Figure 2.

Overview of our matrix decomposition model for predicting effective drug-virus associations

Totals of 850 associations for $n=126$ different BSAs and $m=80$ distinct viruses were collected from the Andersen et al.¹⁷ database. The observed associations were arranged into an $n\times m$ matrix Y by setting $y_{ij}=1$. Unobserved associations were encoded with zeros. Our algorithm decomposes the matrix Y into the product of two matrices, P (of size $n\times k$) and Q (of size $k\times m$). By multiplying the matrices P and Q, we obtain $\hat{Y}$, which models Y, where all the entries are replaced with real numbers—these correspond to our predicted scores. Rows of P are the BSA feature vectors (or BSA signature); columns of Q are the virus feature vectors (virus signature). The lower illustration depicts how our model discovers a low-dimensional signature vector for the antiviral drug zanamivir, and a low-dimensional signature vector for SARS-CoV-2. The dot product of these two signatures is the predicted efficacy of zanamivir against SARS-CoV-2.