| Functional magnetic resonance imaging(fMRI)is a key technology for noninvasive neuroscience research.Blind source separation(BSS)algorithms are widely used in fMRI data analyses.Most of the BSS algorithms such as independent component analysis(ICA)and tensor canonical polyadic decomposition(CPD)are adaptive.These algorithms can theoretically converge to the global optimal solution.However,due to the influence of noise and other factors,these algorithms often converge to different local optimal solutions,so it is important to evaluate the reproducibility of the extracted fMRI components with BSS.Current techniques for evaluating the reproducibility of fMRI components extracted with BSS algorithm are mostly based on a single mode,ignoring the complexity of reproducibility analyses caused by the interaction between two or more modes of data.In order to analyze the reproducibility of the fMRI components extracted with BSS algorithms from two or more modes,tensor clustering algorithms was proposed.The main contributions of this dissertation are as follows:(1)In order to evaluate the reproducibility of ICA algorithm(assuming that the source components are independent of each other),Correlation-Based Tensor Clustering(CBTC)algorithm was proposed.For a given ICA algorithm,the same fMRI data matrix is decomposed K times(each initialization is different),and extracts R components each time;each component is back-projected through the coefficient matrix to form a rank-one matrix.The matrix contains both spatial and temporal information of estimated brain networks corresponding to components and coefficients matrix.The feature to be clustered is a tensor,so tensor clustering algorithm needs to be used;because independent source components are mutual independence across components,correlation coefficients can accurately describe the distance between components,so this study proposed a correlation-based tensor clustering algorithm to cluster R×K rank-1 matrices.The number of clusters is R.When the average of the intra-cluster similarity minus the inter-cluster similarity is closer to 1,the estimation result is more repeatable,otherwise the opposite is true.The effectiveness of this algorithm is demonstrated by simulation and real data.Based on the reproducibility analysis of the independent components,the reliable altered brain areas between diabetic patients and healthy subjects were found.(2)ICA algorithm is widely used in fMRI data processing.The existing ICA algorithm application model cannot estimate all brain networks and the accuracy of the estimation results is relatively low.Based on the reproducibility analysis,this paper proposes a new fMRI group analysis mode,that is,Iterative Subtraction ICA(IS-ICA)algorithm.In the IS-ICA algorithm,the fMRI group analysis method proposed in(1)is used to evaluate the reproducibility of the estimation results;then the Randomly Partition Concatenated ICA(RPC-ICA)algorithm is used to improve the accuracy of highly repeatable components;next,the back projection results of the highly repeatable components is subtracted from the matrix to be decomposed to form a new matrix to be decomposed;Repeat the above process until the highly repeatable components can not be extracted.The IS-ICA algorithm removes the highly repeatable components(brain network,artifacts),so that the lower energy components can be estimated with ICA algorithm,thereby estimating more effective brain network components.In the IS-ICA algorithm,in order to overcome the shortcomings brought by Principal Component Analysis(PCA)dimensionality reduction and improve the accuracy of the estimations,this paper proposed the RPC-ICA algorithm,which divides the decomposition matrix into blocks,each block is decomposed by ICA without dimensionality reduction;The highly repreatable components are used as references,and the reference-based ICA algorithm is iteratively applied to each block to be decomposed,thereby improving the accuracy of the estimated brain network.Compared with traditional ICA algorithm,IS-ICA algorithm can extract more and more accurate components.The spatial distribution of the brain network estimated with IS-ICA is clearer,with fewer noise points,stronger non-Gaussian,and less sensitive to the selection of thresholds and parameters.(3)In order to evaluate the reproducibility of correlated source components represented by CPD algorithms,tensor spectral clustering(TSC)algorithm was proposed.In this algorithm the same Mth-order fMRI data tensor is decomposed K times with different initializations and R components are extracted each time.For each component the M components are outer producted to forms a rank-1 tensor,TSC is used to perform cluster analysis on R×K rank-1 tensors.In TSC,firstly,the reproducibility information of different modes is merged through the outer product of the similarity matrix to construct a transition tensor that fuses multi-mode reproducibility information;higher-order singular value decomposition is used to reduce the dimensionality of the transition tensor,and then combined with hierarchical clustering to realize the reproducibility analyses of related source components;in the clustering results,the closer the similarity within the cluster is to 1,the higher the reproducibility of the component.The effectiveness of the proposed method is proved with mathematical demonstration,data simulation and practical application.The proposed method was applied to unconstrained CPD and sparse constrainted non-negative tensor factorization.These methods exhibit promising performance in the analysis and processing of various neuroimag data such as fMRI data induced by naturalistic stimuli and resting-state fMRI data in the time-frequency domain. |
