Accelerating permutation testing in voxel-wise analysis through subspace tracking: A new plugin for SnPM.

Permutation testing is a non-parametric method for obtaining the max null distribution used to compute corrected p-values that provide strong control of false positives. In neuroimaging, however, the computational burden of running such an algorithm can be significant. We find that by viewing the permutation testing procedure as the construction of a very large permutation testing matrix, T, one can exploit structural properties derived from the data and the test statistics to reduce the runtime under certain conditions. In particular, we see that T is low-rank plus a low-variance residual. This makes T a good candidate for low-rank matrix completion, where only a very small number of entries of T (∼0.35% of all entries in our experiments) have to be computed to obtain a good estimate. Based on this observation, we present RapidPT, an algorithm that efficiently recovers the max null distribution commonly obtained through regular permutation testing in voxel-wise analysis. We present an extensive validation on a synthetic dataset and four varying sized datasets against two baselines: Statistical NonParametric Mapping (SnPM13) and a standard permutation testing implementation (referred as NaivePT). We find that RapidPT achieves its best runtime performance on medium sized datasets (50≤n≤200), with speedups of 1.5× - 38× (vs. SnPM13) and 20x-1000× (vs. NaivePT). For larger datasets (n≥200) RapidPT outperforms NaivePT (6× - 200×) on all datasets, and provides large speedups over SnPM13 when more than 10000 permutations (2× - 15×) are needed. The implementation is a standalone toolbox and also integrated within SnPM13, able to leverage multi-core architectures when available.

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.

Extracting and summarizing white matter hyperintensities using supervised segmentation methods in Alzheimer's disease risk and aging studies.

Precise detection and quantification of white matter hyperintensities (WMH) observed in T2-weighted Fluid Attenuated Inversion Recovery (FLAIR) Magnetic Resonance Images (MRI) is of substantial interest in aging, and age-related neurological disorders such as Alzheimer's disease (AD). This is mainly because WMH may reflect co-morbid neural injury or cerebral vascular disease burden. WMH in the older population may be small, diffuse, and irregular in shape, and sufficiently heterogeneous within and across subjects. Here, we pose hyperintensity detection as a supervised inference problem and adapt two learning models, specifically, Support Vector Machines and Random Forests, for this task. Using texture features engineered by texton filter banks, we provide a suite of effective segmentation methods for this problem. Through extensive evaluations on healthy middle-aged and older adults who vary in AD risk, we show that our methods are reliable and robust in segmenting hyperintense regions. A measure of hyperintensity accumulation, referred to as normalized effective WMH volume, is shown to be associated with dementia in older adults and parental family history in cognitively normal subjects. We provide an open source library for hyperintensity detection and accumulation (interfaced with existing neuroimaging tools), that can be adapted for segmentation problems in other neuroimaging studies.

Predictive markers for AD in a multi-modality framework: an analysis of MCI progression in the ADNI population.

Alzheimer's Disease (AD) and other neurodegenerative diseases affect over 20 million people worldwide, and this number is projected to significantly increase in the coming decades. Proposed imaging-based markers have shown steadily improving levels of sensitivity/specificity in classifying individual subjects as AD or normal. Several of these efforts have utilized statistical machine learning techniques, using brain images as input, as means of deriving such AD-related markers. A common characteristic of this line of research is a focus on either (1) using a single imaging modality for classification, or (2) incorporating several modalities, but reporting separate results for each. One strategy to improve on the success of these methods is to leverage all available imaging modalities together in a single automated learning framework. The rationale is that some subjects may show signs of pathology in one modality but not in another-by combining all available images a clearer view of the progression of disease pathology will emerge. Our method is based on the Multi-Kernel Learning (MKL) framework, which allows the inclusion of an arbitrary number of views of the data in a maximum margin, kernel learning framework. The principal innovation behind MKL is that it learns an optimal combination of kernel (similarity) matrices while simultaneously training a classifier. In classification experiments MKL outperformed an SVM trained on all available features by 3%-4%. We are especially interested in whether such markers are capable of identifying early signs of the disease. To address this question, we have examined whether our multi-modal disease marker (MMDM) can predict conversion from Mild Cognitive Impairment (MCI) to AD. Our experiments reveal that this measure shows significant group differences between MCI subjects who progressed to AD, and those who remained stable for 3 years. These differences were most significant in MMDMs based on imaging data. We also discuss the relationship between our MMDM and an individual's conversion from MCI to AD.

Spatially augmented LPboosting for AD classification with evaluations on the ADNI dataset.

Structural and functional brain images are playing an important role in helping us understand the changes associated with neurological disorders such as Alzheimer's disease (AD). Recent efforts have now started investigating their utility for diagnosis purposes. This line of research has shown promising results where methods from machine learning (such as Support Vector Machines) have been used to identify AD-related patterns from images, for use in diagnosing new individual subjects. In this paper, we propose a new framework for AD classification which makes use of the Linear Program (LP) boosting with novel additional regularization based on spatial "smoothness" in 3D image coordinate spaces. The algorithm formalizes the expectation that since the examples for training the classifier are images, the voxels eventually selected for specifying the decision boundary must constitute spatially contiguous chunks, i.e., "regions" must be preferred over isolated voxels. This prior belief turns out to be useful for significantly reducing the space of possible classifiers and leads to substantial benefits in generalization. In our method, the requirement of spatial contiguity (of selected discriminating voxels) is incorporated within the optimization framework directly. Other methods have made use of similar biases as a pre- or post-processing step, however, our model incorporates this emphasis on spatial smoothness directly into the learning step. We report on extensive evaluations of our algorithm on MR and FDG-PET images from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, and discuss the relationship of the classification output with the clinical and cognitive biomarker data available within ADNI.

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 α-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 P. By analyzing the spectrum of this matrix, under certain conditions, we see that 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× can be achieved while recovering the FWER distribution up to very high accuracy. Further, we show that the estimated α-threshold is also recovered faithfully, and is stable.

Q-MKL: Matrix-induced Regularization in Multi-Kernel Learning with Applications to Neuroimaging.

Multiple Kernel Learning (MKL) generalizes SVMs to the setting where one simultaneously trains a linear classifier and chooses an optimal combination of given base kernels. Model complexity is typically controlled using various norm regularizations on the base kernel mixing coefficients. Existing methods neither regularize nor exploit potentially useful information pertaining to how kernels in the input set 'interact'; that is, higher order kernel-pair relationships that can be easily obtained via unsupervised (similarity, geodesics), supervised (correlation in errors), or domain knowledge driven mechanisms (which features were used to construct the kernel?). We show that by substituting the norm penalty with an arbitrary quadratic function Q 0, one can impose a desired covariance structure on mixing weights, and use this as an inductive bias when learning the concept. This formulation significantly generalizes the widely used 1- and 2-norm MKL objectives. We explore the model's utility via experiments on a challenging Neuroimaging problem, where the goal is to predict a subject's conversion to Alzheimer's Disease (AD) by exploiting aggregate information from many distinct imaging modalities. Here, our new model outperforms the state of the art (p-values ⪡ 10-3). We briefly discuss ramifications in terms of learning bounds (Rademacher complexity).

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.

Learning Kernels for variants of Normalized Cuts: Convex Relaxations and Applications.

We propose a new algorithm for learning kernels for variants of the Normalized Cuts (NCuts) objective - i.e., given a set of training examples with known partitions, how should a basis set of similarity functions be combined to induce NCuts favorable distributions. Such a procedure facilitates design of good affinity matrices. It also helps assess the importance of different feature types for discrimination. Rather than formulating the learning problem in terms of the spectral relaxation, the alternative we pursue here is to work in the original discrete setting (i.e., the relaxation occurs much later). We show that this strategy is useful - while the initial specification seems rather difficult to optimize efficiently, a set of manipulations reveal a related model which permits a nice SDP relaxation. A salient feature of our model is that the eventual problem size is only a function of the number of input kernels and not the training set size. This relaxation also allows strong optimality guarantees, if certain conditions are satisfied. We show that the sub-kernel weights obtained provide a complementary approach for MKL based methods. Our experiments on Caltech101 and ADNI (a brain imaging dataset) show that the quality of solutions is competitive with the state-of-the-art.

MKL for robust multi-modality AD classification.

We study the problem of classifying mild Alzheimer's disease (AD) subjects from healthy individuals (controls) using multi-modal image data, to facilitate early identification of AD related pathologies. Several recent papers have demonstrated that such classification is possible with MR or PET images, using machine learning methods such as SVM and boosting. These algorithms learn the classifier using one type of image data. However, AD is not well characterized by one imaging modality alone, and analysis is typically performed using several image types--each measuring a different type of structural/functional characteristic. This paper explores the AD classification problem using multiple modalities simultaneously. The difficulty here is to assess the relevance of each modality (which cannot be assumed a priori), as well as to optimize the classifier. To tackle this problem, we utilize and adapt a recently developed idea called Multi-Kernel learning (MKL). Briefly, each imaging modality spawns one (or more kernels) and we simultaneously solve for the kernel weights and a maximum margin classifier. To make the model robust, we propose strategies to suppress the influence of a small subset of outliers on the classifier--this yields an alternative minimization based algorithm for robust MKL. We present promising multi-modal classification experiments on a large dataset of images from the ADNI project.

Classification in DTI using shapes of white matter tracts.

Diffusion Tensor Imaging (DTI) provides unique information about the underlying tissue structure of brain white matter in vivo, including both the geometry of fiber bundles as well as quantitative information about tissue properties as characterized by measures such as tensor orientation, anisotropy, and size. Our objective in this paper is to evaluate the utility of shape representations of white matter tracts extracted from DTI data for classification of clinically different population groups (here autistic vs control). As a first step, our algorithm extracts fiber bundles passing through approximately marked regions of interest on affinely aligned brain volumes. The subsequent analysis is entirely based on the geometric modeling of the extracted tracts. A key advantage of using such an abstraction is that it allows us to capture invariant features of brains allowing for efficient large sample size studies. We demonstrate that with the use of an appropriate representation of the tract shapes, classifiers can be built with reasonable prediction accuracies without making heavy use of the spatial normalization machinery needed when using voxel based features.