Scalability with increasing number of cells and features
While early TI methods were developed at a time where profiling more than a thousand cells was exceptional, methods now have to cope with hundreds of thousands of cells, and perhaps soon with more than ten million1. Moreover, the recent application of TI methods on multi-omics single-cell data also showcases the increasing demands on the number of features2. To assess the scalability, we ran each method on up- and downscaled versions of five distinct real datasets. We modelled the running time and memory usage using a Shape Constrained Additive Model3 (Figure 1a). As a control, we compared the predicted time (and memory) with the actual time (resp. memory) on all benchmarking datasets, and found that these were highly correlated overall (> 0.9, Figure 2), and moderately to highly correlated (0.5 – 0.9) for almost every method, depending on to what extent the execution of a method succeeded during the scalability experiments (Figure 3c and Figure 4a).
We found that the scalability of most methods was overall very poor, with most graph and tree methods not finishing within an hour on a dataset with ten thousand cells and ten thousand features (Figure 3c), around the size of a typical droplet-based single-cell dataset1. Running times increased further with increasing number of cells, with only a handful of graph/tree methods completing within a day on a million of cells (PAGA, PAGA Tree, Monocle DDRTree, Stemnet and GrandPrix). Some methods, such as Monocle DDRTree and GrandPrix, also suffered from unsatisfactory running times when given a high number of features.
Methods with a low running time typically had two defining aspects: they had a linear time complexity with respect to the features and/or cells, and adding new cells or features led to a relatively low increase in time (Figure 1b). We found that more than half of all methods had a quadratic or superquadratic complexity with respect to the number of cells, which would make it difficult to apply any of these methods in a reasonable time frame on datasets with more than a thousand cells (Figure 1b).
We also assessed the memory requirements of each methods (Figure 4c). Most methods had reasonable memory requirements for modern workstations or computer clusters (≤12GB) with PAGA and STEMNET in particular having a low memory usage with both a high number of cells or high number of features. Notably, the memory requirements were very high for several methods on datasets with high number of cells (RaceID/StemID, pCreode and MATCHER) or features (Monocle DDRTree, SLICE and MFA).
Altogether, the scalability analysis indicated that the dimensions of the data is an important factor in the choice of method and that method development should pay more attention to maintaining reasonable running times and memory usage.
Figure 1: Scalability of trajectory inference methods. (a) Three examples of average observed running times across five datasets (left) and the predicted running time (right). (b) Overview of the scalability results of all methods, ordered by their average predicted running time from (a). We predicted execution times and memory usage for each method with increasing number of features or cells, and used these values to classify each method into sublinear, linear, quadratic and superquadratic based on the shape of the curve.
Figure 2: Agreement between actual values and predictions for execution times and memory usage.
Figure 3: Detailed results of the four main evaluation criteria: accuracy, scalability, stability and usability. (a) The names of the methods, ordered as in Figure 5. (b) Accuracy of trajectory inference methods across metrics, dataset sources and dataset trajectory types. The performance of a method is generally more stable across dataset sources, but very variable depending on the metric and trajectory type. (c) Predicted execution times for varying numbers of cells and features (# cells × # features). Predictions were made by training a regression model after running each method on bootstrapped datasets with varying numbers of cells and features. (d) Stability results by calculating the average pairwise similarity between models inferred across multiple runs of the same method. (e) Usability scores of the tool and corresponding manuscript, grouped per category. Off-the-shelf methods were directly implemented in R and thus do not have a usability score.
Figure 4: Results from the evaluation, for all methods and across all evaluation criteria. (a) We characterised the methods according to the wrapper type, their required priors, whether the inferred topology is constrained by the algorithm (fixed) or a parameter (param), and the types of inferable topologies. The methods are grouped vertically based on the most complex trajectory type they can infer. (b) The overall results of the evaluation on four criteria: benchmarking using a reference trajectory on real and synthetic data, scalability with increasing number of cells and features, stability across dataset subsamples, and quality of the implementation. (c) Accuracy of trajectory inference methods across metrics, dataset sources and dataset trajectory types. The performance of a method is generally more stable across dataset sources, but very variable depending on the metric and trajectory type. (d) Predicted execution times and memory usage for varying numbers of cells and features (# cells × # features). Predictions were made by training a regression model after running each method on bootstrapped datasets with varying numbers of cells and features. (e) Stability results by calculating the average pairwise similarity between models inferred across multiple runs of the same method. (f) Usability scores of the tool and corresponding manuscript, grouped per category.
1. Svensson, V., Vento-Tormo, R. & Teichmann, S. A. Exponential scaling of single-cell RNA-seq in the past decade. Nature Protocols 13, 599–604 (2018).
2. Cao, J. et al. Joint profiling of chromatin accessibility and gene expression in thousands of single cells. Science eaau0730 (2018). doi:10.1126/science.aau0730
3. Pya, N. & Wood, S. N. Shape constrained additive models. Statistics and Computing 25, 543–559 (2015).