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Microbes & Immunity Big data and DNN-based DTI model in CHP

   elements such as TFs, genes, miRNAs, and lncRNA is
   deleted by AIC in Equations XXII-XXV, its corresponding
   component in R will be reduced to zero. To employ KEGG
   pathways annotation for the core signaling pathways, real

ζ  11 … ζ 1y … ζ 1Y  ρ 11 … ρ 1y … ρ 1Y 
    GWGEN should be truncated to a core GWGEN with
   6,000 significant components based on their significance


 ζ … ζ … ζ  ρ … ρ … ρ from the energy perspective. Based on singular value

 1 l ly lY  m 1 my m mY  decomposition, the network structure projection method,
  
 …  …  PNP, can be described with Equation XXLIII:
  ζ L 1 ζ Ly … ζ LY     ρ M 1 ρ My … ρ MY   R =ΛΣΘ T (XLIII)
 
  ( KL MN *X YZ) (++ + + + ) (KL MN++ + ) ((*K LM N+ + + ) ,
  where R , Λ
  Θ (XY Z++ )*(X YZ++ ) , and Σ is a diagonal matrix (i.e.
 κ 11 … κ 1 y … κ 1 Y 
  Σ = diag[σ ,σ ,…,σ ,…,σ X+Y+Z ]), including X+Y+Z non-
1
i
2
  negative singular values of R with descending order

 κ … κ … κ σ ≥ …≥ σ ≥ … ≥ σ ≥0. In this context, diag(σ σ )

 n1 ny nY  1 I X+Y+Z 1, 2
  σ 1 0
 …  indicates the diagonal matrix of σ and σ (i.e., 0 σ ).
1
2
  κ N1 κ Ny … κ NY   2
The eigenvalue expression (network energy) fraction (E )
(XLI) can be defined by the normalization in Equation XLIV. I
R m−g , R m−m , and R stand for the matrices associated Σ σ 2
I
m−l
i=1
with transcriptional regulatory abilities of miRNAs on E = XY Z++ i 2 ≥ 085. (XLIV)
I
genes, miRNAs, and lncRNAs, respectively, as shown in Σ c=1 σ c
Equation XLII. We selected the top I singular vectors of Θ, such that the
I
Σ σ i ≥ 0 accounts for at least 85% of the total energy. The
i=1
   minimal I was chosen to ensure this proportion. These
   selected singular vectors are then used to construct the
   principal network structure, which captures 85% of the
   network’s energy. Subsequently, the projection of each row
 ω 11 … ω 1z … ω 1Z  λ 11 … λ 1z … λ 1Z 
    in R onto the top I singular vectors is performed. This
   means that all edges of each node (i.e., each protein, gene,


 ω … ω … ω  λ … λ … λ miRNA, and lncRNA) in real GWGENs should be

 1 l lz lZ  m 1 mz m mZ  projected to the top I singular vectors as the following
  
 …  …  equation (Equation XLV):
  ω L 1 ω Lz … ω LZ     λ M 1 λ Mz … λ MZ   Project (, = r ⋅θ T
bi)
  R b i
  for b = 1,2,…,K + L + M + N and i = 1,2,…,I (XLV)
 
  where r represents the b-th row vector of R and i
b
 τ 11 … τ z 1 … τ 1 Z  denotes the i-th column vector of Θ, which is the right-
 
  singular vector of Θ. We further define the 2-norm

τ  … τ … τ projection value of each node to the top I right singular

 n1 nz nZ  vectors using Equation XLVI.
 
 …  I 1
  τ N1 τ Nz … τ NZ   D R b () =  ∑ ( project R ( , bi) 2   2
)
(XLII)  i=1 
In the network matrix R in Equation XXXVIII or for b = 1,2,…, K + L + M + N (XLVI)
real GWGENs of CHP and non-CHP, if an interaction In conclusion, we can obtain the projection values
between any two proteins or regulation between any two of all nodes, including proteins, genes, miRNAs, and
Volume 2 Issue 2 (2025) 86 doi: 10.36922/mi.4620