Table 1 Summary of the experiments and results

Analysis of feature datasets of DNNs of different complexities in different biomedical disciplines

BraTS, TCGA, LINCS L1000, ISIC-2019, DR, COVID

Dense-UNet, MLP, VAE-MLP, SRGAN, ResNet, AlexNet, UNet, mCNN (Table S6), fMLP (Table S5)

Figs. 2–9, S9

MDA significantly outperforms existing data analysis methods such as t-SNE, UMAP, LLE and Isomap.

Robustness test of DNNs against noise

BraTS, COVID

Dense-UNet, U-Net, ResNet, AlexNet

Supplementary Figs. S42–S46

MDA shows the robustness of a DNN to noise through feature space visualization.

Generalizability test of DNNs

TCGA, LINCS L1000

MLP, VAE-MLP

Figs. 4, 5

MDA reveals the generalizability of DNN towards unknown datasets more accurately than other methods.

Neural collapse in DNNs for regression tasks

MNIST, TCGA

mCNN, fMLP

Supplementary Figs. S28, S29

Novel phenomena such as neural collapse can be discovered from MDA visualizations, which is not possible in results from other visualization methods.

Quantification of manifold structure

BraTS, MNIST

ResNet, mCNN

Supplementary Fig. S27

MDA preserves the high dimensional manifold structure in low dimensional representation more accurately than existing methods.

Neural network behavior for extrapolation task

MNIST, TCGA

mCNN, fMLP

Supplementary Figs. S34–S37

MDA offers meaningful visualization of the DNNs’ feature space in extrapolation tasks.

Change in DNNs’ feature space with epoch

BraTS, COVID

Dense-UNet, ResNet

Supplementary Fig. S22

MDA captures the gradual improvement of manifold properties of the DNN feature space over the course of the epochs.