  Automated ranking of pre-trained Deep Neural Networks (DNNs) reduces the
required time for selecting optimal pre-trained DNN and boost the
classification performance in transfer learning. In this paper, we introduce a
novel algorithm to rank pre-trained DNNs by applying a straightforward
distance-based complexity measure named Separation Index (SI) to the target
dataset. For this purpose, at first, a background about the SI is given and
then the automated ranking algorithm is explained. In this algorithm, the SI is
computed for the target dataset which passes from the feature extracting parts
of pre-trained DNNs. Then, by descending sort of the computed SIs, the
pre-trained DNNs are ranked, easily. In this ranking method, the best DNN makes
maximum SI on the target dataset and a few pre-trained DNNs may be rejected in
the case of their sufficiently low computed SIs. The efficiency of the proposed
algorithm is evaluated by using three challenging datasets including Linnaeus
5, Breast Cancer Images, and COVID-CT. For the two first case studies, the
results of the proposed algorithm exactly match with the ranking of the trained
DNNs by the accuracy on the target dataset. For the third case study, despite
using different preprocessing on the target data, the ranking of the algorithm
has a high correlation with the ranking resulted from classification accuracy.
