Source code for dynamo.tools.cell_velocities

import warnings
import numpy as np
import scipy as scp
from numba import jit
import scipy.sparse as sp
from sklearn.utils import sparsefuncs
from sklearn.decomposition import PCA
from .Markov import (
    KernelMarkovChain,
    velocity_on_grid,
    graphize_velocity,
    fp_operator,
    ContinuousTimeMarkovChain,
)
from .connectivity import adj_to_knn

from .metric_velocity import gene_wise_confidence
from .utils import (
    set_transition_genes,
    get_finite_inds,
    get_ekey_vkey_from_adata,
    get_mapper_inverse,
    update_dict,
    get_iterative_indices,
    split_velocity_graph,
    norm,
    einsum_correlation,
    log1p_,
    index_gene,
)

from .dimension_reduction import reduceDimension
from ..dynamo_logger import LoggerManager
from ..utils import areinstance
import anndata
from typing import Union
import scipy

# dynamo logger related
from ..dynamo_logger import (
    main_tqdm,
    main_info,
    main_warning,
    main_critical,
    main_exception,
)


[docs]def cell_velocities( adata: anndata.AnnData, ekey: Union[str, None] = None, vkey: Union[str, None] = None, X: Union[np.array, scipy.sparse.csr_matrix, None] = None, V: Union[np.array, scipy.sparse.csr_matrix, None] = None, X_embedding: Union[str, None] = None, transition_matrix: Union[np.array, scipy.sparse.csr_matrix, None] = None, use_mnn: bool = False, n_pca_components: Union[int, None] = None, transition_genes: Union[str, list, None] = None, min_r2: Union[float, None] = None, min_alpha: Union[float, None] = None, min_gamma: Union[float, None] = None, min_delta: Union[float, None] = None, basis: str = "umap", neigh_key: str = "neighbors", adj_key: str = "distances", add_transition_key: str = None, add_velocity_key: str = None, n_neighbors: int = 30, method: str = "pearson", neg_cells_trick: bool = True, calc_rnd_vel: bool = False, xy_grid_nums: tuple = (50, 50), correct_density: bool = True, scale: bool = True, sample_fraction: Union[float, None] = None, random_seed: int = 19491001, enforce: bool = False, preserve_len: bool = False, **kernel_kwargs, ) -> anndata.AnnData: """Project high dimensional velocity vectors onto given low dimensional embeddings, and/or compute cell transition probabilities. When method='kmc', the Itô kernel is used which not only considers the correlation between the vector from any cell to its nearest neighbors and its velocity vector but also the corresponding distances. We expect this new kernel will enable us to visualize more intricate vector flow or steady states in low dimension. We also expect it will improve the calculation of the stationary distribution or source states of sampled cells. The original "correlation/cosine" velocity projection method is also supported. Kernels based on the reconstructed velocity field is also possible. With the `key` argument, `cell_velocities` can be called by `cell_accelerations` or `cell_curvature` to calculate RNA acceleration/curvature vector for each cell. Arguments --------- adata: :class:`~anndata.AnnData` an Annodata object. ekey: str or None (optional, default None) The dictionary key that corresponds to the gene expression in the layer attribute. By default, ekey and vkey will be automatically detected from the adata object. vkey: str or None (optional, default None) The dictionary key that corresponds to the estimated velocity values in the layers attribute. X: :class:`~numpy.ndarray` or :class:`~scipy.sparse.csr_matrix` or None (optional, default `None`) The expression states of single cells (or expression states in reduced dimension, like pca, of single cells) V: :class:`~numpy.ndarray` or :class:`~scipy.sparse.csr_matrix` or None (optional, default `None`) The RNA velocity of single cells (or velocity estimates projected to reduced dimension, like pca, of single cells). Note that X, V need to have the exact dimensionalities. X_embedding: str or None (optional, default None) The low expression reduced space (pca, umap, tsne, etc.) of single cells that RNA velocity will be projected onto. Note X_embedding, X and V has to have the same cell/sample dimension and X_embedding should have less feature dimension comparing that of X or V. use_mnn: bool (optional, default False) Whether to use mutual nearest neighbors for projecting the high dimensional velocity vectors. By default, we don't use the mutual nearest neighbors. Mutual nearest neighbors are calculated from nearest neighbors across different layers, which which accounts for cases where, for example, the cells from spliced expression may be nearest neighbors but far from nearest neighbors on unspliced data. Using mnn assumes your data from different layers are reliable (otherwise it will destroy real signals). n_pca_components: int (optional, default None) The number of pca components to project the high dimensional X, V before calculating transition matrix for velocity visualization. By default it is None and if method is `kmc`, n_pca_components will be reset to 30; otherwise use all high dimensional data for velocity projection. transition_genes: str, list, or None (optional, default None) The set of genes used for projection of hign dimensional velocity vectors. If None, transition genes are determined based on the R2 of linear regression on phase planes. The argument can be either a dictionary key of .var, a list of gene names, or a list of booleans of length .n_vars. min_r2: float or None (optional, default None) The minimal value of r-squared of the parameter fits for selecting transition genes. min_alpha: float or None (optional, default None) The minimal value of alpha kinetic parameter for selecting transition genes. min_gamma: float or None (optional, default None) The minimal value of gamma kinetic parameter for selecting transition genes. min_delta: float or None (optional, default None) The minimal value of delta kinetic parameter for selecting transition genes. basis: str (optional, default `umap`) The dictionary key that corresponds to the reduced dimension in `.obsm` attribute. Can be `X_spliced_umap` or `X_total_umap`, etc. neigh_key: str (optional, default `neighbors`) The dictionary key for the neighbor information (stores nearest neighbor `indices`) in .uns. adj_key: str (optional, default `distances`) The dictionary key for the adjacency matrix of the nearest neighbor graph in .obsp. add_transition_key: str or None (default: None) The dictionary key that will be used for storing the transition matrix in .obsp. add_velocity_key: str or None (default: None) The dictionary key that will be used for storing the low dimensional velocity projection matrix in .obsm. method: str (optional, default `pearson`) The method to calculate the transition matrix and project high dimensional vector to low dimension, either `kmc`, `fp`, `cosine`, `pearson`, or `transform`. "kmc" is our new approach to learn the transition matrix via diffusion approximation or an Itô kernel. "cosine" or "pearson" are the methods used in the original RNA velocity paper or the scvelo paper (Note that scVelo implementation actually centers both dX and V, so its cosine kernel is equivalent to pearson correlation kernel but we also provide the raw cosine kernel). "kmc" option is arguable better than "correlation" or "cosine" as it not only considers the correlation but also the distance of the nearest neighbors to the high dimensional velocity vector. Finally, the "transform" method uses umap's transform method to transform new data points to the UMAP space. "transform" method is NOT recommended. Kernels that are based on the reconstructed vector field in high dimension is also possible. neg_cells_trick: bool (optional, default True) Whether we should handle cells having negative correlations in gene expression difference with high dimensional velocity vector separately. This option was borrowed from scVelo package (https://github.com/theislab/scvelo) and use in conjunction with "pearson" and "cosine" kernel. Not required if method is set to be "kmc". calc_rnd_vel: bool (default: False) A logic flag to determine whether we will calculate the random velocity vectors which can be plotted downstream as a negative control and used to adjust the quiver scale of the velocity field. xy_grid_nums: tuple (default: (50, 50)). A tuple of number of grids on each dimension. correct_density: bool (default: True) Whether to correct density when calculating the markov transition matrix. scale: bool (default: False) Whether to scale velocity when calculating the markov transition matrix, applicable to the `kmc` kernel. sample_fraction: None or float (default: None) The downsampled fraction of kNN for the purpose of acceleration, applicable to the `kmc` kernel. random_seed: int (default: 19491001) The random seed for numba to ensure consistency of the random velocity vectors. Default value 19491001 is a special day for those who care. key: str or None (default: None) The prefix key that will be prefixed to the keys for storing calculated transition matrix, projection vectors, etc. preserve_len: bool (default: False) Whether to preserve the length of high dimension vector length. When set to be True, the length of low dimension projected vector will be proportionally scaled to that of the high dimensional vector. enforce: bool (default: False) Whether to enforce 1) redefining use_for_transition column in obs attribute; However this is NOT executed if the argument 'transition_genes' is not None. 2) recalculation of the transition matrix. kernel_kwargs: dict A dictionary of paramters that will be passed to the kernel for constructing the transition matrix. Returns ------- adata: :class:`~anndata.AnnData` Returns an updated :class:`~anndata.AnnData` with projected velocity vectors, and a cell transition matrix calculated using either the Itô kernel method or similar methods from (La Manno et al. 2018). """ mapper_r = get_mapper_inverse() layer = mapper_r[ekey] if (ekey is not None and ekey in mapper_r.keys()) else ekey ekey, vkey, layer = get_ekey_vkey_from_adata(adata) if (ekey is None or vkey is None) else (ekey, vkey, layer) if calc_rnd_vel: numba_random_seed(random_seed) if neigh_key is not None and neigh_key in adata.uns.keys() and "indices" in adata.uns[neigh_key]: # use neighbor indices in neigh_key (if available) first for the sake of performance. indices = adata.uns[neigh_key]["indices"] if type(indices) is not np.ndarray: indices = np.array(indices) # simple case: the input is a knn graph if len(indices.shape) > 1: indices = indices[:, :n_neighbors] # general case else: idx = np.ones((len(indices), n_neighbors)) * np.nan for i, nbr in enumerate(indices): idx[i, : len(nbr)] = nbr indices = idx if np.any(np.isnan(indices)): main_warning("Resulting knn index matrix contains NaN. Check if n_neighbors is too large.") elif adj_key is not None and adj_key in adata.obsp.keys(): if use_mnn: neighbors = adata.uns["mnn"] indices, _ = adj_to_knn(neighbors, adata.uns["neighbors"]["indices"].shape[1]) indices = indices[:, 1:] else: knn_indices, _ = adj_to_knn(adata.obsp[adj_key], n_neighbors) # knn_adj = knn_to_adj(knn_indices, knn_dists) # user wouldn't expect such a function to change the neighborhood info... # consider writing them into a new item, or do this in connectivity.neighbors. # adata.uns["neighbors"]["indices"], adata.obsp["distances"] = knn_indices, knn_adj # dist, indices = ( # adata.obsp["distances"], # adata.uns["neighbors"]["indices"], # ) # indices, dist = indices[:, 1:], dist[:, 1:] indices = knn_indices[:, 1:] else: raise Exception( f"Neighborhood info '{adj_key}' is missing in the provided anndata object." "Run `dyn.tl.reduceDimension` or `dyn.tl.neighbors` first." ) if X is None and V is None: if transition_genes is None: if "use_for_transition" not in adata.var.keys() or enforce: use_for_dynamics = True if "use_for_dynamics" in adata.var.keys() else False adata = set_transition_genes( adata, vkey=vkey, min_r2=min_r2, use_for_dynamics=use_for_dynamics, min_alpha=min_alpha, min_gamma=min_gamma, min_delta=min_delta, ) transition_genes = adata.var_names[adata.var.use_for_transition.values] else: if not enforce: main_warning( "A new set of transition genes is used, but because enforce=False, " "the transition matrix might not be recalculated if it is found in .obsp." ) dynamics_genes = ( adata.var.use_for_dynamics if "use_for_dynamics" in adata.var.keys() else np.ones(adata.n_vars, dtype=bool) ) if type(transition_genes) is str: transition_genes = adata.var[transition_genes].to_list() transition_genes = np.logical_and(transition_genes, dynamics_genes.to_list()) elif areinstance(transition_genes, str): transition_genes = adata.var_names[dynamics_genes].intersection(transition_genes).to_list() elif areinstance(transition_genes, bool) or areinstance(transition_genes, np.bool_): transition_genes = np.array(transition_genes) transition_genes = np.logical_and(transition_genes, dynamics_genes.to_list()) else: raise TypeError( "transition genes should either be a key of adata.var, an array of gene names, or of booleans." ) if len(transition_genes) < 1: raise ValueError( "None of the transition genes provided has velocity values. (or `var.use_for_dynamics` is `False`)." ) adata.var["use_for_transition"] = False if type(transition_genes[0]) == bool: adata.var.use_for_transition = transition_genes else: adata.var.loc[transition_genes, "use_for_transition"] = True # X = adata[:, transition_genes].layers[ekey] if X is None else X X = index_gene(adata, adata.layers[ekey], transition_genes) if X is None else X V = ( ( # adata[:, transition_genes].layers[vkey] index_gene(adata, adata.layers[vkey], transition_genes) if vkey in adata.layers.keys() else None ) if V is None else V ) if X.shape != V.shape: raise Exception("X and V do not have the same number of dimensions.") if X_embedding is None: has_splicing, has_labeling = ( adata.uns["dynamics"]["has_splicing"], adata.uns["dynamics"]["has_labeling"], ) if has_splicing and has_labeling: main_warning( "\nYour data has both labeling / splicing data, please ensuring using the right `basis` " "({basis}):" "\n when using `velocity_S`, please use basis based on X_spliced data;" "\n when using `velocity_T, please use basis based X_total. " "\nIf not sure the data in adata.X, you may need to set `basis='X_spliced_umap'`" "(`basis='X_total_umap'`) when using `velocity_S` (`velocity_T`). " "" ) if "_" in basis and any([i in basis for i in ["X_", "spliced_", "unspliced_", "new_", "total"]]): basis_layer, basis = basis.rsplit("_", 1) adata = reduceDimension(adata, layer=basis_layer, reduction_method=basis) X_embedding = adata.obsm[basis] else: if vkey in ["velocity_S", "velocity_T"]: X_embedding = adata.obsm["X_" + basis] else: adata = reduceDimension(adata, layer=layer, reduction_method=basis) X_embedding = adata.obsm[layer + "_" + basis] if X.shape[0] != X_embedding.shape[0]: raise Exception("X and X_embedding do not have the same number of samples.") if X.shape[1] < X_embedding.shape[1]: raise Exception( "The number of dimensions of X is smaller than that of the embedding. Try lower the min_r2, " "min_gamma thresholds." ) V = V.A if sp.issparse(V) else V X = X.A if sp.issparse(X) else X finite_inds = get_finite_inds(V) X, V = X[:, finite_inds], V[:, finite_inds] if finite_inds.sum() < 5 and len(finite_inds) > 100: raise Exception( f"there are only {finite_inds.sum()} genes have finite velocity values. " f"Please make sure the {vkey} is correctly calculated! And if you run kinetic parameters " "estimation for each cell-group via `group` argument, make sure all groups have sufficient " "number of cells, e.g. 50 cells at least. Otherwise some cells may have NaN values for all " "genes." ) if method == "kmc" and n_pca_components is None: n_pca_components = 30 if n_pca_components is not None: X = log1p_(adata, X) X_plus_V = log1p_(adata, X + V) if "velocity_pca_fit" not in adata.uns_keys() or type(adata.uns["velocity_pca_fit"]) == str: pca = PCA( n_components=min(n_pca_components, X.shape[1] - 1), svd_solver="arpack", random_state=0, ) pca_fit = pca.fit(X) X_pca = pca_fit.transform(X) adata.uns["velocity_pca_fit"] = pca_fit adata.uns["velocity_PCs"] = pca_fit.components_.T adata.obsm["X_velocity_pca"] = X_pca X_pca, _, pca_fit = ( adata.obsm["X_velocity_pca"], adata.uns["velocity_PCs"], adata.uns["velocity_pca_fit"], ) Y_pca = pca_fit.transform(X_plus_V) V_pca = Y_pca - X_pca adata.obsm["velocity_pca_raw"] = V_pca X, V = X_pca[:, :n_pca_components], V_pca[:, :n_pca_components] # add both source and sink distribution if method == "kmc": if method + "_transition_matrix" in adata.obsp.keys() and not enforce: T = adata.obsp[method + "_transition_matrix"] if transition_matrix is None else transition_matrix kmc = KernelMarkovChain(P=T) else: kmc = KernelMarkovChain() kmc_args = { "n_recurse_neighbors": 2, "M_diff": 2, "epsilon": None, "adaptive_local_kernel": True, "tol": 1e-7, } kmc_args = update_dict(kmc_args, kernel_kwargs) if method + "_transition_matrix" not in adata.obsp.keys() or not enforce: kmc.fit( X, V, neighbor_idx=indices, sample_fraction=sample_fraction, **kmc_args, ) # T = kmc.P if correct_density: delta_X = kmc.compute_density_corrected_drift( X_embedding, kmc.Idx, normalize_vector=True, scale=scale ) # indices, k = 500 else: delta_X = kmc.compute_drift(X_embedding, num_prop=1, scale=scale) # indices, k = 500 # P = kmc.compute_stationary_distribution() # adata.obs['stationary_distribution'] = P if calc_rnd_vel: kmc = KernelMarkovChain() permute_rows_nsign(V) kmc.fit(X, V, **kmc_args) # neighbor_idx=indices, T_rnd = kmc.P if correct_density: delta_X_rnd = kmc.compute_density_corrected_drift( X_embedding, kmc.Idx, normalize_vector=True ) # indices, k = 500 else: delta_X_rnd = kmc.compute_drift(X_embedding) # P_rnd = kmc.compute_stationary_distribution() # adata.obs['stationary_distribution_rnd'] = P_rnd adata.uns["kmc"] = kmc elif method in ["pearson", "cosine"]: vs_kwargs = { "n_recurse_neighbors": 2, "max_neighs": None, "transform": "sqrt", "use_neg_vals": True, } vs_kwargs = update_dict(vs_kwargs, kernel_kwargs) if method + "_transition_matrix" in adata.obsp.keys() and not enforce: print("Using existing %s found in .obsp." % (method + "_transition_matrix")) T = adata.obsp[method + "_transition_matrix"] if transition_matrix is None else transition_matrix delta_X = projection_with_transition_matrix(X.shape[0], T, X_embedding, correct_density) X_grid, V_grid, D = velocity_on_grid( X_embedding[:, :2], (X_embedding + delta_X)[:, :2], xy_grid_nums=xy_grid_nums, ) else: T, delta_X, X_grid, V_grid, D = kernels_from_velocyto_scvelo( X, X_embedding, V, indices, neg_cells_trick, xy_grid_nums, method, correct_density=correct_density, **vs_kwargs, ) if calc_rnd_vel: permute_rows_nsign(V) (T_rnd, delta_X_rnd, X_grid_rnd, V_grid_rnd, D_rnd,) = kernels_from_velocyto_scvelo( X, X_embedding, V, indices, neg_cells_trick, xy_grid_nums, method, correct_density=correct_density, **vs_kwargs, ) elif method == "fp": graph_kwargs = { "k": 30, "E_func": "sqrt", "normalize_v": False, } graph_kwargs = update_dict(graph_kwargs, kernel_kwargs) fp_kwargs = { "D": 100, } fp_kwargs = update_dict(fp_kwargs, kernel_kwargs) ctmc_kwargs = { "eignum": 30, } ctmc_kwargs = update_dict(ctmc_kwargs, kernel_kwargs) if ( method + "_transition_matrix" in adata.obsp.keys() or method + "_transition_rate" in adata.obsp.keys() ) and not enforce: if method + "_transition_matrix" in adata.obsp.keys(): print("Using existing %s found in .obsp." % (method + "_transition_matrix")) T = adata.obsp[method + "_transition_matrix"] if transition_matrix is None else transition_matrix elif method + "_transition_rate" in adata.obsp.keys(): print("Using existing %s found in .obsp." % (method + "_transition_rate")) R = adata.obsp[method + "_transition_rate"] T = ContinuousTimeMarkovChain(P=R.T).compute_embedded_transition_matrix().T delta_X = projection_with_transition_matrix(T.shape[0], T, X_embedding, correct_density) else: E, _ = graphize_velocity(V, X, nbrs_idx=indices, **graph_kwargs) W = fp_operator(E, **fp_kwargs) ctmc = ContinuousTimeMarkovChain(P=W, **ctmc_kwargs) T = sp.csr_matrix(ctmc.compute_embedded_transition_matrix().T) delta_X = projection_with_transition_matrix(T.shape[0], T, X_embedding, correct_density) adata.obsp["fp_transition_rate"] = ctmc.P.T elif method == "transform": umap_trans, n_pca_components = ( adata.uns["umap_fit"]["fit"], adata.uns["umap_fit"]["n_pca_components"], ) if "pca_fit" not in adata.uns_keys() or type(adata.uns["pca_fit"]) == str: CM = adata.X[:, adata.var.use_for_dynamics.values] from ..preprocessing.utils import pca adata, pca_fit, X_pca = pca(adata, CM, n_pca_components, "X", return_all=True) adata.uns["pca_fit"] = pca_fit X_pca, pca_fit = adata.obsm["X"], adata.uns["pca_fit"] V = adata[:, adata.var.use_for_dynamics.values].layers[vkey] if vkey in adata.layers.keys() else None CM, V = CM.A if sp.issparse(CM) else CM, V.A if sp.issparse(V) else V V[np.isnan(V)] = 0 Y_pca = pca_fit.transform(CM + V) Y = umap_trans.transform(Y_pca) delta_X = Y - X_embedding if method not in ["pearson", "cosine"]: X_grid, V_grid, D = velocity_on_grid(X_embedding[:, :2], delta_X[:, :2], xy_grid_nums=xy_grid_nums) if calc_rnd_vel: X_grid_rnd, V_grid_rnd, D_rnd = velocity_on_grid( X_embedding[:, :2], delta_X_rnd[:, :2], xy_grid_nums=xy_grid_nums ) if preserve_len: basis_len, high_len = np.linalg.norm(delta_X, axis=1), np.linalg.norm(V, axis=1) scaler = np.nanmedian(basis_len) / np.nanmedian(high_len) for i in LoggerManager.progress_logger(range(adata.n_obs), progress_name="rescaling velocity norm"): idx = T[i].indices high_len_ = high_len[idx] T_i = T[i].data delta_X[i] *= T_i.dot(high_len_) / basis_len[i] * scaler if add_transition_key is None: transition_key = method + "_transition_matrix" else: transition_key = add_transition_key adata.obsp[transition_key] = T if add_velocity_key is None: velocity_key, grid_velocity_key = "velocity_" + basis, "grid_velocity_" + basis else: velocity_key, grid_velocity_key = add_velocity_key, "grid_" + add_velocity_key adata.obsm[velocity_key] = delta_X adata.uns[grid_velocity_key] = { "X_grid": X_grid, "V_grid": V_grid, "D": D, } if calc_rnd_vel: if add_transition_key is None: transition_rnd_key = method + "_transition_matrix_rnd" else: transition_rnd_key = add_transition_key + "_rnd" if add_velocity_key is None: velocity_rnd_key, grid_velocity_rnd_key = "velocity_" + basis + "_rnd", "grid_velocity_" + basis + "_rnd" else: velocity_rnd_key, grid_velocity_rnd_key = add_velocity_key + "_rnd", "grid_" + add_velocity_key + "_rnd" X_embedding_rnd = "X_" + basis + "_rnd" adata.obsp[transition_rnd_key] = T_rnd adata.obsm[X_embedding_rnd] = X_embedding adata.obsm[velocity_rnd_key] = delta_X_rnd adata.uns[grid_velocity_rnd_key] = { "X_grid": X_grid_rnd, "V_grid": V_grid_rnd, "D": D_rnd, } return adata
[docs]def confident_cell_velocities( adata, group, lineage_dict, ekey="M_s", vkey="velocity_S", basis="umap", confidence_threshold=0.85, only_transition_genes=False, ): """Confidently compute transition probability and project high dimension velocity vector to existing low dimension embeddings using progeintors and mature cell groups priors. Parameters ---------- adata: :class:`~anndata.AnnData` an Annodata object group: str The column key/name that identifies the cell state grouping information of cells. This will be used for calculating gene-wise confidence score in each cell state. lineage_dict: dict A dictionary describes lineage priors. Keys corresponds to the group name from `group` that corresponding to the state of one progenitor type while values correspond to the group names from `group` that corresponding to the states of one or multiple terminal cell states. The best practice for determining terminal cell states are those fully functional cells instead of intermediate cell states. Note that in python a dictionary key cannot be a list, so if you have two progenitor types converge into one terminal cell state, you need to create two records each with the same terminal cell as value but different progenitor as the key. Value can be either a string for one cell group or a list of string for multiple cell groups. ekey: str or None (default: `M_s`) The layer that will be used to retrieve data for identifying the gene is in induction or repression phase at each cell state. If `None`, .X is used. vkey: str or None (default: `velocity_S`) The layer that will be used to retrieve velocity data for calculating gene-wise confidence. If `None`, `velocity_S` is used. basis: str (optional, default `umap`) The dictionary key that corresponds to the reduced dimension in `.obsm` attribute. confidence_threshold: float (optional, default 0.85) The minimal threshold of the mean of the average progenitors and the average mature cells prior based gene-wise score. Only genes with score larger than this will be considered as confident transition genes for velocity projection. only_transition_genes: bool (optional, default False) Whether only use previous identified transition genes for confident gene selection, followed by velocity projection. Returns ------- adata: :class:`~anndata.AnnData` Returns an updated `~anndata.AnnData` with only confident genes based transition_matrix and projected embedding of high dimension velocity vectors in the existing embeddings of current cell state, calculated using either the Itô kernel method (default) or the diffusion approximation or the method from (La Manno et al. 2018). """ if not any([i.startswith("velocity") for i in adata.layers.keys()]): raise Exception( "You need to first run `dyn.tl.dynamics(adata)` to estimate kinetic parameters and obtain " "raw RNA velocity before running this function." ) if only_transition_genes: if "use_for_transition" not in adata.var.keys(): main_warning( "`dyn.tl.cell_velocities(adata)` is not performed yet. Rolling back to use all feature genes " "as input for supervised RNA velocity analysis." ) genes = adata.var_names[adata.var.use_for_dynamics] else: genes = adata.var_names[adata.var.use_for_transition] else: genes = adata.var_names[adata.var.use_for_dynamics] gene_wise_confidence( adata, group, lineage_dict, genes=genes, ekey=ekey, vkey=vkey, ) adata.var.loc[:, "avg_confidence"] = ( adata.var.loc[:, "avg_prog_confidence"] + adata.var.loc[:, "avg_mature_confidence"] ) / 2 confident_genes = genes[adata[:, genes].var["avg_confidence"] > confidence_threshold] adata.var["confident_genes"] = False adata.var.loc[confident_genes, "confident_genes"] = True X = adata[:, confident_genes].layers[ekey] V = adata[:, confident_genes].layers[vkey] X_embedding = adata.obsm["X_" + basis] cell_velocities( adata, enforce=True, X=X, V=V, X_embedding=X_embedding, basis=basis, transition_genes=confident_genes, ) return adata
[docs]def stationary_distribution(adata, method="kmc", direction="both", calc_rnd=True): """Compute stationary distribution of cells using the transition matrix. Parameters ---------- adata: :class:`~anndata.AnnData` an Annodata object method: str (default: `kmc`) The method to calculate the stationary distribution. direction: str (default: `both`) The direction of diffusion for calculating the stationary distribution, can be one of `both`, `forward`, `backward`. calc_rnd: bool (default: True) Whether to also calculate the stationary distribution from the control randomized transition matrix. Returns ------- adata: :class:`~anndata.AnnData` Returns an updated `~anndata.AnnData` with source, sink stationary distributions and the randomized results, depending on the direction and calc_rnd arguments. """ # row is the source and columns are targets T = adata.obsp["transition_matrix"] if method == "kmc": kmc = KernelMarkovChain() kmc.P = T if direction == "both": adata.obs["sink_steady_state_distribution"] = kmc.compute_stationary_distribution() kmc.P = T.T / T.T.sum(0) adata.obs["source_steady_state_distribution"] = kmc.compute_stationary_distribution() if calc_rnd: T_rnd = adata.obsp["transition_matrix_rnd"] kmc.P = T_rnd adata.obs["sink_steady_state_distribution_rnd"] = kmc.compute_stationary_distribution() kmc.P = T_rnd.T / T_rnd.T.sum(0) adata.obs["source_steady_state_distribution_rnd"] = kmc.compute_stationary_distribution() elif direction == "forward": adata.obs["sink_steady_state_distribution"] = kmc.compute_stationary_distribution() if calc_rnd: T_rnd = adata.obsp["transition_matrix_rnd"] kmc.P = T_rnd adata.obs["sink_steady_state_distribution_rnd"] = kmc.compute_stationary_distribution() elif direction == "backward": kmc.P = T.T / T.T.sum(0) adata.obs["source_steady_state_distribution"] = kmc.compute_stationary_distribution() if calc_rnd: T_rnd = adata.obsp["transition_matrix_rnd"] kmc.P = T_rnd.T / T_rnd.T.sum(0) adata.obs["sink_steady_state_distribution_rnd"] = kmc.compute_stationary_distribution() else: T = T.T if direction == "both": adata.obs["source_steady_state_distribution"] = diffusion(T, backward=True) adata.obs["sink_steady_state_distribution"] = diffusion(T) if calc_rnd: T_rnd = adata.obsp["transition_matrix_rnd"] adata.obs["source_steady_state_distribution_rnd"] = diffusion(T_rnd, backward=True) adata.obs["sink_steady_state_distribution_rnd"] = diffusion(T_rnd) elif direction == "forward": adata.obs["sink_steady_state_distribution"] = diffusion(T) if calc_rnd: T_rnd = adata.uns["transition_matrix_rnd"] adata.obs["sink_steady_state_distribution_rnd"] = diffusion(T_rnd) elif direction == "backward": adata.obs["source_steady_state_distribution"] = diffusion(T, backward=True) if calc_rnd: T_rnd = adata.obsp["transition_matrix_rnd"] adata.obs["source_steady_state_distribution_rnd"] = diffusion(T_rnd, backward=True)
[docs]def generalized_diffusion_map(adata, **kwargs): """Apply the diffusion map algorithm on the transition matrix build from Itô kernel. Parameters ---------- adata: :class:`~anndata.AnnData` AnnData object that contains the constructed transition matrix. kwargs: Additional parameters that will be passed to the diffusion_map_embedding function. Returns ------- adata: :class:`~anndata.AnnData` AnnData object that updated with X_diffusion_map embedding in obsm attribute. """ kmc = KernelMarkovChain() kmc.P = adata.obsp["transition_matrix"] dm_args = {"n_dims": 2, "t": 1} dm_args.update(kwargs) dm = kmc.diffusion_map_embedding(*dm_args) adata.obsm["X_diffusion_map"] = dm
[docs]def diffusion(M, P0=None, steps=None, backward=False): """Find the state distribution of a Markov process. Parameters ---------- M: :class:`~numpy.ndarray` (dimension n x n, where n is the cell number) The transition matrix. P0: :class:`~numpy.ndarray` (default None; dimension is n, ) The initial cell state. steps: int (default None) The random walk steps on the Markov transitioin matrix. backward: bool (default False) Whether the backward transition will be considered. Returns ------- Mu: :class:`~numpy.ndarray` The state distribution of the Markov process. """ if backward is True: M = M.T M = M / M.sum(1) if steps is None: # code inspired from https://github.com/prob140/prob140/blob/master/prob140/markov_chains.py#L284 eigenvalue, eigen = scp.linalg.eig( M, left=True, right=False ) # if not sp.issparse(M) else eigs(M) # source is on the row eigenvector = np.real(eigen) if not sp.issparse(M) else np.real(eigen.T) eigenvalue_1_ind = np.isclose(eigenvalue, 1) mu = eigenvector[:, eigenvalue_1_ind] / np.sum(eigenvector[:, eigenvalue_1_ind]) # Zero out floating poing errors that are negative. indices = np.logical_and(np.isclose(mu, 0), mu < 0) mu[indices] = 0 # steady state distribution else: mu = ( np.nanmean(M.dot(np.linalg.matrix_power(M, steps)), 0) if P0 is None else P0.dot(np.linalg.matrix_power(M, steps)) ) return mu
[docs]def expected_return_time(M, backward=False): """Find the expected returning time. Parameters ---------- M: :class:`~numpy.ndarray` (dimension n x n, where n is the cell number) The transition matrix. backward: bool (default False) Whether the backward transition will be considered. Returns ------- T: :class:`~numpy.ndarray` The expected return time (1 / steady_state_probability). """ steady_state = diffusion(M, P0=None, steps=None, backward=backward) T = 1 / steady_state return T
def kernels_from_velocyto_scvelo( X, X_embedding, V, indices, neg_cells_trick, xy_grid_nums, kernel="pearson", n_recurse_neighbors=2, max_neighs=None, transform="sqrt", use_neg_vals=True, correct_density=True, ): """utility function for calculating the transition matrix and low dimensional velocity embedding via the original pearson correlation kernel (La Manno et al., 2018) or the cosine kernel from scVelo (Bergen et al., 2019).""" n = X.shape[0] if indices is not None: rows = [] cols = [] vals = [] delta_X = np.zeros((n, X_embedding.shape[1])) for i in LoggerManager.progress_logger( range(n), progress_name=f"calculating transition matrix via {kernel} kernel with {transform} transform.", ): velocity = V[i, :] # project V to pca space if velocity.sum() != 0: i_vals = get_iterative_indices(indices, i, n_recurse_neighbors, max_neighs) # np.zeros((knn, 1)) diff = X[i_vals, :] - X[i, :] if transform == "log": diff_velocity = np.sign(velocity) * np.log1p(np.abs(velocity)) diff_rho = np.sign(diff) * np.log1p(np.abs(diff)) elif transform == "logratio": hi_dim, hi_dim_t = X[i, :], X[i, :] + velocity log2hidim = np.log1p(np.abs(hi_dim)) diff_velocity = np.log1p(np.abs(hi_dim_t)) - log2hidim diff_rho = np.log1p(np.abs(X[i_vals, :])) - np.log1p(np.abs(hi_dim)) elif transform == "linear": diff_velocity = velocity diff_rho = diff elif transform == "sqrt": diff_velocity = np.sign(velocity) * np.sqrt(np.abs(velocity)) diff_rho = np.sign(diff) * np.sqrt(np.abs(diff)) if kernel == "pearson": vals_ = einsum_correlation(diff_rho, diff_velocity, type="pearson") elif kernel == "cosine": vals_ = einsum_correlation(diff_rho, diff_velocity, type="cosine") rows.extend([i] * len(i_vals)) cols.extend(i_vals) vals.extend(vals_) vals = np.hstack(vals) vals[np.isnan(vals)] = 0 G = sp.csr_matrix((vals, (rows, cols)), shape=(X_embedding.shape[0], X_embedding.shape[0])) G = split_velocity_graph(G, neg_cells_trick) if neg_cells_trick: G, G_ = G confidence, ub_confidence = G.max(1).A.flatten(), np.percentile(G.max(1).A.flatten(), 98) dig_p = np.clip(ub_confidence - confidence, 0, 1) G.setdiag(dig_p) T = np.expm1(G / 0.1) if neg_cells_trick: if use_neg_vals: T -= np.expm1(-G_ / 0.1) else: T += np.expm1(G_ / 0.1) T.data = T.data + 1 # T = w * (~ direct_neighs).multiply(T) + (1 - w) * direct_neighs.multiply(T) # normalize so that each row sum up to 1 sparsefuncs.inplace_row_scale(T, 1 / np.abs(T).sum(axis=1).A1) T.setdiag(0) T.eliminate_zeros() delta_X = projection_with_transition_matrix(n, T, X_embedding, correct_density) X_grid, V_grid, D = velocity_on_grid( X_embedding[:, :2], (X_embedding + delta_X)[:, :2], xy_grid_nums=xy_grid_nums, ) return T, delta_X, X_grid, V_grid, D def projection_with_transition_matrix(n, T, X_embedding, correct_density=True): delta_X = np.zeros((n, X_embedding.shape[1])) with warnings.catch_warnings(): warnings.simplefilter("ignore") for i in LoggerManager.progress_logger( range(n), progress_name="projecting velocity vector to low dimensional embedding", ): idx = T[i].indices diff_emb = X_embedding[idx] - X_embedding[i, None] diff_emb /= norm(diff_emb, axis=1)[:, None] diff_emb[np.isnan(diff_emb)] = 0 T_i = T[i].data delta_X[i] = T_i.dot(diff_emb) if correct_density: delta_X[i] -= T_i.mean() * diff_emb.sum(0) return delta_X # utility functions for calculating the random cell velocities @jit(nopython=True) def numba_random_seed(seed): """Same as np.random.seed but for numba. Function adapated from velocyto. Parameters ---------- seed: int Random seed value """ np.random.seed(seed) @jit(nopython=True) def permute_rows_nsign(A): """Permute in place the entries and randomly switch the sign for each row of a matrix independently. Function adapted from velocyto Parameters ---------- A: :class:`~numpy.ndarray` A numpy array that will be permuted. """ plmi = np.array([+1, -1]) for i in range(A.shape[1]): np.random.shuffle(A[:, i]) A[:, i] = A[:, i] * np.random.choice(plmi, size=A.shape[0]) """This function can be removed now def embed_velocity( adata, x_basis, v_basis="velocity", emb_basis="X", velocity_gene_tag="transition_genes", num_pca=100, n_recurse_neighbors=2, M_diff=0.25, adaptive_local_kernel=True, normalize_velocity=True, return_kmc=False, **kmc_kwargs, ): if velocity_gene_tag is not None: X = adata.layers[x_basis][:, adata.var[velocity_gene_tag]] V = adata.layers[v_basis][:, adata.var[velocity_gene_tag]] else: X = adata.layers[x_basis] V = adata.layers[v_basis] X = log1p_(adata, X) X_emb = adata.obsm[emb_basis] Idx = adata.uns["neighbors"]["indices"] if num_pca is not None: pca = PCA() pca.fit(X) X_pca = pca.transform(X) Y_pca = pca.transform(X + V) V_pca = Y_pca - X_pca else: X_pca = X V_pca = V kmc = KernelMarkovChain() kmc.fit( X_pca[:, :num_pca], V_pca[:, :num_pca], neighbor_idx=Idx, n_recurse_neighbors=n_recurse_neighbors, M_diff=M_diff, adaptive_local_kernel=adaptive_local_kernel, **kmc_kwargs, ) Uc = kmc.compute_density_corrected_drift(X_emb, normalize_vector=normalize_velocity) if return_kmc: return Uc, kmc else: return Uc"""