Functional brain network(FBN) has emerged as an effective tool in examining the functional abnormalities of the brain network in patients with brain disease. FBN is a mathematical representation of brain

in which the brain region is the node

and a functional connectivity between each pair of brain regions is an edge. The functional connectivity between the brain regions can reveal disease-related abnormalities in brain physiology. The FBN can be measured by several neuroimaging techniques. Functional magnetic resonance imaging(fMRI) is one of the most commonly used neuroimaging techniques. fMRI can detect the functional activities of the brain based on blood oxygen level dependent(BOLD) signals. Moreover

the resting-state fMRI can measure spontaneous fluctuations in BOLD signals

which is useful in exploring the abnormal brain activities in patients with brain disease. Conventional FBN studies of the resting-state fMRI assume the temporal stationarity of FBN across the duration of the scan. However

these static FBN studies ignore the existence of slightly different mental activities during the entire scan session. In addition

recent studies suggest that the FBN exhibit dynamic changes

which may contain powerful information. This paper presents a multi-task fused least absolute shrinkage and selection operation(Lasso) method to construct the dynamic FBN of a resting-state fMRI. The proposed multi-task fused Lasso can preserve the sparsity and temporal smoothness of the dynamic FBN. Specifically

we impose a sparsity constraint to the functional connectivity between the brain regions

which is based on some neurophysiological findings that a brain region only directly interacts with a few other brain regions in neurological processes. In addition

the adjacent fMRI sub-series are required to be similar

which is based on the temporal smoothness of the dynamic FBN. We first use the sliding window approach to generate a sequence of overlapping resting-state fMRI sub-series. Second

the proposed multi-task fused Lasso is used to construct the dynamic FBN. K-means clustering is applied to obtain cluster centroids of these FBNs from the same class. All the cluster centroids are grouped together to form a regression matrix. Finally

the FBNs of the samples are regressed against the regression matrix to obtain the regression coefficients

which serve as features for classification. The classification can further verify the effectiveness of our method for constructing the dynamic FBN. The overall framework can be used for brain disease classification based on fMRI data

in which the features are extracted from the constructed dynamic FBN. We use a public fMRI dataset to verify the classification performance of the dynamic FBN constructed by the multi-task fused Lasso. Three groups of patients with Alzheimer's disease(AD)

patients with early mild cognitive impairment(eMCI) and healthy controls(HCs) from the Alzheimer's disease neuroimaging initiative(ADNI) fMRI dataset are used for the experiment. Accuracy

sensitivity

and specificity are used to assess the classification performance. For the classification of the AD patients and HCs

our method achieves 92.31% accuracy

96.15% sensitivity

and 88.46% specificity. For the classification of the eMCI patients and HCs

our method achieves 80.00% accuracy

83.33% sensitivity

and 76.92% specificity. For the classification of the AD and eMCI patients

our method achieves 84.00% accuracy

84.62% sensitivity

and 83.33% specificity. Experiment results demonstrate the improved performance of our method compared with the static and the traditional dynamic FBN models. The improved classification performance of our method indicates that the features extracted by the multi-task fused Lasso have advantages over the static or the traditional dynamic FBN models for classification purposes. This study presents a method for constructing a dynamic FBN of resting-state fMRI. The overall framework can be used for brain disease classification based on the constructed dynamic FBN. The proposed method can preserve the sparsity and temporal smoothness of the dynamic FBN and improve the classification performance simultaneously. The proposed method may contribute to the diagnosis of brain diseases to some extent. The proposed method can lead to an improved understanding of the dynamic FBN and brain diseases. The multi-task fused Lasso can be used to construct the dynamic FBN

which can explore the useful dynamic information of functional connectivity. In addition

this method can be used for the classification of brain diseases based on fMRI data.