In this paper, we introduce a simple and effective scheme to achieve joint blind source separation (BSS) of multiple datasets using multiset canonical correlation analysis (M-CCA) J. R. Kettenring, ..."Canonical analysis of several sets of variables", Biometrika , vol. 58, pp. 433-451, 1971. We first propose a generative model of joint BSS based on the correlation of latent sources within and between datasets. We specify source separability conditions, and show that, when the conditions are satisfied, the group of corresponding sources from each dataset can be jointly extracted by M-CCA through maximization of correlation among the extracted sources. We compare source separation performance of the M-CCA scheme with other joint BSS methods and demonstrate the superior performance of the M-CCA scheme in achieving joint BSS for a large number of datasets, group of corresponding sources with heterogeneous correlation values, and complex-valued sources with circular and non-circular distributions. We apply M-CCA to analysis of functional magnetic resonance imaging (fMRI) data from multiple subjects and show its utility in estimating meaningful brain activations from a visuomotor task.
The complex fast independent component analysis (c-FastICA) algorithm is one of the most ubiquitous methods for solving the ICA problems with complex-valued data. In this study, we extend the work of ...Bingham and Hyvarinen to the more general case of noncircular sources by deriving a new fixed-point algorithm that uses the information in the pseudo-covariance matrix. This modification provides significant improvement in performance when confronted with noncircular sources, specifically with sub-Gaussian noncircular signals such as binary phase-shift keying (BPSK) signals, where c-FastICA fails to achieve separation. We also present a rigorous local stability analysis that we use to quantify the effects of noncircularity on performance. Simulations are presented to demonstrate the effectiveness of our method.
The generalized Gaussian distribution (GGD) provides a flexible and suitable tool for data modeling and simulation, however the characterization of the complex-valued GGD, in particular generation of ...samples from a complex GGD have not been well defined in the literature. In this correspondence, we provide a thorough presentation of the complex-valued GGD by: (i) constructing the probability density function (pdf); (ii) defining a procedure for generating random numbers from the complex-valued GGD; and (iii) implementing a maximum likelihood estimation (MLE) procedure for the shape and covariance parameters in the complex domain. We quantify the performance of the MLE with simulations and actual radar data.
We present a method for supervised, automatic, and reliable classification of healthy controls, patients with bipolar disorder, and patients with schizophrenia using brain imaging data. The method ...uses four supervised classification learning machines trained with a stochastic gradient learning rule based on the minimization of Kullback-Leibler divergence and an optimal model complexity search through posterior probability estimation. Prior to classification, given the high dimensionality of functional MRI (fMRI) data, a dimension reduction stage comprising two steps is performed: first, a one-sample univariate t-test mean-difference T score approach is used to reduce the number of significant discriminative functional activated voxels, and then singular value decomposition is performed to further reduce the dimension of the input patterns to a number comparable to the limited number of subjects available for each of the three classes. Experimental results using functional brain imaging (fMRI) data include receiver operation characteristic curves for the three-way classifier with area under curve values around 0.82, 0.89, and 0.90 for healthy control versus nonhealthy, bipolar disorder versus nonbipolar, and schizophrenia patients versus nonschizophrenia binary problems, respectively. The average three-way correct classification rate (CCR) is in the range of 70%-72%, for the test set, remaining close to the estimated Bayesian optimal CCR theoretical upper bound of about 80% , estimated from the one nearest-neighbor classifier over the same data.
Complex ICA Using Nonlinear Functions Adali, T.; Hualiang Li; Novey, M. ...
IEEE transactions on signal processing,
09/2008, Volume:
56, Issue:
9
Journal Article
Peer reviewed
We introduce a framework based on Wirtinger calculus for nonlinear complex-valued signal processing such that all computations can be directly carried out in the complex domain. The two main ...approaches for performing independent component analysis, maximum likelihood, and maximization of non-Gaussianity-which are intimately related to each other-are studied using this framework. The main update rules for the two approaches are derived, their properties and density matching strategies are discussed along with numerical examples to highlight their relationships.
Event-related potential (ERP) studies of the brain's response to infrequent, target (oddball) stimuli elicit a sequence of physiological events, the most prominent and well studied being a complex, ...the P300 (or P3) peaking approximately 300 ms post-stimulus for simple stimuli and slightly later for more complex stimuli. Localization of the neural generators of the human oddball response remains challenging due to the lack of a single imaging technique with good spatial and temporal resolution. Here, we use independent component analyses to fuse ERP and fMRI modalities in order to examine the dynamics of the auditory oddball response with high spatiotemporal resolution across the entire brain. Initial activations in auditory and motor planning regions are followed by auditory association cortex and motor execution regions. The P3 response is associated with brainstem, temporal lobe, and medial frontal activity and finally a late temporal lobe “evaluative” response. We show that fusing imaging modalities with different advantages can provide new information about the brain.
Despite the known benefits of data-driven approaches, the lack of approaches for identifying functional neuroimaging patterns that capture both individual variations and inter-subject correspondence ...limits the clinical utility of rsfMRI and its application to single-subject analyses. Here, using rsfMRI data from over 100k individuals across private and public datasets, we identify replicable multi-spatial-scale canonical intrinsic connectivity network (ICN) templates via the use of multi-model-order independent component analysis (ICA). We also study the feasibility of estimating subject-specific ICNs via spatially constrained ICA. The results show that the subject-level ICN estimations vary as a function of the ICN itself, the data length, and the spatial resolution. In general, large-scale ICNs require less data to achieve specific levels of (within- and between-subject) spatial similarity with their templates. Importantly, increasing data length can reduce an ICN's subject-level specificity, suggesting longer scans may not always be desirable. We also find a positive linear relationship between data length and spatial smoothness (possibly due to averaging over intrinsic dynamics), suggesting studies examining optimized data length should consider spatial smoothness. Finally, consistency in spatial similarity between ICNs estimated using the full data and subsets across different data lengths suggests lower within-subject spatial similarity in shorter data is not wholly defined by lower reliability in ICN estimates, but may be an indication of meaningful brain dynamics which average out as data length increases.
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