A novel metric reveals previously unrecognized distortion in dimensionality reduction of scRNA-Seq data
Preprint posted on July 02, 2019 https://www.biorxiv.org/content/10.1101/689851v1
What I like about this study:
I would like to highlight two aspects of this study. Firstly, the topic is simply critical to anyone who has ever analyzed scRNA-seq data (which is becoming increasingly ubiquitous in cellular biology). Dimensionality reduction is the first step in almost every algorithm and analysis pipeline, and a fundamental assumption is that this step preserves important (biologically-relevant) information from the original high-dimensional data. If in fact this step distorts the data, as the authors convincingly argue, biological conclusions from scRNA-seq data would need to be scrutinized. Secondly, this paper is exceptionally well-written. I appreciate that the authors use analogies and toy cases that are both illustrative and clear, even to those without a mathematics or statistical background.
scRNA-seq data is inherently high dimensional, with increasingly sensitive methods capable of detecting thousands of genes per cell. Higher dimensional data, while providing potentially more information, is more difficult to analyze – many algorithms fail to scale up to higher dimensions, for example [1, 2]. A large number of methods exist to transform high dimensional data to low dimensional data while preserving key aspects of the structure (see below for a toy example on several methods) . These methods, including the frequently used t-SNE and UMAP algorithms, underlie nearly all scRNA-seq analysis pipelines, including commonly used algorithms for clustering and trajectory analysis . A fundamental assumption is that dimensionality reduction preserves important structure in the high dimensional data or, at the very worst, does not skew the structure significantly.
The authors challenge this assumption using several illustrative cases. As a toy geometrical example, the authors first generated hyperspheres (generalizations of spheres to higher dimensions). In a clever approach, the authors generated lower dimensional hyperspheres in higher dimensions. For example, they could construct a 3-dimensional hypersphere in 5 dimensions by taking a vector of 3 numbers (the 3-dimensional hypersphere) and adding on 2 zeros at the end to make it 5-dimensional. It is trivial to reduce the dimensions of this sphere to 3 or 4 dimensions, e.g. transform the point [1 1 1 0 0] → [1 1 1 0] (4-dimension) or [1 1 1 0 0] → [1 1 1] (3 dimensions). Thus, the authors expected that standard dimensionality reduction techniques should readily succeed in transforming these hyperspheres to lower dimensions, or at the very least preserve local neighbors between different points. Instead, the authors found that even in this simple toy case, all of the methods introduced huge distortions, such that most points had hugely different neighboring points in low dimensions as compared to high dimensions. Increasing the number of points sampled did not improve the mapping but in fact made it worse.
The authors then used their approach to analyze dimensionality reduction of real scRNA-seq data. Consistently, they found huge distortions in data even when reducing to relatively high dimensions. This is particularly problematic as most pipelines reduce data to 2 or 3 dimensions (as these are easily visualized). Indeed, the authors tested several commonly used pipelines for clustering and trajectory generation and found that they are affected by dimensionality reduction.
This manuscript affects any research group using scRNA-seq techniques. As an example, in developmental biology a common approach is to reconstruct developmental trajectories of various lineages to study how cells differentiate and specify. If dimensionality reduction inherently skews the data, then the results of these analyses are questionable.
There is no question that these results are disturbing, and motivate the need to develop improved scRNA-seq pipelines (either by developing better dimensionality reduction methods or eliminating their need). In the meantime, however, I do wonder if current techniques are good enough for now, particularly for clustering. While local neighborhoods may be distorted, tSNE and UMAP plots do places cells with similar gene expression close to one another – this can be readily seen by plotting marker genes, for example. Particularly for smaller studies or studies where differences between cell types is clearly defined, tSNE and UMAP may suffice despite the distortions they may introduce. Likewise, while clearly dimensionality reduction does affect cell-to-cell distances, current trajectory reconstruction methods do at least partially correlate with other biological parameters (for example, developmental age). While we should be cautious about interpretation, I suspect that computational methods combined with biological intuition can at least be passable until better methods are developed.
 Stegle O, Teichmann SA, Marioni JC. Computational and analytical challenges in single-cell transcriptomics. Nat Rev Genet (2015), 16(3):133-45.
 Friedman JH. On Bias, Variance, 0/1 – Loss, and the Curse-of-Dimensionality. Data Mining and Knowledge Discovery (1997), 1:55-77.
 Manifold Learning, scikit documentation. Link: https://scikit-learn.org/stable/modules/manifold.html
Posted on: 16th August 2019Read preprint
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