cellrank.kernels.ConnectivityKernel

class cellrank.kernels.ConnectivityKernel(adata, conn_key='connectivities', check_connectivity=False)

Kernel which computes transition probabilities based on similarities among cells.

As a measure of similarity, we currently support:

• transcriptomic similarities, computed using, e.g., neighbors(), see [Wolf et al., 2018].

• spatial similarities, computed using, e.g., spatial_neighbors(), see [Palla et al., 2021].

The resulting transition matrix is symmetric and thus cannot be used to learn about the direction of the biological process. To include this direction, consider combining with a velocity-derived transition matrix via VelocityKernel.

Optionally, we apply a density correction as described in [Coifman et al., 2005], where we use the implementation of [Haghverdi et al., 2016].

Parameters

• adata (AnnData) – Annotated data object.

• conn_key (str) – Key in obsp where connectivity matrix describing cell-cell similarity is stored.

• check_connectivity (bool) – Check whether the underlying kNN graph is connected.

Attributes table

adata	Annotated data object.
backward	None.
connectivities	Underlying connectivity matrix.
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([density_normalize])	Compute transition matrix based on transcriptomic similarity.
copy(*[, deep])	Return a copy of self.
from_adata(adata, key[, copy])	Read the kernel 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])	Serialize self to a file using pickle.
write_to_adata([key, copy])	Write the transition matrix and parameters used for computation to the underlying adata object.

Attributes

adata

ConnectivityKernel.adata

Annotated data object.

backward

ConnectivityKernel.backward

None.

connectivities

ConnectivityKernel.connectivities

Underlying connectivity matrix.

kernels

ConnectivityKernel.kernels

Underlying base kernels.

params

ConnectivityKernel.params

Parameters which are used to compute the transition matrix.

shape

ConnectivityKernel.shape

(n_cells, n_cells).

transition_matrix

ConnectivityKernel.transition_matrix

Row-normalized transition matrix.

Methods

compute_transition_matrix

ConnectivityKernel.compute_transition_matrix(density_normalize=True)

Compute transition matrix based on transcriptomic similarity.

Uses symmetric, weighted kNN graph to compute symmetric transition matrix. The connectivities are computed using neighbors(). Depending on the parameters used there, they can be UMAP connectivities or Gaussian-kernel-based connectivities with adaptive kernel width.

Parameters

density_normalize (bool) – Whether to use the underlying kNN graph for density normalization.

Return type

ConnectivityKernel

Returns

: Returns self and updates transition_matrix and params.

copy

ConnectivityKernel.copy(*, deep=False)

Return a copy of self.

Parameters

deep (bool) – Whether to use deepcopy().

Return type

Kernel

Returns

: Copy of self.

from_adata

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

Read the kernel saved using write_to_adata().

Parameters

• adata (AnnData) – Annotated data object.

• key (str) – Key in obsp where the transition matrix is stored. The parameters should be stored in adata.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

ConnectivityKernel.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 obsm containing the basis.

• key_added (Optional[str]) – If not None, save the result to adata.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 velocity_embedding_stream(). Otherwise, use 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 above-mentioned plotting function.

Return type

None

Returns

: Nothing, just plots and modifies obsm with a key based on the key_added.

plot_random_walks

ConnectivityKernel.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 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.

  • Sequence - sequence of cell ids in 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 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.

  • Sequence - sequence of cell ids in 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 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 Parallel for valid options.

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

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

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

• kwargs (Any) – Keyword arguments for 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

ConnectivityKernel.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 obs where clustering is stored.

• time_key (str) – Key in 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.

• figsize – Size of the figure.

• dpi – Dots per inch.

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

• show (bool) – If False, return 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 ConnectivityKernel.read(fname, adata=None, copy=False)

De-serialize self from a file.

Parameters

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

• adata (Optional[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. If adata is a view, it is always copied.

Return type

IOMixin

Returns

: The de-serialized object.

write

ConnectivityKernel.write(fname, write_adata=True)

Serialize self to a file using pickle.

Parameters

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

• write_adata (bool) – Whether to save adata object.

Return type

None

Returns

: Nothing, just writes itself to a file.

write_to_adata

ConnectivityKernel.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.

• copy (bool) – Whether to copy the transition_matrix.

Return type

None

Returns

: Updates the adata with the following fields:

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

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