Gaussian interaction profile kernel similarity

Similar lncRNAs may be associated with different diseases that have similar pathological characteristics, and vice versa. Based on this assumption, the kernel similarity between lncRNAs and diseases can be calculated by the Gaussian interaction profile (GIP). The GIP kernel similarities were computed based on the lncRNA-disease interaction matrix obtained from the LncRNADisease dataset. The GIP similarities GKL(li,lj) of lncRNAs can be computed as follows:

where A(li) and A(lj) represent the ith and jth columns information in the association matrix A. Let λ be a parameter that can control the width of the kernel boundary and is represented by the average number of diseases associated with each lncRNA, which is defined as follows:

where nl denotes the number of lncRNAs.

Similarly, we can obtain the GIP kernel similarity of disease di and disease dj as follows:

where A(di) and A(dj) denote the ith and jth rows information in the lncRNA-disease association matrix A. Let λ be a parameter that can control the width of the kernel boundary and is represented by the average number of lncRNAs associated with each disease, which can be calculated as follows:

where nd denotes the number of diseases.