Conventional functional connectivity (FC), referred to as low-order FC, estimates temporal correlation of the resting-state functional magnetic resonance imaging (rs-fMRI) time series between any pair of brain regions, simply ignoring the potentially high-level relationship among these brain regions. A high-order FC based on "correlation's correlation" has emerged as a new approach for abnormality detection of brain disease. However, separate construction of the low- and high-order FC networks overlooks information exchange between the two FC levels. Such a higher-level relationship could be more important for brain diseases study. In this paper, we propose a novel framework, namely "hybrid high-order FC networks" by exploiting the higher-level dynamic interaction among brain regions for early mild cognitive impairment (eMCI) diagnosis. For each sliding window-based rs-fMRI sub-series, we construct a whole-brain associated high-order network, by estimating the correlations between the topographical information of the high-order FC sub-network from one brain region and that of the low-order FC sub-network from another brain region. With multi-kernel learning, complementary features from multiple time-varying FC networks constructed at different levels are fused for eMCI classification. Compared with other state-of-the-art methods, the proposed framework achieves superior diagnosis accuracy, and hence could be promising for understanding pathological changes of brain connectome
