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Uncurl is a python package for analyzing single-cell RNA-seq data.


Uncurl can be installed from PyPI: pip install uncurl-seq.

Alternatively, uncurl can be installed from source: After cloning the repository, first run pip install -r requirements.txt to install the required libraries. Then, run pip install .

Requirements: numpy, scipy, cython, scikit-learn

Tested on python 2.7, 3.5+ on Linux.

For parallel state estimation, OpenMP is required.

To run tests: python test

After the python package is installed, uncurl can be used from R using reticulate. See Using UNCURL in R


See the examples folder for example scripts, and the notebooks folder for Jupyter notebooks.

For a detailed tutorial, see Tutorial.ipynb in the notebooks folder.

Full documentation


Presented at ISMB 2018.

Mukherjee, S., Zhang, Y., Fan, J., Seelig, G. & Kannan, S. Scalable preprocessing for sparse scRNA-seq data exploiting prior knowledge. Bioinformatics 34, i124–i132 (2018).


State Estimation

The simplest way to use state estimation is to use the run_state_estimation function, which can be used to call any of the state estimation functions for different distributions. The possible distributions are 'Poiss', 'LogNorm', 'Gaussian', 'NB' (negative binomial), or 'ZIP' (zero-inflated Poisson). Generally, 'Poiss' is recommended for sparse or count-valued datasets. Currently the NB and ZIP options are unsupported.

Before running state estimation, it is often a good idea to subset the number of genes. This can be done using the function max_variance_genes, which bins the genes by mean expression, and selects a top fraction of genes by variance from each bin. It also removes genes that have all zero expression counts.


import numpy as np
from uncurl import max_variance_genes, run_state_estimation

data = np.loadtxt('counts.txt')

# sparse data (matrix market format)
data_sparse ='matrix.mtx')

# max variance genes, default parameters
genes = max_variance_genes(data_sparse, nbins=5, frac=0.2)
data_subset = data_sparse[genes,:]

M, W, ll = run_state_estimation(data_subset, clusters=4, dist='Poiss', disp=False, max_iters=30, inner_max_iters=100, initialization='tsvd', threads=8)

M2, W2, cost = run_state_estimation(data_subset, clusters=4, dist='LogNorm')


run_state_estimation is actually a wrapper around several other functions for state estimation.

The poisson_estimate_state function is used to estimate cell types using the Poisson Convex Mixture Model. It can take in dense or sparse matrices of reals or integers as input, and can be accelerated by parallelization. The input is of shape (genes, cells). It has three outputs: two matrices M and W, and ll, the negative log-likelihood. M is a (genes, clusters) matrix, and W is a (clusters, cells) matrix where each column sums to 1. The outputs W and M*W can be used for further visualization or dimensionality reduction, as described latter.

There are a number of different initialization methods and options for poisson_estimate_state. By default, it is initialized using truncated SVD + K-means, but it can also be initialized using poisson_cluster or just K-means.


from uncurl import max_variance_genes, poisson_cluster, poisson_estimate_state

# poisson state estimation
M, W, ll = poisson_estimate_state(data_subset, 2)

# labels in 0...k-1
labels = W.argmax(0)

# optional arguments
M, W, ll = poisson_estimate_state(data_subset, clusters=2, disp=False, max_iters=30, inner_max_iters=150, initialization='tsvd', threads=8)

# initialization by providing means and weights
assignments_p, centers = poisson_cluster(data_subset, 2)
M, W, ll = poisson_estimate_state(data_subset, 2, init_means=centers, init_weights=assignments_p)

The log_norm_nmf function is a wrapper around scikit-Learn's NMF class that performs a log-transform and per-cell count normalization before running NMF. It returns two matrices, W and H, which correspond to the M and W returned by poisson_estimate_state. It can also take sparse matrix inputs.


from uncurl import log_norm_nmf

W, H = log_norm_nmf(data_subset, k=2)

Distribution Selection

The DistFitDataset function is used to determine the distribution of each gene in a dataset by calculating the fit error for the Poisson, Normal, and Log-Normal distributions. It currently only works for dense matrices. For large datasets, we recommend taking a small random subset of less than 1000 cells.


import numpy as np
from uncurl import DistFitDataset

data = np.loadtxt('counts.txt')

fit_errors = DistFitDataset(data)

poiss_fit_errors = fit_errors['poiss']
norm_fit_errors = fit_errors['norm']
lognorm_fit_errors = fit_errors['lognorm']

The output, fit_errors, contains the fit error for each gene, for each of the three distributions when fitted to the data using maximum likelihood.

Qualitative to Quantitative Framework

The qualNorm function is used to convert binary (or otherwise) data with shape (genes, types) into starting points for clustering and state estimation.


from uncurl import qualNorm
import numpy as np

data = np.loadtxt('counts.txt')
bin_data = np.loadtxt('binary.txt')
starting_centers = qualNorm(data, bin_data)
assignments, centers = poisson_cluster(data, 2, init=starting_centers)


The poisson_cluster function does Poisson clustering with hard assignments. It takes an array of features by examples and the number of clusters, and returns two arrays: an array of cluster assignments and an array of cluster centers.


from uncurl import poisson_cluster
import numpy as np

# data is a 2d array of floats, with dimensions genes x cells
data = np.loadtxt('counts.txt')
assignments_p, centers = poisson_cluster(data, 2)


Imputation is done by simply multiplying the resulting matrices M and W, resulting in a new matrix of the same dimensionality as the original.

For an example using UNCURL for imputation, see this notebook.

Dimensionality Reduction

We recommend using standard dimensionality reduction techniques such as t-SNE and PCA. They can be run on either W or MW = When running t-SNE on MW, we suggest taking the log and then doing a PCA or truncated SVD, as you would do for the original input data. This is the basis for the UNCURL + tSNE results in our paper. When using t-SNE on W, we suggest using a symmetric relative entropy metric, which is available as uncurl.sparse_utils.symmetric_kld (this can be passed in to scikit-learn's t-SNE implementation). Cosine distance has also worked better than Euclidean distance on W.

Alternatively, we provide an MDS-based dimensionality reduction method that takes advantage of the convex mixture model. It is generally less accurate than t-SNE, but much faster. See docs for unsupported methods.

Lineage Estimation & Pseudotime

The output MW of UNCURL can be used as input for other lineage estimation tools.

We also have implemented our own lineage estimation tools but have not thoroughly validated them. See docs for unsupported methods.

Using UNCURL in R

UNCURL has been tested in R using the reticulate library. There first has to be a python installation that has uncurl installed. Example:



# The 'import' function is provided by reticulate, and allows python libraries to be imported in R.
uncurl <- import("uncurl")

# Say that 'sce' is a SingleCellExperiment object.
# See
# for an example.

data <- counts(sce)
k = 10
results <- uncurl$run_state_estimation(data, k)

# m and w are matrices of numeric values.
# m is of shape (genes, k), an w is of shape (k, cells).
m <- results[[1]]
w <- results[[2]]

# This gets the cluster labels using argmax.
cluster_labels <- apply(w, 2, which.max)


Unsupported methods included in the package:

Miscellaneous uncurl parameters (non-default parameters and things we tried):

Included datasets

Real datasets:

10x_pooled_400.mat: 50 cells each from 8 cell types: CD19+ b cells, CD14+ monocytes, CD34+, CD56+ NK, CD4+/CD45RO+ memory t, CD8+/CD45RA+ naive cytotoxic, CD4+/CD45RA+/CD25- naive t, and CD4+/CD25 regulatory t. Source: 10x genomics.

GSE60361_dat.mat: subset of data from Zelsel et al. 2015.

SCDE_test.mat: data from Islam et al. 2011.

Synthetic datasets:

BranchedSynDat.mat: simulated lineage dataset with 3 branches

SynMouseESprog_1000.mat: simulated lineage dataset showing linear differentiation