where \(\mathbb{M}_{pos}^{k}\), \(\mathbb{M}_{neg}^{k}\) represent the \(k\)-th molecule of positive molecule set and negative molecule set which are used to validate the relevance, \(K_{pos}\)\(K_{neg}\) represent the molecule number of \(\mathbb{M}_{pos}^{k}\), \(\mathbb{M}_{neg}^{k}\)\(\mathbf{1}(\cdot)\) denotes that when satisfying the condition in parentheses, the function outputs 1, otherwise 0.
The value scope of the calculated \(Diff_g\) is from -1 to 1. The situation when \(Diff_g>0\) denotes that \(g\) shows positive relevance to the property. As \(Diff_g\) gets greater, the relevance of the obtained fragment \(g\) is much higher.
Construction and verification of property relation map. The property relation map was constructed with the obtained attribution fragments of all forty-two tasks. We considered that property tasks with similar attribution fragments are generally more related. Therefore, we clustered all attribution fragments in the form of Morgan fingerprints [40\cite{bib65}], and calculated how similar the attribution fragments are between each task pair. The calculation method is as follows: For each cluster, we determined whether the fragments of task \(a\) and task \(b\) appeared in this cluster. If the fragments of the two tasks both appeared, we recorded the number of fragments that appeared, respectively. When all the clusters were traversed, we summarized the total number of fragments for task \(a\) and task \(b\) that appeared in the same clusters, and calculated the ratios of these fragments to the total number of fragments for the two tasks. The two ratios were averaged as the similarity based on attribution fragments for task \(a\) and task \(b\). With the above calculation process, the similarity between every two tasks was obtained, and then the property relation map \(\mathbb{F}\) was constructed (the shape of \(\mathbb{F}\) is 42*41). The relationship between the task and itself is the closest (that is, 1) by default. In the following verification process, we do not consider the relationship between the task and itself.
In the verification process, we first calculated the similarity matrix \(\mathbb{S}\) of all \(N_{42}^2\) task pairs (the shape of \(\mathbb{S}\) is 42*41) based on transfer learning [30\cite{bib25}], and used the approximation degree of \(\mathbb{F}\) and \(\mathbb{S}\) to verify the reliability of the property relation map. However, to unify the measure dimension of the two different methods, we needed to make a transform rule to re-rank the similarity matrix  \(\mathbb{F}\) and \(\mathbb{S}\). For each target task \(j\), the similarity sequence \(\mathbb{F}^j\) and \(\mathbb{S}^j\), which denote the similarities of the target task \(j\) and the other forty-one source tasks with the two methods, were sorted according to the numerical values, respectively. The task with the highest value ranks 41, the one with the lowest value ranks 1, and the rest of the tasks ranks by analogy. Therefore, for the target task \(j\), we got two 41-dimensional rank sequences \(F^j\) and \(S^j\). The above transformation was applied to all the forty-two target tasks, and then we got the rank matrix \(F\) and \(S\), both with the shape 42*41.