145 lines
4.8 KiB
Python
145 lines
4.8 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 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 random_graph_favor_border(n=3000, seed = None):
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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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vps = np.zeros((n, 2))
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for i in range(0, n):
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r_x = rng.random()
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if rng.random() > 0.5:
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while (r_x > 0.3 and r_x < 0.7):
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r_x = rng.random()
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r_y = rng.random()
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if rng.random() > 0.5:
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while (r_y > 0.3 and r_y < 0.7):
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r_y = rng.random()
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vps[i][0] = r_x
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vps[i][1] = r_y
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return vps, seed
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def random_graph_favor_center(n=3000, seed = None):
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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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vps = np.zeros((n, 2))
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for i in range(0, n):
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r_x = rng.random()
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if rng.random() > 0.7:
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while (r_x < 0.4 or r_x > 0.6):
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r_x = rng.random()
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r_y = rng.random()
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if rng.random() > 0.7:
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while (r_y < 0.4 or r_y > 0.6):
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r_y = rng.random()
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vps[i][0] = r_x
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vps[i][1] = r_y
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return vps, seed
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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, seed, weight, convex_hull, ax, method, method_name):
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# calculate centrality values
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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, 'Models', 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()
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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, 5))
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# draw without any centrality measure `vp`
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plot.graph_plot(fig_graph, ax_graph, g, vp, convex_hull, f"Pointcloud (seed: {seed}\n{method_name}")
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fig_graph.savefig("Pointcloud_graph.svg", format='svg')
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fig = plt.figure(figsize=(15, 10))
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axs = fig.subplots(2, 4)
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i = 0
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for ax in axs:
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# TODO select corresponding centrality measure method
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apply(g, seed, weight, convex_hull, ax, closeness, "Closeness")
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apply(g, seed, weight, convex_hull, ax, pagerank, "PageRank")
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apply(g, seed, weight, convex_hull, ax, betweeness, "Betweeness")
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apply(g, seed, weight, convex_hull, ax, eigenvector, "Eigenvector")
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apply(g, seed, weight, convex_hull, ax, katz, "Katz")
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# TODO to implement
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# - Laplacian
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# - Leverage
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# - Degree (seriously?)
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i += 1
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fig.savefig(f"Comparison_Pointcloud.svg", format='svg')
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