Estimating high-order brain functional networks by correlation-preserving embedding

Brain functional network (FN) has emerged as a potential tool for identifying mental and neurological diseases. Traditional FN estimation methods such as Pearson's correlation (PC) and sparse representation (SR), despite their popularity, can only model low-order relationships between brain regions (i.e., nodes of FN), thus failing to capture more complex interaction in the brain. Recently, researchers proposed to estimate high-order FN (HoFN) and successfully used them in the early diagnosis of neurological diseases. In practice, however, such HoFN is constructed by directly considering the columns (or rows) of the adjacency matrix of low-order FN (LoFN) as node feature vectors that may contain some redundant or noisy information In addition, it is not really reflected whether the original low-order relationship is maintained during the construction of the HoFN. To address these problems, we propose correlation-preserving embedding (COPE) to re-code the LoFN prior to constructing HoFN. Specifically, we first use SR to construct traditional LoFN. Then, we embed the LoFN via COPE to generate the new node representation for removing the potentially redundant/noisy information in original node feature vectors and simultaneously maintaining the low-order relationship between brain regions. Finally, the expected HoFN is estimated by SR based on the new node representation. To verify the effectiveness of the proposed scheme, we conduct experiments on 137 subjects from the public Alzheimer's Disease Neuroimaging Initiative (ADNI) database to identify subjects with mild cognitive impairment (MCI) from normal controls. Experimental results show that the proposed scheme can achieve better performance than the baseline method.