Average Cell Shapes

avg_shape(obj_names: list[str], gw_dist_dict: dict[tuple[str, str], float], iodms: dict[str, numpy.ndarray[Any, numpy.dtype[numpy.float64]]], gw_coupling_mat_dict: dict[tuple[str, str], scipy.sparse._coo.coo_array])

Compute capped and uncapped average distance matrices. In both cases the distance matrix is rescaled so that the minimal distance between two points is 1. The “capped” distance matrix has a max distance of 2.

Parameters

  • obj_names (list[str]) – Keys for the gw_dist_dict and iodms.

  • gw_dist_dict (dict[tuple[str, str], float]) – Dictionary mapping ordered pairs (cellA_name, cellB_name) to Gromov-Wasserstein distances.

  • iodms (dict[str, numpy.ndarray[Any, numpy.dtype[numpy.float64]]]) – (intra-object distance matrices) - Maps object names to intra-object distance matrices. Matrices are assumed to be given in vector form rather than squareform.

  • gw_coupling_mat_dict (dict[tuple[str, str], scipy.sparse._coo.coo_array]) – Dictionary mapping ordered pairs (cellA_name, cellB_name) to Gromov-Wasserstein coupling matrices from cellA to cellB.

avg_shape_spt(cell_names: list[str], gw_dist_dict: dict[tuple[str, str], float], icdms: dict[str, numpy.ndarray[Any, numpy.dtype[numpy.float64]]], gw_coupling_mat_dict: dict[tuple[str, str], scipy.sparse._coo.coo_array], k: int) → tuple[numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float64]]]

Given a set of cells together with their intracell distance matrices and the (precomputed) pairwise GW coupling matrices between cells, construct a morphological “average” of cells in the cluster. This function:

  • aligns all cells in the cluster with each other using the coupling matrices

  • takes a “local average” of all intracell distance matrices, forming a distance matrix which models the average local connectivity structure of the neurons

  • draw a neighborh

  • draws a minimum spanning tree through the intracell distance graph, allowing us to visualize this average morphology

Parameters

  • cell_names (list[str]) – The cluster you want to take the average of, expressed as a list of names of cells in the cluster. These should be names that occur in the keys for the other dictionary arguments.

  • gw_dist_dict (dict[tuple[str, str], float]) – Dictionary mapping ordered pairs (cellA_name, cellB_name) to Gromov-Wasserstein distances between them, as returned by cajal.utilities.dist_mat_of_dict.

  • icdms (dict[str, numpy.ndarray[Any, numpy.dtype[numpy.float64]]]) – (intra-cell distance matrices) - Maps cell names to intra-cell distance matrices. Matrices are assumed to be given in vector form rather than squareform. Intracell distances are computed by any of the sampling functions in sample_swc, sample_seg, etc. and are read from file by cell_iterator_csv.

  • gw_coupling_mat_dict (dict[tuple[str, str], scipy.sparse._coo.coo_array]) – Dictionary mapping ordered pairs (cellA_name, cellB_name) to Gromov-Wasserstein coupling matrices from cellA to cellB, with cellA_name < cellB_name lexicographically

  • k (int) – how many neighbors in the nearest-neighbors graph in step 3

Returns

A pair (adjacency_matrix, confidence) where adjacency_matrix is a Numpy matrix of shape (n, n) (where n is the number of points in each sampled cell) and confidence is an array of shape (n) adjacency_matrix has values between 0 and 2. When “confidence” at a node in the average graph is high, the node is not very close to its nearest neighbor. We can think of this as saying that this node in the averaged graph is a kind of poorly amalgamated blend of different features in different graphs. Conversely, when confidence is low, and the node is close to its nearest neighbor, we interpret this as meaning that this node and its nearest neighbor appear together in many of the graphs being averaged, so this is potentially a good representation of some edge that really appears in many of the graphs.

Return type

tuple[numpy.ndarray[Any, numpy.dtype[numpy.float64]], numpy.ndarray[Any, numpy.dtype[numpy.float64]]]