aspirate was taken and was subjected to the AFB Staining, LJ Culture, Histopathology, PCR, MGIT 960, Gene Xpert, and the test results were compared. Result and Conclusion: 35.8% (24/67) of women were diagnosed with genital tuberculosis using the diagnostic criteria. With culture as the gold standard, the positivity of genital TB was 19.4% (13/67). Majority of infertile patients with low index of suspicion clinically were positive for genital tuberculosis. Therefore, all the patients of infertility should be routinely evaluated for genital tuberculosis. PCR and MGIT 960 have shown promising results in the newer methods. LJ culture and histopathology are still the most reliable and available diagnostic methods. The usefulness of AFB Staining and GeneXpert remains questionable.

Incorporating Domain Knowledge in Matching Problems via Harmonic Analysis.

Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in practice. Here, we investigate if this difficulty can be mitigated when some additional piece of information is available: (a) that all QAP instances of interest come from the same application, and (b) the correct solution for a set of such QAP instances is given. We propose a new approach to accelerate the solution of QAPs based on learning parameters for a modified objective function from prior QAP instances. A key feature of our approach is that it takes advantage of the algebraic structure of permutations, in conjunction with special methods for optimizing functions over the symmetric group 𝕊 n in Fourier space. Experiments show that in practical domains the new method can outperform existing approaches.

Wavelet based multi-scale shape features on arbitrary surfaces for cortical thickness discrimination.

Hypothesis testing on signals defined on surfaces (such as the cortical surface) is a fundamental component of a variety of studies in Neuroscience. The goal here is to identify regions that exhibit changes as a function of the clinical condition under study. As the clinical questions of interest move towards identifying very early signs of diseases, the corresponding statistical differences at the group level invariably become weaker and increasingly hard to identify. Indeed, after a multiple comparisons correction is adopted (to account for correlated statistical tests over all surface points), very few regions may survive. In contrast to hypothesis tests on point-wise measurements, in this paper, we make the case for performing statistical analysis on multi-scale shape descriptors that characterize the local topological context of the signal around each surface vertex. Our descriptors are based on recent results from harmonic analysis, that show how wavelet theory extends to non-Euclidean settings (i.e., irregular weighted graphs). We provide strong evidence that these descriptors successfully pick up group-wise differences, where traditional methods either fail or yield unsatisfactory results. Other than this primary application, we show how the framework allows performing cortical surface smoothing in the native space without mappint to a unit sphere.

Topology-based kernels with application to inference problems in Alzheimer's disease.

Alzheimer's disease (AD) research has recently witnessed a great deal of activity focused on developing new statistical learning tools for automated inference using imaging data. The workhorse for many of these techniques is the support vector machine (SVM) framework (or more generally kernel-based methods). Most of these require, as a first step, specification of a kernel matrix K between input examples (i.e., images). The inner product between images I(i) and I(j) in a feature space can generally be written in closed form and so it is convenient to treat K as "given." However, in certain neuroimaging applications such an assumption becomes problematic. As an example, it is rather challenging to provide a scalar measure of similarity between two instances of highly attributed data such as cortical thickness measures on cortical surfaces. Note that cortical thickness is known to be discriminative for neurological disorders, so leveraging such information in an inference framework, especially within a multi-modal method, is potentially advantageous. But despite being clinically meaningful, relatively few works have successfully exploited this measure for classification or regression. Motivated by these applications, our paper presents novel techniques to compute similarity matrices for such topologically-based attributed data. Our ideas leverage recent developments to characterize signals (e.g., cortical thickness) motivated by the persistence of their topological features, leading to a scheme for simple constructions of kernel matrices. As a proof of principle, on a dataset of 356 subjects from the Alzheimer's Disease Neuroimaging Initiative study, we report good performance on several statistical inference tasks without any feature selection, dimensionality reduction, or parameter tuning.