149 lines
5.2 KiB
Python
149 lines
5.2 KiB
Python
import math
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import matplotlib.pyplot as plt
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import numpy as np
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from graph_tool.all import *
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from src import centrality
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from src import plot
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from src import fitting
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def leverage(g, weight):
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# VertexPropertyMap
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vp = g.new_vertex_property("double")
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for v in g.vertices():
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li = 0.0
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neighbours = g.get_all_neighbours(v)
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ki = len(neighbours)
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# sum
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for nv in neighbours:
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other_neighbours = g.get_all_neighbours(nv)
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kj = len(other_neighbours)
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li += (ki - kj) / (ki + kj)
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li /= ki
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vp[v] = li
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return vp
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def random_graph(n=5000, seed=None):
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"""
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Uniformly random point cloud generation.
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`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.
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@return [numpy.ndarray] Array of shape(n, 2) containing the coordinates for each point of the generated point cloud.
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"""
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if seed is None:
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import secrets
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seed = secrets.randbits(128)
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rng = np.random.default_rng(seed=seed)
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return rng.random((n, 2)), seed
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def sub_spatial_graph(adata, percentage):
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sub_adata = np.array([])
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distance_of_center = 0.5 * percentage
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for point in adata:
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if point[0] > 0.5 - distance_of_center and point[0] <= 0.5 + distance_of_center:
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if point[1] > 0.5 - distance_of_center and point[1] <= 0.5 + distance_of_center:
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sub_adata = np.append(sub_adata, [point[0], point[1]])
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sub_adata = sub_adata.reshape(sub_adata.shape[0] // 2, 2)
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return spatial_graph(sub_adata)
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def spatial_graph(adata):
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"""
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Generate the spatial graph using delaunay for the given `adata`.
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`adata` will contain the calculated spatial graph contents in the keys
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adata.obsm['spatial']` in case the `adata` is created from a dataset of *squidpy*.
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@return [Graph] generated networkx graph from adata.obsp['spatial_distances']
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"""
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g, pos = graph_tool.generation.triangulation(adata, type="delaunay")
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g.vp["pos"] = pos
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weight = g.new_edge_property("double")
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for e in g.edges():
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weight[e] = math.sqrt(sum(map(abs, pos[e.source()].a - pos[e.target()].a)))**2
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return g, weight
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def apply(g, weight, convex_hull, ax, method, method_name):
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# calculate centrality values
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vp = None
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if method_name == "Betweeness":
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vp, ep = method(g, weight=weight)
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elif method_name == "Eigenvector":
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ep, vp = method(g, weight=weight)
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elif method_name == "Hits":
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ep, vp, hub_centrality = method(g, weight=weight)
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else:
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vp = method(g, weight=weight)
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vp.a = np.nan_to_num(vp.a) # correct floating point values
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# normalization
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min_val, max_val = vp.a.min(), vp.a.max()
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vp.a = (vp.a - min_val) / (max_val - min_val)
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# generate model based on convex hull and associated centrality values
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quantification = plot.quantification_data(g, vp, convex_hull)
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# optimize model's piece-wise linear function
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d = quantification[:, 0]
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C = quantification[:, 1]
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m_opt, c0_opt, b_opt, aic_opt = fitting.fit_piece_wise_linear(d, C)
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# TODO
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# should this be part of the plotting function itself, it should not be necessary for me to do this
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d_curve = np.linspace(min(d), max(d), 500)
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C_curve = np.piecewise(
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d_curve,
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[d_curve <= b_opt, d_curve > b_opt],
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[lambda x: m_opt * x + c0_opt, lambda x: m_opt * b_opt + c0_opt]
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)
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# plot model containing modeled piece-wise linear function
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plot.quantification_plot(ax, quantification, d_curve, C_curve, method_name, aic_opt)
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#
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# - Create a random point cloud and calculate a triangulation on it
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# - For that graph calculate the convex hull
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# - Draw the graph with the convex hull
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# - For each centrality measure
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# - apply centrality measure to the next axis
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# - Draw the corresponding resulting models into a grid
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#
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points, seed = random_graph(n=5000)
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g, weight = spatial_graph(points)
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g = GraphView(g)
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# calculate convex hull
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convex_hull = centrality.convex_hull(g)
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# plot graph with convex_hull
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fig_graph, ax_graph = plt.subplots(figsize=(15, 12))
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# draw without any centrality measure `vp`
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vp = g.new_vertex_property("double")
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plot.graph_plot(fig_graph, ax_graph, g, vp, convex_hull, f"Pointcloud (seed: {seed})")
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fig_graph.savefig("point_cloud_diff_comparison_5000_pagerank_leverage.svg", format='svg')
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fig = plt.figure(figsize=(15, 12))
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row1, row2 = fig.subplots(2, 2)
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ax1, ax2 = row1
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apply(g, weight, convex_hull, ax1, pagerank, "PageRank")
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apply(g, weight, convex_hull, ax2, leverage, "Leverage")
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g_sub, weight_sub = sub_spatial_graph(points, 0.5)
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g_sub = GraphView(g_sub)
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convex_hull = centrality.convex_hull(g_sub)
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# plot graph with convex_hull
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fig_graph, ax_graph = plt.subplots(figsize=(15, 12))
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# draw without any centrality measure `vp`
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vp = g_sub.new_vertex_property("double")
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plot.graph_plot(fig_graph, ax_graph, g_sub, vp, convex_hull, f"Pointcloud (50% of original)")
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fig_graph.savefig("point_cloud_diff_comparison_5000_sub_pagerank_leverage.svg", format='svg')
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ax1, ax2 = row2
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apply(g_sub, weight_sub, convex_hull, ax1, pagerank, "PageRank")
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apply(g_sub, weight_sub, convex_hull, ax2, leverage, "Leverage")
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fig.savefig(f"model_diff_comparison_5000_pagerank_leverage.svg", format='svg')
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