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A deep manifold-regularized learning model for improving phenotype prediction from multi-modal data

A preprint version of the article is available at bioRxiv.


The phenotypes of complex biological systems are fundamentally driven by various multi-scale mechanisms. Multi-modal data, such as single-cell multi-omics data, enable a deeper understanding of underlying complex mechanisms across scales for phenotypes. We have developed an interpretable regularized learning model, deepManReg, to predict phenotypes from multi-modal data. First, deepManReg employs deep neural networks to learn cross-modal manifolds and then to align multi-modal features onto a common latent space. Second, deepManReg uses cross-modal manifolds as a feature graph to regularize the classifiers for improving phenotype predictions and also for prioritizing the multi-modal features and cross-modal interactions for the phenotypes. We apply deepManReg to (1) an image dataset of handwritten digits with multi-features and (2) single-cell multi-modal data (Patch-seq data) including transcriptomics and electrophysiology for neuronal cells in the mouse brain. We show that deepManReg improves phenotype prediction in both datasets, and also prioritizes genes and electrophysiological features for the phenotypes of neuronal cells.

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Fig. 1: DeepManReg: a deep manifold-regularized learning model for improving phenotype prediction from multi-modal data.
Fig. 2: Multi-modal feature alignment of handwritten digits.
Fig. 3: Regularized classification results for the mfeat digits dataset.
Fig. 4: The network showing the relationships across two modalities (genes and electrophysiology).
Fig. 5: Regularized classification results for single-cell multi-modal data in the mouse visual cortex.

Data availability

The multiple-features (mfeat) dataset is available from ref. 11. The Patch-seq transcriptomics data and electrophysiological data are available from ref. 12. The simulated multi-omics data and gene regulatory network (that is, the example model data of dyngen for five genes) are available from ref. 16. Source data are provided with this paper.

Code availability

Code for deepManReg implementation and data analysis are available at An interactive version of the code base is provided in ref. 38.


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We thank K. Huynh (Stony Brook University) for useful discussions. This work was supported by National Institutes of Health grants nos. R01AG067025, R21CA237955 and U01MH116492 to D.W. and U54HD090256 to Waisman Center. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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Authors and Affiliations



D.W. and N.D.N. conceptualized the study. D.W. and N.D.N. designed the algorithm and methodology. N.D.N. and J.H. implemented software. D.W., N.D.N. and J.H. performed analysis. D.W., N.D.N. and J.H. wrote the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Daifeng Wang.

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The authors declare no competing interests.

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Peer review information

Nature Computational Science thanks James J. Cai, Bamdev Mishra and Daniel Osorio for their contribution to the peer review of this work. Handling editor: Ananya Rastogi, in collaboration with the Nature Computational Science team.

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Supplementary information

Supplemental Materials

Supplementary Figs. 1–6, Algorithm and Table 1.

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Supplementary Data 1

Prioritized top 20 genes and top 5 electrophysiological features of cell layers in the mouse visual cortex by feature importance scores of deepManReg.

Source data

Source Data Fig. 2

Numerical data for scatter plots in Fig. 2

Source Data Fig. 3

Numerical data for the plots in Fig. 3; source data for panels a, b and c are in separate folders.

Source Data Fig. 5

Numerical data for the plots in Fig. 5; source data for panels a, b and c are in separate folders.

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Nguyen, N.D., Huang, J. & Wang, D. A deep manifold-regularized learning model for improving phenotype prediction from multi-modal data. Nat Comput Sci 2, 38–46 (2022).

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