# Context

Despite scRNA-Seq data provides a snapshot of gene expression at a
particular time point, expression levels are captured across individual
cells. It captures the heterogeneity of cells within a population. If
biological tissue was not a steady state, it may be possible to retrieve
trajectories, such as developmental lineage or disease progression.
Trajectory inferences and RNA velocity leverage the information within
that snapshot to infer such cellular trajectories. Ordering cells is a
first step to understand the underlying biological processes driving
cell fate decisions and differentiation events.

Abbreviations :

**TI** : trajectory inference

**kNN**
: k-nearest neighbors

# Method principles

In section, we make a overview of two main methods to order cells :
**trajectory inference** and **RNA
velocity**.

## Trajectory inference

**Trajectory inference** is based on the gene expression
profile. It looks at distance between cells : cells with similar
transcriptomic profile are close, and cells with distinct profile are
distant. Based on transcriptomic profiles, it finds paths between cells,
leading to trajectories.

**Figure** from Wolf et al.Â (2019).
*Partition-based graph abstraction generates a topology-preserving
map of single cells. High-dimensional gene expression data is
represented as a kNN graph by choosing a suitable low-dimensional
representation and an associated distance metric for computing
neighborhood relations. [â€¦] We use PCA-based representations and
Euclidean distance. [â€¦] By discarding spurious edges with low weights,
PAGA graphs reveal the denoised topology of the data at a chosen
resolution and reveal its connected and disconnected regions. [â€¦] We
order cells within each partition according to their distance from a
root cell. A PAGA path then averages all single-cell paths that pass
through the corresponding groups of cells. This allows to trace gene
expression changes along complex trajectories at single-cell
resolution*

There are more than **50 methods to perform trajectory
inference** because : - many input types are possible (count
matrix, normalized matrix, reduced space) - many ways to compute
distance - many ways to find a path

**How to choose a trajectory inference method ?**