Resting-state functional connectivity (FC) is a crucial technique for exploring the functional organization of the brain (Chen et al, 2020; Van Den Heuvel and Pol, 2010). Brain disorders such as autism and depression often exhibit atypical connectivity patterns when compared to healthy individuals across various brain functional networks (Canario et al, 2021; Hu et al, 2021; Tse et al, 2024). The evaluation of FC is typically performed by analyzing the correlations among regions of interest (ROIs) within the brain, using the blood oxygen level-dependent (BOLD) signal obtained from functional magnetic resonance imaging (fMRI) scans. In recent years, advanced learning techniques, particularly deep learning, have been successfully utilized to analyze resting-state FC, which could aid in the development of diagnostic tools and enhance our understanding of the functional activity associated with various brain disorders (Hu et al, 2024; Khosla et al, 2019).

These techniques typically learn patterns from two distinct types of FC: static FC (sFC) and dynamic FC (dFC). sFC operates under the premise that FC among different brain regions remains consistent over time. It represents enduring patterns of brain connectivity and emphasizes the spatial characteristics of functional brain networks (Matkovič et al, 2023). In contrast, dFC typically employs a sliding window correlation (SWC) method to assess these connections. It assumes that FC can fluctuate over time and focuses on the spatio-temporal characteristics of functional brain networks (Preti et al, 2017; Shakil et al, 2016). Furthermore, researchers have emphasized the notion that it may be unrealistic to view brain connections as either completely static or entirely dynamic. This perspective stems from the understanding that the brain must maintain a balance between stability and adaptability (Liu et al, 2016). Consequently, researchers begun to integrate sFC and dFC in their learning of FC. For example, sFC and dFC were treated as multi-channel inputs and fused using convolutional operations for the early detection of mild cognitive impairment (MCI) (Kam et al, 2019). Long short-term memory networks were employed to capture the dynamic characteristics of dFC, directly concatenating the feature vectors of both sFC and dFC during the feature fusion stage (Tan et al, 2023). A Transformer architecture was utilized to extract feature representations of sFC and dFC separately, subsequently fusing these features through a cross-attention mechanism (Kan et al, 2023). Spatial and temporal cross-attention mechanisms were introduced to extract features from sFC and dFC, respectively (Sheng et al, 2023). A dual-stream convolutional neural network that incorporates both static and dynamic channels was proposed to facilitate the exchange of information between these two types of features (Huang et al, 2023). This combination of sFC and dFC has significantly enhanced our ability to detect brain disorders by leveraging their complementary information.

From a different perspective, there is a significant distinction between the time scales of fMRI signals used to generate sFC and dFC data. sFC is typically derived from signals recorded throughout the entire fMRI scans, while dFC is calculated by dividing the fMRI signals into smaller segments using equally sized sliding windows (Savva et al, 2019). In this context, sFC represents the computation of FC over a longer time scale with a single, large window, without any sliding. Conversely, dFC employs a smaller window size, reflecting a shorter time scale, to evaluate FC through a sliding window approach. But it is also important to note that brain disorders can exhibit variability in FCs, and atypical changes in functional signals may not be detectable across all time scales; instead, they may manifest at specific moments and particular scales (Fiorenzato et al, 2019; Liu et al, 2023a). Intuitively, in addition to utilizing sFCs and dFCs derived from signals at their respective time scales, we should also consider signals across a broader range of time scales to generate FCs for a more comprehensive analysis. Specifically, we can utilize multi-timescale functional connectivities (mFCs) among brain regions, represented as a collection of FCs, to identify brain disorders. This collection includes FC matrices obtained from fMRI signals across various time scales. It specifically encompasses sFC, and multiple dFCs that employ different sliding window sizes. However, learning to identify brain disorders from healthy individuals using mFCs presents a significant challenge, which arises from the complex spatio-temporal patterns that may emerge at specific times and particular scales within mFCs.

This study examines multiple instance learning (MIL) (Dietterich et al, 1997; Ilse et al, 2018) as a method for addressing the challenges associated with diagnosing brain disorders using mFC data. MIL is a weakly supervised learning approach in which a single class label is assigned to a bag of instances. This methodology has been applied for the early detection of MCI by analyzing brain functional networks, which include data from multiscale atlas-based dynamic functional networks (Liu et al, 2021) and brain functional networks with topological priors based on brain parcellation (Liu et al, 2023b). In this framework, based on the multiple instance assumption, a bag (which consist of various FC matrices across different scales from a subject) is labeled as indicative of a disorder if it contains at least one instance (such as an FC matrix from a segmented window within a specific time frame) that is associated with that label.

In this paper, we present a comprehensive methodology designed for the concurrent learning of mFCs aimed at identifying brain disorders. First, we segmented the entire resting-state fMRI scan signals using non-overlapping sliding windows of varying sizes, to construct mFCs between brain regions as the input for our model. Second, we developed a deep MIL network, specifically a two-stage multi-stream network (TMN), designed to capture mFC features across different timescales to distinguish brain disorders from healthy controls. By leveraging the multiple instance hypothesis, the TMN employs a multi-stream architecture to process inputs at various timescales, framing the classification of the subject's mFC as a two-stage MIL problem. In the initial stage of TMN, each stream is tasked with capturing FC features at a specific timescale. In the next phase, the features from all streams are combined to create a comprehensive representation for prediction. Third, we propose utilizing the inputXgrad method (Shrikumar et al, 2017) to explain the trained model and examine the significant FCs that contribute to the identification of brain disorders within the model.