In this work, we present an additive model for space-time data that splits the data into a temporally correlated component and a spatially correlated component. We model the spatially correlated portion using a time-varying Gaussian graphical model. Under assumptions on the smoothness of changes in covariance matrices, we derive strong single sample convergence results, confirming our ability to estimate meaningful graphical structures as they evolve over time. We apply our methodology to the discovery of time-varying spatial structures in human brain fMRI signals.
In the context of fMRI, the work of @cite_8 used a similar kernel-weighted estimator for the spatial covariance, however they modeled the temporal covariance with a simple AR-1 model which they did not estimate, and their estimator did not attempt to remove. Similarly, @cite_5 used a smoothed kernel estimator for @math with a penalty to further promote smoothness, but did not model the temporal correlations. Our additive model allows the direct estimation of the temporal behavior, revealing a richer structure than a simple AR-1, and allowing for effective denoising of the data, and hence better estimation of the spatial graph structures.
@cite_5 @cite_8
2024545575 61705880 2000292092 2050497240
Standard group analyses of fMRI data rely on spatial and temporal averaging of individuals. This averaging operation is only sensible when the mean is a good representation of the group. This is not the case if subjects are not homogeneous, and it is therefore a major concern in fMRI studies to assess this group homogeneity. We present a method that provides relevant distances or similarity measures between temporal series of brain functional images belonging to different subjects. The method allows a multivariate comparison between data sets of several subjects in the time or in the space domain. These analyses assess the global intersubject variability before averaging subjects and drawing conclusions across subjects, at the population level. We adapt the RV coefficient to measure meaningful spatial or temporal similarities and use multidimensional scaling to give a visual representation of each subject's position with respect to other subjects in the group. We also provide a measure for detecting subjects that may be outliers. Results show that the method is a powerful tool to detect subjects with specific temporal or spatial patterns, and that, despite the apparent loss of information, restricting the analysis to a homogeneous subgroup of subjects does not reduce the statistical sensitivity of standard group fMRI analyses. Research in recent years has provided some evidence of temporal non-stationarity of functional connectivity in resting state fMRI. In this paper, we present a novel methodology that can decode connectivity dynamics into a temporal sequence of hidden network "states" for each subject, using a Hidden Markov Modeling (HMM) framework. Each state is characterized by a unique covariance matrix or whole-brain network. Our model generates these covariance matrices from a common but unknown set of sparse basis networks, which capture the range of functional activity co-variations of regions of interest (ROIs). Distinct hidden states arise due to a variation in the strengths of these basis networks. Thus, our generative model combines a HMM framework with sparse basis learning of positive definite matrices. Results on simulated fMRI data show that our method can effectively recover underlying basis networks as well as hidden states. We apply this method on a normative dataset of resting state fMRI scans. Results indicate that the functional activity of a subject at any point during the scan is composed of combinations of overlapping task-positive negative pairs of networks as revealed by our basis. Distinct hidden temporal states are produced due to a different set of basis networks dominating the covariance pattern in each state. Many machine learning and pattern classification methods have been applied to the diagnosis of Alzheimer’s disease (AD) and its prodromal stage, i.e., mild cognitive impairment (MCI). Recently, rather than predicting categorical variables as in classification, several pattern regression methods have also been used to estimate continuous clinical variables from brain images. However, most existing regression methods focus on estimating multiple clinical variables separately and thus cannot utilize the intrinsic useful correlation information among different clinical variables. On the other hand, in those regression methods, only a single modality of data (usually only the structural MRI) is often used, without considering the complementary information that can be provided by different modalities. In this paper, we propose a general methodology, namely Multi-Modal Multi-Task (M3T) learning, to jointly predict multiple variables from multi-modal data. Here, the variables include not only the clinical variables used for regression but also the categorical variable used for classification, with different tasks corresponding to prediction of different variables. Specifically, our method contains two key components, i.e., (1) a multi-task feature selection which selects the common subset of relevant features for multiple variables from each modality, and (2) a multi-modal support vector machine which fuses the above-selected features from all modalities to predict multiple (regression and classification) variables. To validate our method, we perform two sets of experiments on ADNI baseline MRI, FDG-PET, and cerebrospinal fluid (CSF) data from 45 AD patients, 91 MCI patients, and 50 healthy controls (HC). In the first set of experiments, we estimate two clinical variables such as Mini Mental State Examination (MMSE) and Alzheimer’s Disease Assessment Scale - Cognitive Subscale (ADAS-Cog), as well as one categorical variable (with value of ‘AD’, ‘MCI’ or ‘HC’), from the baseline MRI, FDG-PET, and CSF data. In the second set of experiments, we predict the 2-year changes of MMSE and ADAS-Cog scores and also the conversion of MCI to AD from the baseline MRI, FDG-PET, and CSF data. The results on both sets of experiments demonstrate that our proposed M3T learning scheme can achieve better performance on both regression and classification tasks than the conventional learning methods. Abstract Estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks. We introduce a nonparametric approach to global estimation of the spatial covariance structure of a random function Z(x, t) observed repeatedly at times ti (i = 1, …, T) at a finite number of sampling stations xi (i = 1, 2, …, N) in the plane. Our analyses assume temporal stationarity but do not assume spatial stationarity (or isotropy). We analyze the spatial dispersions var(Z(xi, t) − Z(xj, t)) as a natural metric for the spatial covariance structure and model these as a general smooth function of the geographic coordinates of station pairs (xi, xj ). The model is constructed in two steps. First, using nonmetric multidimensional scaling (MDS) we compute a two-dimensional representation of the sampling stations for which a monotone function of interpoint distances δij approximates the spatial dispersions. MDS transforms the problem...