cellrank.external.kernels.StationaryOTKernel

class cellrank.external.kernels.StationaryOTKernel(adata, g, terminal_states=None, **kwargs)

Stationary optimal transport kernel from [Zhang et al., 2021].

This class requires the statOT package, which can be installed as pip install statot POT.

Parameters:

• adata (anndata.AnnData) – Annotated data object.

• terminal_states (Union[str, Series, None]) – Key in anndata.AnnData.obs or a categorical pandas.Series where non-NaN values mark the terminal states. If None, terminal states are assumed to be present in anndata.AnnData.obs ['terminal_states'].

• g (Union[str, ndarray]) – Key in anndata.AnnData.obs containing relative growth rates for cells or the array itself.

• kwargs (Any) – Keyword arguments for the parent class.

Attributes table

adata	Annotated data object.
backward	None.
kernels	Underlying base kernels.
params	Parameters which are used to compute the transition matrix.
shape	(n_cells, n_cells).
transition_matrix	Row-normalized transition matrix.

Methods table

compute_transition_matrix(eps, dt[, basis, ...])	Compute transition matrix using stationary OT [Zhang et al., 2021].
copy([deep])	Not implemented.
from_adata(adata, key[, copy])	Read kernel object saved using write_to_adata().
plot_projection([basis, key_added, ...])	Plot transition_matrix as a stream or a grid plot.
plot_random_walks([n_sims, max_iter, seed, ...])	Plot random walks in an embedding.
plot_single_flow(cluster, cluster_key, time_key)	Visualize outgoing flow from a cluster of cells [Mittnenzweig et al., 2021].
read(fname[, adata, copy])	De-serialize self from a file.
write(fname[, write_adata, ext])	Serialize self to a file.
write_to_adata([key, copy])	Write the transition matrix and parameters used for computation to the underlying adata object.

Attributes

adata

StationaryOTKernel.adata

Annotated data object.

Return type:

AnnData

backward

StationaryOTKernel.backward

None.

Return type:

None

kernels

StationaryOTKernel.kernels

Underlying base kernels.

Return type:

Tuple[KernelExpression, ...]

params

StationaryOTKernel.params

Parameters which are used to compute the transition matrix.

Return type:

Dict[str, Any]

shape

StationaryOTKernel.shape

(n_cells, n_cells).

Return type:

Tuple[int, int]

transition_matrix

StationaryOTKernel.transition_matrix

Row-normalized transition matrix.

Return type:

Union[ndarray, csr_matrix]

Methods

compute_transition_matrix

StationaryOTKernel.compute_transition_matrix(eps, dt, basis='X_pca', cost_norm_method=None, method='ent', tol=0.0, thresh=0.0, maxiter=5000, C=None, verbose=False, **kwargs)

Compute transition matrix using stationary OT [Zhang et al., 2021].

Parameters:

• eps (float) – Regularization parameter.

• dt (float) – Choice of the time step over which to fit the model.

• basis (str) – Key in anndata.AnnData.obsm where the basis is stored.

• cost_norm_method (Optional[str]) – Cost normalization method to use. Use “mean” to ensure mean(C) = 1 or refer to ot.utils.cost_normalization() for more information.

• method (Literal[‘ent’, ‘quad’, ‘unbal’]) –

  Choice of regularization. Valid options are:

  • ’ent’ - entropy.

  • ’quad’ - L2-norm.

  • ’unbal’ - unbalanced transport (not yet implemented).

• tol (float) – Relative tolerance for OT solver convergence.

• thresh (float) – Threshold for output transition probabilities.

• maxiter (int) – Maximum number of iterations for OT solver.

• C (Optional[ndarray]) – Cost matrix for optimal transport problem.

• verbose (bool) – Detailed output on convergence of OT solver.

• kwargs (Any) – Additional keyword arguments.

Return type:

StationaryOTKernel

Returns:

Self and updates transition_matrix and params.

copy

StationaryOTKernel.copy(deep=False)

Not implemented.

Return type:

ErroredKernel

from_adata

classmethod StationaryOTKernel.from_adata(adata, key, copy=False)

Read kernel object saved using write_to_adata().

Parameters:

• adata (anndata.AnnData) – Annotated data object.

• key (str) – Key in anndata.AnnData.obsp where the transition matrix is stored. The parameters should be stored in anndata.AnnData.uns ['{key}_params'].

• copy (bool) – Whether to copy the transition matrix.

Return type:

Kernel

Returns:

The kernel with explicitly initialized properties:

• transition_matrix - the transition matrix.

• params - parameters used for computation.

plot_projection

StationaryOTKernel.plot_projection(basis='umap', key_added=None, recompute=False, stream=True, connectivities=None, **kwargs)

Plot transition_matrix as a stream or a grid plot.

Parameters:

• basis (str) – Key in anndata.AnnData.obsm containing the basis.

• key_added (Optional[str]) – If not None, save the result to anndata.AnnData.obsm ['{key_added}']. Otherwise, save the result to ‘T_fwd_{basis}’ or T_bwd_{basis}, depending on the direction.

• recompute (bool) – Whether to recompute the projection if it already exists.

• stream (bool) – If True, use scvelo.pl.velocity_embedding_stream(). Otherwise, use scvelo.pl.velocity_embedding_grid().

• connectivities (Optional[spmatrix]) – Connectivity matrix to use for projection. If None, use ones from the underlying kernel, is possible.

• kwargs (Any) – Keyword argument for the chosen plotting function.

Return type:

None

Returns:

Nothing, just plots and modifies anndata.AnnData.obsm with a key based on key_added.

plot_random_walks

StationaryOTKernel.plot_random_walks(n_sims=100, max_iter=0.25, seed=None, successive_hits=0, start_ixs=None, stop_ixs=None, basis='umap', cmap='gnuplot', linewidth=1.0, linealpha=0.3, ixs_legend_loc=None, n_jobs=None, backend='loky', show_progress_bar=True, figsize=None, dpi=None, save=None, **kwargs)

Plot random walks in an embedding.

This method simulates random walks on the Markov chain defined though the corresponding transition matrix. The method is intended to give qualitative rather than quantitative insights into the transition matrix. Random walks are simulated by iteratively choosing the next cell based on the current cell’s transition probabilities.

Parameters:

• n_sims (int) – Number of random walks to simulate.

• max_iter (Union[int, float]) – Maximum number of steps of a random walk. If a float, it can be specified as a fraction of the number of cells.

• seed (Optional[int]) – Random seed.

• successive_hits (int) – Number of successive hits in the stop_ixs required to stop prematurely.

• start_ixs (Union[Sequence[str], Mapping[str, Union[str, Sequence[str], Tuple[float, float]]], None]) –

  Cells from which to sample the starting points. If None, use all cells. Can be specified as:

  • dict - dictionary with 1 key in anndata.AnnData.obs with values corresponding to either 1 or more clusters (if the column is categorical) or a tuple specifying [min, max] interval from which to select the indices.

  • typing.Sequence - sequence of cell ids in anndata.AnnData.obs_names.

  For example {'dpt_pseudotime': [0, 0.1]} means that starting points for random walks will be sampled uniformly from cells whose pseudotime is in [0, 0.1].

• stop_ixs (Union[Sequence[str], Mapping[str, Union[str, Sequence[str], Tuple[float, float]]], None]) –

  Cells which when hit, the random walk is terminated. If None, terminate after max_iters. Can be specified as:

  • dict - dictionary with 1 key in anndata.AnnData.obs with values corresponding to either 1 or more clusters (if the column is categorical) or a tuple specifying [min, max] interval from which to select the indices.

  • typing.Sequence - sequence of cell ids in anndata.AnnData.obs_names.

  For example {'clusters': ['Alpha', 'Beta']} and successive_hits = 3 means that the random walk will stop prematurely after cells in the above specified clusters have been visited successively 3 times in a row.

• basis (str) – Basis in anndata.AnnData.obsm to use as an embedding.

• cmap (Union[str, LinearSegmentedColormap]) – Colormap for the random walk lines.

• linewidth (float) – Width of the random walk lines.

• linealpha (float) – Alpha value of the random walk lines.

• ixs_legend_loc (Optional[str]) – Legend location for the start/top indices.

• show_progress_bar (bool) – Whether to show a progress bar. Disabling it may slightly improve performance.

• n_jobs (Optional[int]) – Number of parallel jobs. If -1, use all available cores. If None or 1, the execution is sequential.

• backend (str) – Which backend to use for parallelization. See joblib.Parallel for valid options.

• figsize (Optional[Tuple[float, float]]) – Size of the figure.

• dpi (Optional[int]) – Dots per inch.

• save (Union[str, Path, None]) – Filename where to save the plot.

• kwargs (Any) – Keyword arguments for scvelo.pl.scatter().

Return type:

None

Returns:

Nothing, just plots the figure. Optionally saves it based on save. For each random walk, the first/last cell is marked by the start/end colors of cmap.

plot_single_flow

StationaryOTKernel.plot_single_flow(cluster, cluster_key, time_key, clusters=None, time_points=None, min_flow=0, remove_empty_clusters=True, ascending=False, legend_loc='upper right out', alpha=0.8, xticks_step_size=1, figsize=None, dpi=None, save=None, show=True)

Visualize outgoing flow from a cluster of cells [Mittnenzweig et al., 2021].

Parameters:

• cluster (str) – Cluster for which to visualize outgoing flow.

• cluster_key (str) – Key in anndata.AnnData.obs where clustering is stored.

• time_key (str) – Key in anndata.AnnData.obs where experimental time is stored.

• clusters (Optional[Sequence[Any]]) – Visualize flow only for these clusters. If None, use all clusters.

• time_points (Optional[Sequence[Union[float, int]]]) – Visualize flow only for these time points. If None, use all time points.

• min_flow (float) – Only show flow edges with flow greater than this value. Flow values are always in [0, 1].

• remove_empty_clusters (bool) – Whether to remove clusters with no incoming flow edges.

• ascending (Optional[bool]) – Whether to sort the cluster by ascending or descending incoming flow. If None, use the order as in defined by clusters.

• alpha (Optional[float]) – Alpha value for cell proportions.

• xticks_step_size (Optional[int]) – Show only every other n-th tick on the x-axis. If None, don’t show any ticks.

• legend_loc (Optional[str]) – Position of the legend. If None, do not show the legend.

• figsize (Optional[Tuple[float, float]]) – Size of the figure.

• dpi (Optional[int]) – Dots per inch.

• save (Union[str, Path, None]) – Filename where to save the plot.

• show (bool) – If False, return matplotlib.pyplot.Axes.

Return type:

Optional[Axes]

Returns:

The axes object, if show = False. Nothing, just plots the figure. Optionally saves it based on save.

Notes

This function is a Python re-implementation of the following original R function with some minor stylistic differences. This function will not recreate the results from [Mittnenzweig et al., 2021], because there, the Metacell model [Baran et al., 2019] was used to compute the flow, whereas here the transition matrix is used.

read

static StationaryOTKernel.read(fname, adata=None, copy=False)

De-serialize self from a file.

Parameters:

• fname (Union[str, Path]) – Filename from which to read the object.

• adata (Optional[AnnData]) – anndata.AnnData object to assign to the saved object. Only used when the saved object has adata and it was saved without it.

• copy (bool) – Whether to copy adata before assigning it or not. If adata is a view, it is always copied.

Return type:

IOMixin

Returns:

The de-serialized object.

write

StationaryOTKernel.write(fname, write_adata=True, ext='pickle')

Serialize self to a file.

Parameters:

• fname (Union[str, Path]) – Filename where to save the object.

• write_adata (bool) – Whether to save adata object or not, if present.

• ext (Optional[str]) – Filename extension to use. If None, don’t append any extension.

Return type:

None

Returns:

Nothing, just writes itself to a file using pickle.

write_to_adata

StationaryOTKernel.write_to_adata(key=None, copy=False)

Write the transition matrix and parameters used for computation to the underlying adata object.

Parameters:

key (Optional[str]) – Key used when writing transition matrix to adata. If None, the key will be determined automatically.

Return type:

None

Returns:

Updates the adata with the following fields:

• .obsp['{key}'] - the transition matrix.

• .uns['{key}_params'] - parameters used for the calculation.