import math import matplotlib.pyplot as plt from matplotlib.collections import LineCollection import matplotlib as mpl import numpy as np import squidpy as sq import scipy import spatialdata as sd from spatialdata_io.experimental import to_legacy_anndata 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 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 g.ep["weight"] = weight return g, weight def plot_graph_nodes(g, centralities, fig, ax, name): pos = g.vp["pos"] x = [] y = [] for v in g.vertices(): ver = pos[v] x.append(ver[0]) y.append(ver[1]) sc = ax.scatter(x, y, s=1, c=centralities, cmap=plt.cm.plasma) ax.set_title(name) fig.colorbar(sc, ax=ax) def plot_relationship_nodes(g, vp, convex_hull, fig, ax, name): quantification = plot.quantification_data(g, vp, 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, M=100) # 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] ) ax.set_title(name) ax.set_xlabel('Distance to Bounding-Box') ax.set_ylabel('Centrality') ax.scatter(quantification[:, 0], quantification[:, 1], c=quantification[:, 1], cmap=plt.cm.plasma, s=0.2) ax.plot(d_curve, C_curve, color='g', linewidth=1, label=f"m = {m_opt} | b = {b_opt} | c = {c0_opt}") ax.legend() def plot_degree_distribution(g, fig, ax, name): ax.set_title(name) ax.set_ylabel('Degree') ax.set_xlabel('# Occurances') degrees = g.get_total_degrees(list(g.vertices())) bins = degrees.max() - degrees.min() counts, bins, patches = ax.hist(degrees, bins=bins, orientation='horizontal') # Label the percentages below the x-axis... # bin_centers = 0.5 * np.diff(bins) + bins[:-1] # for count, x in zip(counts, bin_centers): # # Label the percentages # percent = '%0.000f%%' % (100 * float(count) / counts.sum()) # ax.annotate(percent, xy=(x, 0), xycoords=('data', 'axes fraction'), # xytext=(0, -18), textcoords='offset points', va='top', ha='center') points, seed = random_graph(n=2000, seed=231533135843957409942915332448253409428) g, weight = spatial_graph(points) # adata = merfish() # g, weight = spatial_graph(adata.obsm['spatial']) g = GraphView(g) # relationship with betweenness scoring for both node and edges vp = pagerank(g, weight=weight) vp.a = np.nan_to_num(vp.a) # correct floating point values # plot graph fig = plt.figure(figsize=(16, 9), layout='constrained') fig.suptitle(f"Artical (n = 2000 | seed {seed})", fontsize=16) ax1, ax2 = fig.subplots(1, 2) # relationship with betweenness scoring for both node and edges vp = pagerank(g, weight=weight) vp.a = np.nan_to_num(vp.a) # correct floating point values # normalize centrality values min_val, max_val = vp.a.min(), vp.a.max() vp.a = (vp.a - min_val) / (max_val - min_val) # compare relationships convex_hull = centrality.convex_hull(g) plot_degree_distribution(g, fig, ax2, "Degree Distribution") plot_relationship_nodes(g, vp, convex_hull, fig, ax1, "Pagerank Centrality with fitted model") fig.savefig(f"degree_distribution_vs_pagerank_artifical.pdf", format='pdf')