189 lines
6.7 KiB
Python
189 lines
6.7 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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# import squidpy as sq
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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 merfish():
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"""
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Merfish dataset from `squidpy`.
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"""
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adata = sq.datasets.merfish()
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adata = adata[adata.obs.Bregma == -9].copy()
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return adata
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def mibitof():
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"""
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Mibitof dataset from `squidpy`.
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"""
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adata = sq.datasets.mibitof()
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return adata
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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 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.obps['spatial_distances']` and `adata.obsm['spatial']` afterwards too.
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@return [Graph] generated networkx graph from adata['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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# generate spatial graph from a given dataset
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# g, weight = spatial_graph(merfish().obsm['spatial'])
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for i in range(1, 10):
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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 centrality values
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vp = closeness(g, weight=weight)
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vp.a = np.nan_to_num(vp.a) # correct floating point values
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# ep.a = np.nan_to_num(ep.a) # correct floating point values
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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 = plt.figure(figsize=(15, 5))
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ax0, ax1 = fig.subplots(1, 2)
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plot.graph_plot(fig, ax0, g, vp, convex_hull, f"Random Graph (seed: {seed})\nCloseness")
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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 = 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(ax1, quantification, d_curve, C_curve, 'Models')
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# linear regression model
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m_reg, c_reg = fitting.fit_linear_regression(d, C)
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x = np.linspace(min(d), max(d), 500)
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y = m_reg * x + c_reg
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ax1.plot(x, y, color='k', linewidth=1, label="Simple Linear Regression")
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ax1.legend()
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fig.savefig(f"random_point_clouds/{i}_closeness.svg", format='svg')
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# ---------------------------------------------------------------------------------------------
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# calculate centrality values
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vp, ep = betweenness(g, weight=weight)
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vp.a = np.nan_to_num(vp.a) # correct floating point values
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# ep.a = np.nan_to_num(ep.a) # correct floating point values
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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 = plt.figure(figsize=(15, 5))
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ax0, ax1 = fig.subplots(1, 2)
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plot.graph_plot(fig, ax0, g, vp, convex_hull, f"Random Graph (seed: {seed})\nBetweenness")
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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 = 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(ax1, quantification, d_curve, C_curve, 'Models')
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# linear regression model
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m_reg, c_reg = fitting.fit_linear_regression(d, C)
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x = np.linspace(min(d), max(d), 500)
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y = m_reg * x + c_reg
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ax1.plot(x, y, color='k', linewidth=1, label="Simple Linear Regression")
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ax1.legend()
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fig.savefig(f"random_point_clouds/{i}_betweenness.svg", format='svg')
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# ---------------------------------------------------------------------------------------------
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# calculate centrality values
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vp = pagerank(g, weight=weight)
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vp.a = np.nan_to_num(vp.a) # correct floating point values
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# ep.a = np.nan_to_num(ep.a) # correct floating point values
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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 = plt.figure(figsize=(15, 5))
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ax0, ax1 = fig.subplots(1, 2)
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plot.graph_plot(fig, ax0, g, vp, convex_hull, f"Random Graph (seed: {seed})\nPageRank")
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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 = 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(ax1, quantification, d_curve, C_curve, 'Models')
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# linear regression model
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m_reg, c_reg = fitting.fit_linear_regression(d, C)
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x = np.linspace(min(d), max(d), 500)
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y = m_reg * x + c_reg
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ax1.plot(x, y, color='k', linewidth=1, label="Simple Linear Regression")
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ax1.legend()
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fig.savefig(f"random_point_clouds/{i}_pagerank.svg", format='svg')
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