boundary-aware-centrality/comparison_edge_scores.py

import math

import matplotlib.pyplot as plt
import numpy as np
import squidpy as sq
from graph_tool.all import *

from src import centrality
from src import plot
from src import fitting


def merfish():
    """
    Merfish dataset from `squidpy`.
    """
    adata = sq.datasets.merfish()
    adata = adata[adata.obs.Bregma == -9].copy()
    return adata


def mibitof():
    """
    Mibitof dataset from `squidpy`.
    """
    adata = sq.datasets.mibitof()
    return adata


def degree(g, weight):
    # VertexPropertyMap
    vp = g.new_vertex_property("double")
    for v in g.vertices():
        neighbours = g.get_all_neighbours(v)
        vp[v] = len(neighbours)
    return vp


def leverage(g, weight):
    # VertexPropertyMap
    vp = g.new_vertex_property("double")
    for v in g.vertices():
        li = 0.0
        neighbours = g.get_all_neighbours(v)
        ki = len(neighbours)
        if ki == 0:
            continue
        # sum
        for nv in neighbours:
            other_neighbours = g.get_all_neighbours(nv)
            kj = len(other_neighbours)
            li += (ki - kj) / (ki + kj)
        li /= ki
        vp[v] = li
    return vp


def path(g, weight):
    # NOTE is this not just betweenness?
    ep = g.new_vertex_property("double")
    for v in g.vertices():
        for u in g.vertices():
            if (v == u):
                continue
            paths = graph_tool.topology.all_shortest_paths(g, v, u, weights=weight, edges=True)
            for edges in paths:
                for edge in edges:
                    for idx, g_e in enumerate(g.edges()):
                        if (g_e == edge):
                            # NOTE we end up counting twice!
                            ep[idx] += 0.5;
                            break
    # for e in g.edges():
    #     ep[e] /= 2;
    return ep


def random_graph(n=5000, seed=None):
    """
    Uniformly random point cloud generation.
    `n` [int] Number of points to generate. Default 5000 seems like a good starting point in point density and corresponding runtime for the subsequent calculations.
    @return [numpy.ndarray] Array of shape(n, 2) containing the coordinates for each point of the generated point cloud.
    """
    if seed is None:
        import secrets
        seed = secrets.randbits(128)
    rng = np.random.default_rng(seed=seed)
    return rng.random((n, 2)), seed


def spatial_graph(adata):
    """
    Generate the spatial graph using delaunay for the given `adata`.
    `adata` will contain the calculated spatial graph contents in the keys
    adata.obsm['spatial']` in case the `adata` is created from a dataset of *squidpy*.
    @return [Graph] generated networkx graph from adata.obsp['spatial_distances']
    """
    g, pos = graph_tool.generation.triangulation(adata, type="delaunay")
    g.vp["pos"] = pos
    weight = g.new_edge_property("double")
    for e in g.edges():
        weight[e] = math.sqrt(sum(map(abs, pos[e.source()].a - pos[e.target()].a)))**2
    return g, weight


def apply(g, seed, weight, convex_hull, ax, method, method_name):
    # calculate centrality values
    ep = None
    if method_name == "Betweeness":
        vp, ep = method(g, weight=weight)
    else:
        ep = method(g, weight=weight)
    ep.a = np.nan_to_num(ep.a) # correct floating point values

    # normalization
    min_val, max_val = ep.a.min(), ep.a.max()
    ep.a = (ep.a - min_val) / (max_val - min_val)

    quantification = plot.quantification_data_edges(g, ep, convex_hull)

    # optimize model's piece-wise linear function
    d = quantification[:, 0]
    C = quantification[:, 1]
    m_opt, c0_opt, b_opt, aic_opt = fitting.fit_piece_wise_linear(d, C)

    # TODO
    # should this be part of the plotting function itself, it should not be necessary for me to do this
    d_curve = np.linspace(min(d), max(d), 500)
    C_curve = np.piecewise(
        d_curve,
        [d_curve <= b_opt, d_curve > b_opt],
        [lambda x: m_opt * x + c0_opt, lambda x: m_opt * b_opt + c0_opt]
    )
    # plot model containing modeled piece-wise linear function
    plot.quantification_plot(ax, quantification, d_curve, C_curve, method_name, aic_opt)


#
# - Create a random point cloud and calculate a triangulation on it
# - For that graph calculate the convex hull
# - Draw the graph with the convex hull
# - For each centrality measure
#   - apply centrality measure to the next axis
# - Draw the corresponding resulting models into a grid
#
points, seed = random_graph(n=5000)
g, weight = spatial_graph(points)
g = GraphView(g)
# calculate convex hull
convex_hull = centrality.convex_hull(g)

# plot graph with convex_hull
fig_graph, ax_graph = plt.subplots(figsize=(15, 12))
# draw without any centrality measure `ep`
ep = g.new_edge_property("double")
plot.graph_plot(fig_graph, ax_graph, g, ep, convex_hull, f"Pointcould (seed: {seed})", True) # draw edges
fig_graph.savefig(f"comparison_edge_scores_artificial_graph.svg", format='svg')

fig = plt.figure(figsize=(15, 12))
row1, row2 = fig.subplots(2, 4)

# TODO run, betweenness, k-path, eigenedge, etc.
# - some share similarities to the node based counter parts

ax1, ax2, ax3, ax4 = row1
apply(g, None, weight, convex_hull, ax1, betweenness, "Betweeness")

# ax1, ax2, ax3, ax4 = row2
# apply(g, None, weight, convex_hull, ax1, katz, "Katz")
# apply(g, None, weight, convex_hull, ax2, hits, "Hits")
# apply(g, None, weight, convex_hull, ax3, leverage, "Leverage")
# apply(g, None, weight, convex_hull, ax4, degree, "Degree")

fig.savefig(f"Comparison_edge_centralities_artificial_.svg", format='svg')