Learning dictionaries from correlated data: Application to fMRI data analysis

Simultaneously capturing excessive variations and smooth dynamics of the underlying neural activity using spatiotemporal basis expansion and multisubject fMRI data

In the last decade, dictionary learning (DL) has gained popularity over independent component analysis (ICA) within the blind source separation (BSS) framework for functional magnetic resonance imaging (fMRI) signals. Despite its rising popularity, a primary challenge in DL remains model fitting. It is susceptible to overfitting because the conventional loss function strives to correspond too closely to the training data. However, in the case of multi-subject (MS) analysis, it becomes imperative to overfit in order to acquire the source diversities across different brains. In this paper, an attempt has been made to resolve this predicament by concurrently preserving and mitigating the effect of high variance. A novel algorithm named joint analysis and synthesis DL (JASDL) has been proposed that simultaneously learns the overfitted trends to retain the data-centric cross-subject diversities and wellfitted trends by adequately regularizing the model complexity. This fusion was achieved by benefiting from modeling each subject's data in terms of both spatiotemporal (ST) prior information (PI) and MS-ST components. The PI consisted of biological priors derived from neuroscience knowledge, such as brain network templates, and mathematical priors derived from basis functions, such as three-dimensional (3D) cubic basis splines (B-splines). In contrast, MS-ST components were estimated using the computationally most parsimonious sparse ST blind source separation (ssBSS) method. Using the proposed analysis/synthesis cost function that exploits tri and quad-factorization for matrix approximation, the JASDL algorithm can model temporal smoothness and spatial reduction of false positives while retaining MS variations. Its efficacy was evaluated by comparing it with existing DL techniques using both experimental and synthetic fMRI datasets. Overall, the mean of correlation and F-score was found to be [Formula: see text] higher for the JASDL synthesis dictionary than the state-of-the-art subject-wise sequential DL (swsDL).

Three layered sparse dictionary learning algorithm for enhancing the subject wise segregation of brain networks

Independent component analysis (ICA) and dictionary learning (DL) are the most successful blind source separation (BSS) methods for functional magnetic resonance imaging (fMRI) data analysis. However, ICA to higher and DL to lower extent may suffer from performance degradation by the presence of anomalous observations in the recovered time courses (TCs) and high overlaps among spatial maps (SMs). This paper addressed both problems using a novel three-layered sparse DL (TLSDL) algorithm that incorporated prior information in the dictionary update process and recovered full-rank outlier-free TCs from highly corrupted measurements. The associated sequential DL model involved factorizing each subject's data into a multi-subject (MS) dictionary and MS sparse code while imposing a low-rank and a sparse matrix decomposition restriction on the dictionary matrix. It is derived by solving three layers of feature extraction and component estimation. The first and second layers captured brain regions with low and moderate spatial overlaps, respectively. The third layer that segregated regions with significant spatial overlaps solved a sequence of vector decomposition problems using the proximal alternating linearized minimization (PALM) method and solved a decomposition restriction using the alternating directions method (ALM). It learned outlier-free dynamics that integrate spatiotemporal diversities across brains and external information. It differs from existing DL methods owing to its unique optimization model, which incorporates prior knowledge, subject-wise/multi-subject representation matrices, and outlier handling. The TLSDL algorithm was compared with existing dictionary learning algorithms using experimental and synthetic fMRI datasets to verify its performance. Overall, the mean correlation value was found to be 26 % higher for the TLSDL than for the state-of-the-art subject-wise sequential DL (swsDL) technique.

A novel subject-wise dictionary learning approach using multi-subject fMRI spatial and temporal components

The conventional dictionary learning (DL) algorithms aim to adapt the dictionary/sparse code to individual functional magnetic resonance imaging (fMRI) data. Thus, lacking the capability to consolidate the spatiotemporal diversities offered by other subjects. Considering that subject-wise (sw) data matrix can be decomposed into the sparse linear combination of multi-subject (MS) time courses and MS spatial maps, two new algorithms, sw sequential DL (swsDL) and sw block DL (swbDL), have been proposed. They are based on the novel framework, defined by the mixing model, where base matrices prepared by operating a computationally fast sparse spatiotemporal blind source separation method over multiple subjects are employed to adapt the mixing matrices to sw training data. They solve the optimization models formulated using [Formula: see text]/[Formula: see text]-norm penalization/constraints through dictionary/sparse code pair update and alternating minimization approach. They are unique because no existing sparse DL method can incorporate MS spatiotemporal components while updating sw atoms/sparse codes, which can eventually be assembled using neuroscience knowledge to extract group-level dynamics. Various fMRI datasets are used to evaluate and compare the performance of the proposed algorithms with existing state-of-the-art algorithms. Specifically, overall, a [Formula: see text] increase in the mean correlation value and [Formula: see text] reduction in the mean computation time exhibited by swsDL and swbDL, respectively, over the adaptive consistent sequential dictionary algorithm.

Sequential Dictionary Learning From Correlated Data: Application to fMRI Data Analysis

Sequential dictionary learning via the K-SVD algorithm has been revealed as a successful alternative to conventional data driven methods, such as independent component analysis for functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are however structured data matrices with notions of spatio-temporal correlation and temporal smoothness. This prior information has not been included in the K-SVD algorithm when applied to fMRI data analysis. In this paper, we propose three variants of the K-SVD algorithm dedicated to fMRI data analysis by accounting for this prior information. The proposed algorithms differ from the K-SVD in their sparse coding and dictionary update stages. The first two algorithms account for the known correlation structure in the fMRI data by using the squared Q, R-norm instead of the Frobenius norm for matrix approximation. The third and last algorithms account for both the known correlation structure in the fMRI data and the temporal smoothness. The temporal smoothness is incorporated in the dictionary update stage via regularization of the dictionary atoms obtained with penalization. The performance of the proposed dictionary learning algorithms is illustrated through simulations and applications on real fMRI data.