NND is a toolkit that unmixes bulk tumor samples. Given a non-negative bulk RNA expression matrix B \in R_+^{m x n}, where each row i is a gene, each column j is a tumor sample, our goal is to infer an expression profile matrix C \in R_+^{m x k}, where each column l is a cell community, and a fraction matrix F \in R_+^{k x n}, such that:

  B ~= C F. 

To be more specific, NND solves the following problem:

min_{C, F} || B - C F ||_{Fr}^2, 

      s.t. C_{il} >= 0,              i=1,...,m, l=1,...,k,

           F_{lj} >= 0,              l=1,...,k, j=1,...,n,

           \sum_{l=1}^{k} F_{lj} = 1,           j=1,...,n.

NND transfers the above problem equivalently into optimizating a neural network, which can be solved using through gradient descent.

NND has the following functions:

• compress_module: Integrate gene module knowledge to reduce noise.
• estimate_number: Estimate the number of cell populations automatically.
• estimate_clones: Utilize core NND algorithm to unmix the cell populations.
• estimate_marker: Estimate other biomarkers of cell populations given bulk marker data.

The code runs on Python 3, and requires cvxopt and PyTorch. Most other packages are available in the Anaconda.

You can find a brief tutorial with code and output in tutorial.ipynb.

If you find NND helpful, please cite the following paper: Yifeng Tao, Haoyun Lei, Adrian V. Lee, Jian Ma, and Russell Schwartz. Neural network deconvolution method for resolving pathway-level progression of tumor clonal expression programs with application to breast cancer brain metastases. Frontiers in Physiology, 11:1055. 2020.

@article{tao2020nnd,
  title = {Neural Network Deconvolution Method for Resolving Pathway-Level Progression of Tumor Clonal Expression Programs with Application to Breast Cancer Brain Metastases},
  author = {Tao, Yifeng and Lei, Haoyun and Lee, Adrian V. and Ma, Jian and Schwartz, Russell},
  journal = {Frontiers in Physiology},
  volume = {11},
  pages = {1055},
  year = {2020},
  url = {https://www.frontiersin.org/article/10.3389/fphys.2020.01055},
  doi = {10.3389/fphys.2020.01055},
  issn = {1664-042X},
}

We further developed the NND method into Robust and Accurate Deconvolution (RAD), which follows the same APIs to NND, but is faster and more accurate compared with NND and competing algorithms.