Nicolle M. Correa

Canonical Correlation Analysis for Data Fusion and Group Inferences

We have presented two CCA-based approaches for data fusion and group analysis of biomedical imaging data and demonstrated their utility on fMRI, sMRI, and EEG data. The results show that CCA and M-CCA are powerful tools that naturally allow the analysis of multiple data sets. The data fusion and group analysis methods presented are completely data driven, and use simple linear mixing models to decompose the data into their latent components. Since CCA and M-CCA are based on second-order statistics they provide a relatively lessstrained solution as compared to methods based on higherorder statistics such as ICA. While this can be advantageous, the flexibility also tends to lead to solutions that are less sparse than those obtained using assumptions of non-Gaussianity-in particular superGaussianity-at times making the results more difficult to interpret. Thus, it is important to note that both approaches provide complementary perspectives, and hence it is beneficial to study the data using different analysis techniques.

Comparison of blind source separation algorithms for FMRI using a new Matlab toolbox: GIFT

We study the performance of five blind source separation (BSS) algorithms when applied to analysis of functional magnetic resonance imaging (fMRI) data. We introduce a Matlab-based toolbox, the group ICA of fMRI toolbox (GIFT), which enables analysis of groups of subjects using BSS algorithms, in particular those based on independent component analysis (ICA). We use the visualization and computational tools included in GIFT to quantitatively analyze the performance of different BSS algorithms for fMRI analysis and discuss the results.

Multi-set canonical correlation analysis for the fusion of concurrent single trial ERP and functional MRI

Functional magnetic resonance imaging (fMRI) data and electroencephalography (EEG) data provide complementary spatio-temporal information about brain function. Methods to couple the relative strengths of these modalities usually involve two stages: first forming a feature set from each dataset based on one criterion followed by exploration of connections among the features using a second criterion. We propose a data fusion method for simultaneously acquired fMRI and EEG data that combines these steps using a single criterion for finding the cross-modality associations and performing source separation. Using multi-set canonical correlation analysis (M-CCA), we obtain a decomposition of the two modalities, into spatial maps for fMRI data and a corresponding temporal evolution for EEG data, based on trial-to-trial covariation across the two modalities. Additionally, the analysis is performed on data from a group of subjects in order to make group inferences about the covariation across modalities. Being multivariate, the proposed method facilitates the study of brain connectivity along with localization of brain function. M-CCA can be easily extended to incorporate different data types and additional modalities. We demonstrate the promise of the proposed method in finding covarying trial-to-trial amplitude modulations (AMs) in an auditory task involving implicit pattern learning. The results show approximately linear decreasing trends in AMs for both modalities and the corresponding spatial activations occur mainly in motor, frontal, temporal, inferior parietal, and orbito-frontal areas that are linked both to sensory function as well as learning and expectation--all of which match activations related to the presented paradigm.

Canonical Correlation Analysis for Feature-Based Fusion of Biomedical Imaging Modalities and Its Application to Detection of Associative Networks in Schizophrenia

Typically data acquired through imaging techniques such as functional magnetic resonance imaging (fMRI), structural MRI (sMRI), and electroencephalography (EEG) are analyzed separately. However, fusing information from such complementary modalities promises to provide additional insight into connectivity across brain networks and changes due to disease. We propose a data fusion scheme at the feature level using canonical correlation analysis (CCA) to determine inter-subject covariations across modalities. As we show both with simulation results and application to real data, multimodal CCA (mCCA) proves to be a flexible and powerful method for discovering associations among various data types. We demonstrate the versatility of the method with application to two datasets, an fMRI and EEG, and an fMRI and sMRI dataset, both collected from patients diagnosed with schizophrenia and healthy controls. CCA results for fMRI and EEG data collected for an auditory oddball task reveal associations of the temporal and motor areas with the N2 and P3 peaks. For the application to fMRI and sMRI data collected for an auditory sensorimotor task, CCA results show an interesting joint relationship between fMRI and gray matter, with patients with schizophrenia showing more functional activity in motor areas and less activity in temporal areas associated with less gray matter as compared to healthy controls. Additionally, we compare our scheme with an independent component analysis based fusion method, joint-ICA that has proven useful for such a study and note that the two methods provide complementary perspectives on data fusion.

Automatic Identification of Functional Clusters in fMRI Data Using Spatial Dependence

In independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data, extracting a large number of maximally independent components provides a detailed functional segmentation of brain. However, such high-order segmentation does not establish the relationships among different brain networks, and also studying and classifying components can be challenging. In this study, we present a multidimensional ICA (MICA) scheme to achieve automatic component clustering. In our MICA framework, stable components are hierarchically grouped into clusters based on higher order statistical dependence-mutual information-among spatial components, instead of the typically used temporal correlation among time courses. The final cluster membership is determined using a statistical hypothesis testing method. Since ICA decomposition takes into account the modulation of the spatial maps, i.e., temporal information, our ICA-based approach incorporates both spatial and temporal information effectively. Our experimental results from both simulated and real fMRI datasets show that the use of spatial dependence leads to physiologically meaningful connectivity structure of brain networks, which is consistently identified across various ICA model orders and algorithms. In addition, we observe that components related to artifacts, including cerebrospinal fluid, arteries, and large draining veins, are grouped together and encouragingly distinguished from other components of interest.

Wavelet-based fMRI analysis: 3-D denoising, signal separation, and validation metrics

We present a novel integrated wavelet-domain based framework (w-ICA) for 3-D denoising functional magnetic resonance imaging (fMRI) data followed by source separation analysis using independent component analysis (ICA) in the wavelet domain. We propose the idea of a 3-D wavelet-based multi-directional denoising scheme where each volume in a 4-D fMRI data set is sub-sampled using the axial, sagittal and coronal geometries to obtain three different slice-by-slice representations of the same data. The filtered intensity value of an arbitrary voxel is computed as an expected value of the denoised wavelet coefficients corresponding to the three viewing geometries for each sub-band. This results in a robust set of denoised wavelet coefficients for each voxel. Given the de-correlated nature of these denoised wavelet coefficients, it is possible to obtain more accurate source estimates using ICA in the wavelet domain. The contributions of this work can be realized as two modules: First, in the analysis module we combine a new 3-D wavelet denoising approach with signal separation properties of ICA in the wavelet domain. This step helps obtain an activation component that corresponds closely to the true underlying signal, which is maximally independent with respect to other components. Second, we propose and describe two novel shape metrics for post-ICA comparisons between activation regions obtained through different frameworks. We verified our method using simulated as well as real fMRI data and compared our results against the conventional scheme (Gaussian smoothing+spatial ICA: s-ICA). The results show significant improvements based on two important features: (1) preservation of shape of the activation region (shape metrics) and (2) receiver operating characteristic curves. It was observed that the proposed framework was able to preserve the actual activation shape in a consistent manner even for very high noise levels in addition to significant reduction in false positive voxels.

Fusion of fMRI, sMRI, and EEG data using canonical correlation analysis

Typically data acquired through imaging techniques such as functional magnetic resonance imaging (fMRI), structural MRI (sMRI), and electroencephalography (EEG) are analyzed separately. Each modality records brain structure and function at different scales, and fusing information from such complementary modalities promises to provide additional insight into connectivity across brain networks and changes due to disease. Recently, a number of methods have been proposed for data integration and fusion of two brain imaging modalities. We propose a new data fusion scheme based on canonical correlation analysis that enables the detection of associations across multiple modalities. Our multimodal canonical correlation analysis (mCCA) scheme works at the feature level using multi-set CCA to determine inter-subject covariations across modalities. We apply mCCA to fMRI, sMRI, and EEG data collected from patients diagnosed with schizophrenia and healthy controls. Through data collected from an auditory oddball task, we show that the fusion of multiple modalities detects more specific associations as compared to fusion of two modalities.

Application of Independent Component Analysis With Adaptive Density Model to Complex-Valued fMRI Data

Independent component analysis (ICA) has proven quite useful for the analysis of real world datasets such as functional resonance magnetic imaging (fMRI) data, where the underlying nature of the data is hard to model. It is particularly useful for the analysis of fMRI data in its native complex form since very little is known about the nature of phase. Phase information has been discarded in most analyses as it is particularly noisy. In this paper, we show that a complex ICA approach using a flexible nonlinearity that adapts to the source density is the more desirable one for performing ICA of complex fMRI data compared to those that use fixed nonlinearity, especially when noise level is high. By adaptively matching the underlying fMRI density model, the analysis performance can be improved in terms of both the estimation of spatial maps and the task-related time courses, especially for the estimation of phase of the time course. We also define a procedure for analysis and visualization of complex-valued fMRI results, which includes the construction of bivariate t-maps for multiple subjects and a complex-valued ICASSO scheme for evaluating the consistency of ICA algorithms.

Independent subspace analysis with prior information for fMRI data

Independent component analysis (ICA) has been successfully applied for the analysis of functional magnetic resonance imaging (fMRI) data. However, independence might be too strong a constraint for certain sources. In this paper, we present an independent subspace analysis (ISA) framework that forms independent subspaces among the estimated sources having dependencies by a hierarchial clustering approach and subsequently separates the dependent sources in the task-related subspace using prior information. We study the incorporation of two types of prior information to transform the sources within the task-related subspace: sparsity and task-related time courses. We demonstrate the effectiveness of our proposed method for source separation of multi-subject fMRI data from a visuomotor task. Our results show that physiologically meaningful dependencies among sources can be identified using our subspace approach and the dependent estimated components can be further separated effectively using a subsequent transformation.

Independent component analysis of 2-D electrophoresis gels.

We present a novel application of independent component analysis (ICA), an exploratory data analysis technique, to two‐dimensional electrophoresis (2‐DE) gels, which have been used to analyze differentially expressed proteins across groups. Unlike currently used pixel‐wise statistical tests, ICA is a data‐driven approach that utilizes the information contained in the entire gel data. We also apply ICA on wavelet‐transformed 2‐DE gels to address the high dimensionality and noise problems typically found in 2‐DE gels. Also, we use an analysis‐of‐variance (ANOVA) approach as a benchmark for comparison. Using simulated data, we show that ICA detects the group differences accurately in both the spatial and wavelet domains. We also apply these techniques to real 2‐DE gels. ICA proves to be much faster than ANOVA, and unlike ANOVA it does not depend on the selection of a threshold. Application of principal component analysis reduces the dimensionality and tends to improve the performance by reducing the noise.