Yi Ou Li

Estimating the Number of Independent Components for Functional Magnetic Resonance Imaging Data

Multivariate analysis methods such as independent component analysis (ICA) have been applied to the analysis of functional magnetic resonance imaging (fMRI) data to study brain function. Because of the high dimensionality and high noise level of the fMRI data, order selection, i.e., estimation of the number of informative components, is critical to reduce over/underfitting in such methods. Dependence among fMRI data samples in the spatial and temporal domain limits the usefulness of the practical formulations of information‐theoretic criteria (ITC) for order selection, since they are based on likelihood of independent and identically distributed (i.i.d.) data samples. To address this issue, we propose a subsampling scheme to obtain a set of effectively i.i.d. samples from the dependent data samples and apply the ITC formulas to the effectively i.i.d. sample set for order selection. We apply the proposed method on the simulated data and show that it significantly improves the accuracy of order selection from dependent data. We also perform order selection on fMRI data from a visuomotor task and show that the proposed method alleviates the over‐estimation on the number of brain sources due to the intrinsic smoothness and the smooth preprocessing of fMRI data. We use the software package ICASSO (Himberg et al. [ 2004 ]: Neuroimage 22:1214–1222) to analyze the independent component (IC) estimates at different orders and show that, when ICA is performed at overestimated orders, the stability of the IC estimates decreases and the estimation of task related brain activations show degradation. Hum Brain Mapp, 2007.

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.

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.

A feature-selective independent component analysis method for functional MRI

In this work, we propose a simple and effective scheme to incorporate prior knowledge about the sources of interest (SOIs) in independent component analysis (ICA) and apply the method to estimate brain activations from functional magnetic resonance imaging (fMRI) data. We name the proposed method as feature-selective ICA since it incorporates the features in the sample space of the independent components during ICA estimation. The feature-selective scheme is achieved through a filtering operation in the source sample space followed by a projection onto the demixing vector space by a least squares projection in an iterative ICA process. We perform ICA estimation of artificial activations superimposed into a resting state fMRI dataset to show that the feature-selective scheme improves the detection of injected activation from the independent component estimated by ICA. We also compare the task-related sources estimated from true fMRI data by a feature-selective ICA algorithm versus an ICA algorithm and show evidence that the feature-selective scheme helps improve the estimation of the sources in both spatial activation patterns and the time courses.

Sample dependence correction for order selection in fMRI analysis

Multivariate analysis methods such as independent component analysis (ICA) have been applied to the analysis of functional magnetic resonance imaging (fMRI) data to study the brain function. The selection of the proper number of signals of interest is an important step in the analysis to reduce the risk of over/underfilling. The inherent sample dependence in the spatial or temporal dimension of the fMRI data violates the assumption of independent and identically distributed (i.i.d.) samples and limits the usefulness of the practical formulations of information-theoretic order selection criteria. We propose a novel method using an entropy rate matching principle to mitigate the effects of such sample dependence in order selection. We perform order selection experiments on the simulated fMRI data and show that the incorporation of the proposed method significantly improves the accuracy of the order selection by different criteria. We also use the proposed method to estimate the number of latent sources in fMRI data acquired from multiple subjects performing a visuomotor paradigm. We show that the proposed method improves the order selection by alleviating the over-estimation due to the intrinsic smoothness and the effect of smooth preprocessing on the fMRI data

Group Study of Simulated Driving fMRI Data by Multiset Canonical Correlation Analysis

In this work, we apply a novel statistical method, multiset canonical correlation analysis (M-CCA), to study a group of functional magnetic resonance imaging (fMRI) datasets acquired during simulated driving task. The M-CCA method jointly decomposes fMRI datasets from different subjects/sessions into brain activation maps and their associated time courses, such that the correlation in each group of estimated activation maps across datasets is maximized. Therefore, the functional activations across all datasets are extracted in the order of consistency across different dataset. On the other hand, M-CCA preserves the uniqueness of the functional maps estimated from each dataset by avoiding concatenation of different datasets in the analysis. Hence, the cross-dataset variation of the functional activations can be used to test the hypothesis of functional-behavioral association. In this work, we study 120 simulated driving fMRI datasets and identify parietal-occipital regions and frontal lobe as the most consistently engaged areas across all the subjects and sessions during simulated driving. The functional-behavioral association study indicates that all the estimated brain activations are significantly correlated with the steering operation during the driving task. M-CCA thus provides a new approach to investigate the complex relationship between the brain functions and multiple behavioral variables, especially in naturalistic tasks as demonstrated by the simulated driving study.

On ICA of complex-valued fMRI: Advantages and order selection

Functional magnetic resonance imaging (fMRI) data are originally acquired as complex-valued images, while virtually all fMRI studies only use the magnitude of the data in the analysis. Since little is known for devising models for the phase, independent component analysis (ICA) emerges as a promising technique for data-driven analysis of fMRI data in its native complex form. In this paper, we compare the performance of ICA on real-valued and complex-valued fMRI data and show the advantages of the complex approach. We also develop complex-valued order selection scheme to improve the estimation of the number of independent components in complex-valued fMRI data using information-theoretic criteria. Comparisons on order selection using real-valued and complex-valued fMRI data demonstrate the more informative nature of complex data.

CCA for joint blind source separation of multiple datasets with application to group FMRI analysis

In this work, we propose a scheme for joint blind source separation (BSS) of multiple datasets using canonical correlation analysis (CCA). The proposed scheme jointly extracts sources from each dataset in the order of between-set source correlations. We show that, when sources are uncorrelated within each dataset and correlated across different datasets only on corresponding indices, (i) CCA on two datasets achieves BSS when the sources from the two datasets have distinct between-set correlation coefficients, and (ii) CCA on multiple datasets (M-CCA) achieves BSS with a more relaxed condition on the between-set source correlation coefficients compared to CCA on two datasets. We present simulation results to demonstrate the properties of CCA and M-CCA on joint BSS. We apply M-CCA to group functional magnetic resonance imaging (fMRI) data acquired from several subjects performing a visuomotor task and obtain interesting brain activations as well as their correlation profiles across different subjects in the group.