## 1 Introduction  
The human brain is a complex system with different regions dedicated to different functions, which are locally segregated but globally integrated to process information. At present, many brain imaging techniques have been used to characterize and quantify the brain, such as functional magnetic resonance imaging (fMRI). It measures the changes in the blood oxygen level dependent (BOLD) signal, which can reveal correlations in neural activity between distant brain regions [1; 2; 3]. These correlations are of fundamental interest to neuroscientists for the comprehensive and noninvasive exploration of human brain. It was discovered that different brain regions actively interact with each other even when an individual subject is at rest, i.e., without performing any cognitive tasks. Therefore, resting-state fMRI (rs-fMRI) has been widely used to investigate regional associations of brain networks [4; 5], which can give an insight to the brain's functional organization. In particular, it can be used to examine altered or aberrant functional networks as a result of aging or brain disorders [6; 7; 8]. Functional connectivity (FC) based on fMRI data reflects the functionally integrated relationship between spatially separated brain regions. The analysis of FC has the potential to further our understanding of the neural mechanisms underlying brain development, psychiatric, and neurological disorders. The measurement of FC is critical for the identification of developmental differences and diagnosis of diseases [9; 10]. Previously, FC was assumed to be stationary over the scanning time, and most fMRI studies applied a static functional connectivity (sFC) analysis, i.e., calculating the correlations of whole fMRI time courses for the entire resting state scan. Now many works have shown that brain functional connectivity is dynamic over time, which is more successful in uncovering the disruptions of the human brain in disease conditions. In such analyses, brain functional connectivity can vary within a short period (e.g., tens of seconds). Thus, many methods have been proposed to estimate dynamic functional connectivity (dFC) [11; 12]. Among them, the sliding window based method is the most widely used [13; 14; 15; 16]. It is commonly assumed that the brain operates as a set of distributed sub-networks that co-activate over time; as a consequence, there is a great interest in identifying these intrinsic connectivity networks (ICNs) derived from FC data [17]. Identifying ICNs is based on the evidence that neural systems use parsimonious representations to efficiently process information while minimizing redundancy [17]. There are two most commonly used approaches to identify ICNs. One is the seed-based correlation analysis [18]. This method starts with a prior specified seed region or voxel, and calculates the correlations with other regions or voxels to get a connection map with respect to the seed. Since the choice of seed may affect connectivity findings towards specific, small or overlapping sub-systems, this method has a limited ability to study multiple systems simultaneously [19]. Another way to find the ICNs is based on data-driven methods, such as independent component analysis (ICA), independent vector analysis (IVA), principle component analysis (PCA), non-negative matrix factorization (NMF), and a sparse representation and dictionary learning (SRDL). However, it is still a great challenge to identify ICNs from FC data because the FC data usually have high dimension but a small sample size, i.e., n\(\triangleright\)p, where n is the sample size and p is the number of features. For such data, it is too difficult to discover the potential information contained in the data from a limited number of observations, which form a cognitive concept of the data or complete identification task [20].