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Layers, while the other was mainly expressed in deeper layers. This suggests that an anatomical or developmental factor may underlie variability in the response. While commonly used approaches based on clustering or pseudotemporal ordering of cells are poorly suited to achieve such insights from single-cell data, these findings emerge naturally from our matrix factorization approach.We have made our tools and analyses easily accessible so that researchers can readily use cNMF and further develop on the approach. We have deposited all the cNMF code on Github https://github.com/dylkot/cNMF/ (Kotliar, 2019; copy archived at https://github.com/elifesciences-publications/cNMF) and have made available all of the analysis scripts for figures contained in this manuscript on Code Ocean (https://doi.org/10.24433/CO.9044782e-cb96-4733-8a4f-bf42c21399e6) for easy exploration and re-execution.As others apply this approach, one key consideration will be the choice of the three input parameters required by cNMF: the number of components to be found (K), the percentage of replicates to use as nearest neighbors for outlier-detection, and a distance threshold for defining outliers. While the choice of K must ultimately reflect the resolution desired by the analyst, we propose two simple decision aids based on (1) considering the trade-off between factorization stability and reconstruction error and (2) looking at the proportion of variance explained by K principal components to estimate the dimensionality of the data (Figure 2—figure supplement 3, Figure 3—figure supplement 1, Figure 4—figure supplement 1). In addition, we noticed that choosing consecutive values of K primarily influenced individual components at the margin, suggesting that cNMF may be robust to this choice within a reasonable range of options (Figure 5 and ‘Choosing the number of components’ section of the Materials and methods). Robustness of cNMF to the number of components (K). Line plots of the maximum Pearson correlation between each of the cNMF components presented in the main analysis, and the cNMF components that result from multiple choices of K. For the simulated data, for which we have access to ground truth, we plot the correlation between the inferred components for each choice of K and the ground truth 14 components. We highlight components corresponding to activity GEPs with distinct colors and denote the number of identity GEPs contained on the same plot in parenthesis in the legend. A dashed line indicates the K choice that was presented in the main analysis. Pearson correlations are computed considering only the 2000 most over-dispersed genes and on vectors normalized by the computed sample standard deviation of each gene. https://doi.org/10.7554/eLife.43803.024 The additional two parameters allow users to optionally identify outlier replicates to filter before averaging across replicates. This improves overall accuracy by removing infrequent solutions that often represent merges or splits of the true GEPs. Using 30% of the number of replicates as nearest neighbors worked well for all datasets we analyzed, and an appropriate outlier distance threshold was clear in our applications based on the long tail in the distance distribution (Figure 2—figure supplement 3, Figure 3—figure supplement 1, Figure 4—figure supplement 1).Our approach is an initial step toward disentangling identity and activity

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Approaches performed worse as they inappropriately assigned activity GEP genes to these identity programs, resulting in an elevated FDR. This illustrates how matrix factorization can outperform clustering for inference of the genes associated with activity and identity GEPs.We decided to proceed with cNMF to analyze the real datasets due its accuracy, processing speed, and interpretability. First, it yielded the most accurate inferences in our simulated data. Second, NMF was the fastest of the basic factorization algorithms considered, which is especially useful given the need to run multiple replicates and given the growing sizes of scRNA-Seq datasets (Figure 2—figure supplement 6). Third, the non-negativity assumption of NMF naturally results in usage and component matrices that can be normalized and interpreted as probability distributions—that is, where the usage matrix reflects the probability of each GEP being used in each cell, and the component matrix reflects the probability of a specific transcript expressed in a GEP being a specific gene. The other high-performing factorization method, cICA, produced negative values in the components and usages which precludes this interpretation.Beyond identifying the activity program itself, we found that cNMF could also accurately infer which cells expressed the activity program and what proportion of their expression was derived from the activity program (Figure 2f). With an expression usage threshold of 10%, cNMF accurately classified 91% of cells expressing the activity program and 94% of cells that did not express the program. Moreover, we observed a high Pearson correlation between the inferred and simulated usages in cells that expressed the program (R = 0.74 for all simulations combined, R = 0.68 for the example simulation in Figure 2a). Thus, cNMF can be used both to infer which cells express the activity program, as well as what proportion of their transcripts derive from that program.We further demonstrated that cNMF was robust to the presence of doublets—instances where two cells are mistakenly labeled as a single cell. Due to limitations in the current tissue dissociation and single-cell sequencing technologies, some number of ‘cells’ in an scRNA-Seq dataset will actually correspond to doublets. Several computational methods have been developed to identify cells that correspond to doublets, but this is still an important artifact in scRNA-Seq data (McGinnis et al., 2018; Wolock et al., 2018). We found that cNMF correctly modeled doublets as a combination of the GEPs for the two combined cell types (Figure 2g). Moreover, we found that cNMF could accurately infer the GEPs even in a simulated dataset composed of 50% doublets (Figure 2—figure supplement 7). This illustrates another benefit of representing cells in scRNA-Seq data as a mixture of GEPs rather than classifying them into discrete clusters.In all the simulations described above, the 13 cell-types occurred at uniform frequencies. This allowed us to treat all identity programs as replicates of each other for evaluating inference accuracy, rather than having to separately consider rare GEPs which should, all else equal, be harder to infer than common ones. However, this is an approximation of reality where cell-type proportions can

cNMF/Tutorials/R_vignette.Rmd at master dylkot/cNMF - GitHub

And activity GEPs.In this instance, cNMF did not learn a single GEP for each donor (I.e. batch) but rather identified multiple hybrid identity-donor GEPs corresponding to individual cell-types derived from distinct sets of donors. This is likely due to the fact that the batch effect modulated the expression of different sets of genes in different cell-types, and therefore, no single shared ‘batch-effect’ GEP could capture the impact on each cell-type. To avoid incorporating variation between batches into the inferred GEPs for datasets containing significant batch-effect, batch-effect correction can be performed prior to running cNMF. Data availability All of the analyzed real datasets are publicly available and the relevant GEO accession codes are included in the manuscript. All of the simulated and real data can be accessed through Code Ocean at the following URL: https://doi.org/10.24433/CO.9044782e-cb96-4733-8a4f-bf42c21399e6. cNMF code is available on Github https://github.com/dylkot/cNMF/ (copy archived at https://github.com/elifesciences-publications/cNMF). The following data sets were generated The following previously published data sets were used References Article and author information Author details Dylan Kotliar Department of Systems Biology, Harvard Medical School, Boston, United States Broad Institute of MIT and Harvard, Cambridge, United States Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, United States Contribution Conceptualization, Resources, Data curation, Software, Formal analysis, Investigation, Methodology Contributed equally with Adrian Veres For correspondence [email protected] Competing interests No competing interests declared "This ORCID iD identifies the author of this article:" 0000-0002-7968-645X Adrian Veres Department of Systems Biology, Harvard Medical School, Boston, United States Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, United States Harvard Stem Cell Institute, Harvard University, Cambridge, United States Contribution Conceptualization, Software, Formal analysis, Investigation, Methodology Contributed equally with Dylan Kotliar Competing interests No competing interests declared M Aurel Nagy Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, United States Department of Neurobiology, Harvard Medical School, Boston, United States Contribution Resources, Formal analysis Competing interests No competing interests declared "This ORCID iD identifies the author of this article:" 0000-0003-4608-1152 Eran Hodis Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, United States Biophysics Program, Harvard University, Cambridge, United States Contribution Investigation, Helped analyze data during an early version of the project that shaped the specifics of the methodology and analysis Competing interests No competing interests declared Pardis C Sabeti Department of Systems Biology, Harvard Medical School, Boston, United States Broad Institute of MIT and Harvard, Cambridge, United States Howard Hughes Medical Institute, Chevy Chase, United States Contribution Supervision, Funding acquisition, Writing—original draft Competing interests No competing interests declared Funding National Institute of General Medical Sciences (T32GM007753) Dylan Kotliar Adrian Veres M Aurel Nagy Eran Hodis National Institute of Allergy and Infectious Diseases (R01AI099210) Pardis C Sabeti U.S. Food and Drug Administration (HHSF223201810172C) Dylan Kotliar Pardis C Sabeti The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. Acknowledgements We thank Allon Klein, Samuel Wolock, Aubrey Faust, Chris Edwards, Stephen Schaffner, Eric. Results for : enf cnmf. STANDARD - 254 GOLD - 254. Report. Report. Report Filter results Порнорассказы/ Порнорассказы принц Порнорассказы нассали в рот Порнорассказы незнакомка Онанизм порнорассказы Председатель порнорассказы Порнорассказы порножурналы

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Stimulus (Figure 5—figure supplement 1a - left). By contrast, there was significant variability between organoids in the Quadrato et al. (2017) data that was primarily associated with the bioreactors in which the organoids were grown (Figure 5—figure supplement 1b - left). This variability was discussed in the original manuscript and validated using immunohistochemistry, and thus represents true biological signal that we would hope for cNMF to discern.We also considered whether any GEPs could be attributed to just one or a small number of replicates which could suggest that they are not reproducible within the experiment. We therefore looked at what percentage of the aggregate usage of a GEP derived from cells in each replicate. We found that each GEP contributed to cells from multiple independent replicates in both datasets (Figure 5—figure supplement 1, right panels). No GEP derived more than 15% of its usage from a single replicate in the visual cortex data or more than 45% of its usage from a single replicate in the organoid data. Furthermore, each organoid GEP was the maximum contributing GEP for a cell in at least six distinct organoid replicates, and each visual cortex GEP was the maximum contributor for a cell in at least 10 distinct mouse replicates. This supports our conclusion that the inferred GEPs represent reproducible signals within the primary organoid and visual cortex datasets.We also analyzed a human pancreatic islet scRNA-Seq dataset where variability between four donors resulted in more substantial batch-effects to see how that would impact the behavior of cNMF (Baron et al., 2016). Applied to this dataset of 10,939 cells, cNMF identified 16 GEPs that corresponded well with the cell-type clusters described in the initial publication (Figure 5—figure supplement 2). Our application of cNMF failed to identify GEPs corresponding to a few cell-types described in Baron et al. (2016) (e.g. cells distinguished as delta and gamma cell-types were assigned the same GEP). However, many of the cell types that were missed by cNMF were only distinguished through iterative sub-clustering in the initial publication, which we did not attempt.Notably, we identified multiple GEPs for many cell-type clusters that corresponded to ‘donor of origin.’ For example, we identified separate GEPs corresponding to acinar cells derived from donors 1 and 3, and acinar cells derived from donors 2 and 4, and similarly for alpha, ductal, and stellate cells. One potential contributor to the batch-effect could be that donors 1 and 3 were male and donors 2 and 4 were female. Consistent with this, we noticed that among the genes that were most differentially expressed between donors 1 and 3 compared to donors 2 and 4 in alpha, beta, and acinar cells were XIST on the X chromosome and RPSY1 on the Y chromosome (linear regression F-test p-values−243 for for XIST and p-values−145 for RPSY1 for all 3 cell-types tested). But in general, the fact that cNMF is discerning multiple GEPs for the same cell-types suggests that technical sources of variation such as batch-effect can confound the identification of identity

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GEPs in scRNA-seq data. We evaluated this in simulated data of 15,000 cells composed of 13 cell types, one cellular activity program that is active to varying extents in a subset of cells of four cell types, and a 6% doublet rate (Figure 2A). We generated 20 replicates of this simulation, each at three different ‘signal to noise’ ratios, in order to determine how matrix factorization accuracy varies with noise level (Materials and methods). cNMF infers identity and activity expression programs in simulated data. (a) t-distributed stochastic neighbor embedding (tSNE) plot of an example simulation showing different cell types with marker colors, doublets as gray Xs, and cells expressing the activity gene expression program (GEP) with a black edge. (b) Pearson correlation between the true GEPs and the GEPs inferred by cNMF for the simulation in (a). (c) Same tSNE plot as (a) but colored by the simulated or the cNMF inferred usage of an example identity program (left) or the activity program (right). (d) Percentage of 20 simulation replicates where an inferred GEP had Pearson correlation greater than 0.80 with the true activity program for each signal to noise ratio (parameterized by the mean log2 fold-change for a differentially expressed gene). (e) Receiver Operator Characteristic (except with false discovery rate rather than false positive rate) showing prediction accuracy of genes associated with the activity GEP. (f) Scatter plot comparing the simulated activity GEP usage and the usage inferred by cNMF for the simulation in (a). For cells with a simulated usage of 0, the inferred usage is shown as a box and whisker plot with the box corresponding to interquartile range and the whiskers corresponding to 5th and 95th percentiles. (g) Contour plot of the true GEP usage on the Y-axis and the second true GEP usage for doublets or the second highest GEP usage inferred by cNMF for singletons for the simulation in (a). 1000 randomly selected cells are overlayed as a scatter plot for each group. https://doi.org/10.7554/eLife.43803.003 We first analyzed the performance of ICA, LDA, and NMF and noticed that they yielded different solutions when run several times on the same input simulated data. We ran each method 200 times and assigned the components in each run to their most correlated ground-truth program. We saw that there was significant variability among the components assigned to the same program -- particularly for NMF and LDA (Figure 2—figure supplement 1). Unlike PCA, which has an exact solution, these factorizations use stochastic optimization algorithms to obtain approximate solutions in a solution space including many local optima. We observed that such local optima frequently corresponded to solutions where a simulated GEP was split into multiple inferred components and/or multiple GEPs were merged into a single component (Figure 2—figure supplement 2a). This variability reduces the interpretability of the solutions and may decrease the accuracy as well.To overcome the issue of variability of solutions, we employed a meta-analysis approach, which we call consensus matrix factorization, that averages over multiple replicates to increase the

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Are speculative, but they highlight the ability of cNMF to identify intriguing GEPs in an unbiased fashion. Discussion In this study, we distinguished between cell type (identity) and cell type independent (activity) gene expression programs (GEPs) to motivate our use of matrix factorization, which represents cells as linear combinations of multiple GEPs. However, we note that some biological programs are not neatly classified as either identity or activity GEPs. For example, cell states reflecting oncogenic transformation, or a cell’s position along a morphological gradient blur the distinction between identity and activity. In addition, stochastic fluctuations in individual transcription factors could result in coordinated gene expression changes (Thattai and van Oudenaarden, 2001) and might be better described as a third program category, rather than as an identity or activity GEP. While the identity/activity distinction might not be appropriate in every case, matrix factorization should, in principle, be appropriate for representing all gene expression states that can be reasonably approximated as a linear mixture of programs.Furthermore, in this study, we have provided an empirical foundation for the use of matrix factorization to simultaneously infer identity and activity programs from scRNA-Seq data. We first show with simulations that despite their simplifying assumptions, ICA, LDA, and NMF (but not PCA) can infer components that align well with GEPs. However, due to the stochastic nature of these algorithms, the interpretability and accuracy of individual solutions can be low. This led us to develop a consensus approach that empirically increased the accuracy and robustness of the solutions. cNMF inferred the most accurate identity and activity programs of all the methods we tested. Moreover, it yielded results in interpretable units of gene expression (transcripts per million) and could accurately infer the percentage of each cell’s expression that was derived from each GEP. These properties made it the most promising approach for GEP inference on real datasets.We then explored the utility of cNMF on real data, recapitulating known GEPs, identifying novel ones, and further characterizing their usage. We first validated cNMF with several expected activity programs serving as positive controls. We then identified several unexpected but highly plausible programs, a hypoxia program in brain organoids and a depolarization-induced activity program in untreated neurons. Finally, we identified three novel programs in visual cortex neurons that we speculate may correspond to a neurosecratory phenotype, new synapse formation, and a stress response program. Beyond simply discovering activity programs, cNMF clarified the underlying cell types in these datasets by disentangling activity and identity programs from the mixed single-cell profiles. For example, we found that a brain organoid subpopulation that was initially annotated as proliferative precursors actually includes replicating cells of several cell types such as an immature skeletal muscle cell that is differentiating into slow-twitch and fast-twitch muscle populations. Furthermore, joint analysis of identity and activity GEPs allowed us to quantify the relative prevalence of activities across cell types. For example, we found in the visual cortex data that one depolarization-induced late response program was predominantly expressed in neurons of superficial cortical

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Vary over multiple orders of magnitude. We therefore also performed simulations containing biologically plausible cell-type proportions derived from the published clustering of a dataset analyzed later in this manuscript (Hrvatin et al., 2018) (Materials and methods). When we kept all of the other simulation parameters identical to those of the initial simulations, some identity GEPs from rare cell-types were missed by cNMF, cICA, and Louvain clustering (Figure 2—figure supplement 8a). However, when we increased the distinctness of the identity GEPs of the cell types, they could still be inferred by both cICA and cNMF with similar relative performances to what we saw in the primary benchmarking analysis (Figure 2—figure supplement 8b). This suggests that the simplification of uniform cell-type frequencies does not significantly impact our conclusions. cNMF deconvolutes hypoxia and cell-cycle activity GEPs from identity GEPs in brain organoid data Having demonstrated its performance and utility on simulated data, we then used cNMF to re-analyze a published scRNA-Seq dataset of 52,600 single cells isolated from human brain organoids (Quadrato et al., 2017). The initial report of this data confirmed that organoids contain excitatory cell types homologous to those in the cerebral cortex and retina as well as unexpected cells of mesodermal lineage, but further resolution can be gained on the precise cell types and how they differentiate over time. As organoids contain many proliferating cell types, we sought to use this data to confirm that cNMF could detect activity programs—in this case, cell cycles programs—in real data, and to explore what biological insights could be gained from their identification.We identified 31 distinct programs in this dataset that could be further parsed into identity and activity programs (Figure 3—figure supplement 1). We distinguished between identity and activity programs by using the fact that activity programs can occur in multiple diverse cell types while identity programs represent a single-cell type. Most cells had high usage of just a single GEP, which is consistent with expressing just an identity program (Figure 3a). When cells expressed multiple GEPs, those typically had correlated expression profiles, suggesting that they correspond to identity programs of closely related cell types or cells transitioning between two developmental states, rather than activity programs (Figure 3—figure supplement 2). By contrast, three GEPs were co-expressed with many distinct and uncorrelated programs, suggesting that they represent activity programs that occur across diverse cell types (Figure 3a–b). Consistent with this, the 28 suspected identity programs were well separated by the cell-type clusters reported in Quadrato et al. (2017) while the three suspected activity programs were expressed by cells across multiple clusters (Figure 3—figure supplements 3–4). Except for a few specific cases discussed below, we used these published cluster labels to annotate our identity GEPs. Deconvolution of activity programs from cell identity in brain organoid data. (a) Heatmap showing percent usage of all GEPs (rows) in all cells (columns). Identity GEPs are shown on top and activity GEPs are shown below. Cells are grouped by their maximum identity GEP and fit into columns of a. Results for : enf cnmf. STANDARD - 254 GOLD - 254. Report. Report. Report Filter results

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2015) and modulates nonsense mediated decay activity (Gardner, 2008). In the initial report of this data, staining for a single hypoxia gene, HIF1A, failed to detect significant levels of hypoxia. Indeed, HIF1A is not strongly associated with this GEP, at least not at the transcriptional level. This highlights the ability of our unbiased approach to detect unanticipated activity programs in scRNA-Seq data.Having identified proliferation and hypoxia activity programs, we sought to quantify their relative rates across cell types in the data. We found that 3079 cells (5.9%) expressed the G1/S program and 2043 cells (3.9%) expressed the G2/M program (with usage >= 10%). Classifying cells into cell types according to their most used identity program, we found that many distinct populations were replicating. For example, cNMF detected a rare population, included with the forebrain cluster in the original report, that we label as ‘stem-like’ based on high expression of pluripotency markers (e.g. LIN28A, L1TD1, MIR302B, DNMT3B) (Supplementary file 1). These cells showed the highest rates of proliferation with over 38% of them expressing a cell-cycle program in addition to the ‘stem-like’ identity GEP (Figure 3f).cNMF was further able to refine cell types by disentangling the contributions of identity and activity programs to the gene expression of cells. For example, we found that a cell cluster labeled in Quadrato et al. (2017) as ‘proliferative precursors’, based on high expression of cell-cycle genes, is composed of multiple cell types including immature muscle and dopaminergic neurons (Figure 3—figure supplement 4). The predominant identity GEP of cells in this cluster is most strongly associated with the gene PAX7, a marker of self-renewing muscle stem cells (Pawlikowski et al., 2009) (Supplementary file 1). Indeed, this GEP has high (>10%) usage in 41% of cells who’s most used GEP is the immature muscle program, suggesting it may be a precursor of muscle cells. This relationship was not readily identifiable by clustering because the majority of genes associated with the cluster were cell cycle related.We also saw a wide range of cell types expressing the hypoxia program, with the highest rates in C6-1, neuroepithelial-1, type 2 muscle, and dopaminergic-2 cell types. The lowest levels of hypoxia program usage occurred in forebrain, astroglial, retinal, and type 1 muscle cell types (Figure 3g). The hypoxia response program is widespread in this dataset with 5788 cells (11%) of all cells expressing it (usage >10%). This illustrates how inferring activity programs in scRNA-Seq data using cNMF makes it possible to compare the rates of cellular activities across cell types. cNMF identifies depolarization induced and novel activity programs in scRNA-Seq of mouse visual cortex neurons Next we turned to another published dataset to further validate cNMF and to illustrate how it can be combined with scRNA-Seq of experimentally manipulated cells to uncover more subtle activity programs. We re-analyzed scRNA-Seq data from 15,011 excitatory pyramidal neurons or inhibitory interneurons from the visual cortex of dark-reared mice that were suddenly exposed to 0 hr, 1 hr, or 4 hr of light (Hrvatin et al.,

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Robustness of the solution. The method which is adapted from a similar procedure in mutational signature discovery (Alexandrov et al., 2013) proceeds as follows: we run the factorization multiple times, filter outlier components (which tend to represent noise or merges/splits of GEPs), cluster the components over all replicates combined, and take the cluster medians as our consensus estimates. With these estimates fixed, we are able to compute a final usage matrix specifying the contribution of each GEP in each cell and to transform our GEP estimates from normalized units to biologically meaningful ones such as transcripts per million (TPM). This approach also provides us with a guide for determining K, the number of components to use, by selecting a value that provides a reasonable trade-off between error and stability (Figure 2—figure supplement 3a, see Materials and methods for details). We refer to this approach as consensus matrix factorization based on its analogy with consensus clustering (Monti et al., 2003) and to its application to LDA, NMF, and ICA, as cLDA, cNMF, and cICA respectively. While consensus clustering has been previously applied to bulk gene expression analysis using hard-clustering derived by binarizing NMF factors (Brunet et al., 2004), our approach does not require any hard cluster assignments.Consensus matrix factorization inferred components underlying the GEPs as well as which cells expressed each GEP (Figure 2b–c, Figure 2—figure supplement 4a). By contrast, principal components were linear combinations of the true GEPs. Beyond increasing the robustness of the solution, the consensus approach also increased the ability of factorization to deconvolute the true GEPs - most dramatically for LDA and NMF which had the most stochastic variability. cNMF successfully deconvoluted the activity and identity GEPs more frequently than the other matrix factorizations considered (Figure 2d, Figure 2—figure supplement 2).We next sought to benchmark the sensitivity and specificity of each matrix factorization method for inferring which genes are associated with each GEP. We also evaluated the performance of hard clustering for this task because clustering is the most common way GEPs are identified in practice. We evaluated the commonly used Louvain community detection clustering algorithm (Blondel et al., 2008; Levine et al., 2015) but also considered an upper bound on how well any discrete clustering could perform by using ground-truth to assign cells to a cluster of its cell type or to an activity cluster if it had >= 40% simulated contribution from the activity GEP (Figure 2—figure supplement 4b). We evaluated the association between genes and GEPs using linear regression and measured accuracy using a receiver operator characteristic (Materials and methods).We found that cNMF was most accurate at inferring genes in the activity program, with a sensitivity of 61% at a false discovery rate (FDR) of 5% (Figure 2e). cICA and the ground-truth clustering were the next most accurate with 57% and 56% sensitivity at a 5% FDR, respectively. cNMF also performed the best at inferring identity GEPs of the 4 cell types that expressed the activity (Figure 2—figure supplement 5). As expected, the clustering. Results for : enf cnmf. STANDARD - 254 GOLD - 254. Report. Report. Report Filter results

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From several choices of K before proceeding. We do not recommend necessarily using the maximum stability solution of the error vs. stability plot as this can frequently miss true biological signal and, indeed would have led to the incorrect choice for the simulated data (Figure 2—figure supplement 3).Given the uncertainty of the choice of K, we confirmed that the conclusions of this manuscript are robust to this decision. When we varied K within a range of ±four around the choice used in the manuscript, we found approximately the same core set of GEPs with a single new GEP being discerned with each consecutive step in K. For each step below the selected K, approximately a single GEP was lost, but for choices above the selected K, components approximately matching the original K programs (I.e. with Pearson correlation >0.7) were found (Figure 5). This suggests that cNMF yields relatively stable solutions for a moderate range of K values. Comparison of cNMF with other methods Request a detailed protocol We compared cNMF with consensus and standard versions of LDA and ICA as well as with PCA, Louvain clustering and a hard clustering based on assignment of cells to their ground-truth labels. We used the implementations of LDA, ICA, and PCA in scikit-learn and the implementation of Louvain clustering in scanpy (Wolf et al., 2018). For ICA, we used the FastICA implementation with default options for all the parameters. For LDA, we used the batch algorithm and all other parameters as defaults. We defined the consensus estimates across 200 replicates in the same way as for cNMF but with a slight modification for ICA. Because ICA is under-determined with respect to the signs of the solutions, some iterations will yield a given component pointed in one direction while others produce approximately the same component but pointed in the opposite direction (multiplied by −1). Therefore, we aligned the orientation of components from across replicates by identifying any components whose median usage across all cells was positive and scaled those and the corresponding usages by −1.For Louvain clustering, we used 14 principal components to compute distances between cells and used 200 nearest neighbors to define the KNN graph. We chose 14 principal components based on the fact that the data was simulated based on a 14-dimensional basis and, therefore, the biological variation in the data can be captured by 14 PCs and subsequent components correspond to noise. This choice is also justified by choosing the elbow on scree plot in Figure 2—figure supplement 3. We used 200 nearest neighbors for the clustering as this is a relatively large number to minimize variance but it is still smaller than the smallest discrete population (0.3*15,000*(1/13)=346 cells from a specific cell-type that expresses the activity program).For ground-truth assignment clustering, we assigned each cell to a cluster defined by its true identity program, except for cells which had greater that 40% usage of the activity program, which we assigned to an activity program cluster. Then we determined a GEP