295 lines
11 KiB
Python
295 lines
11 KiB
Python
import math
|
|
|
|
import matplotlib.pyplot as plt
|
|
import numpy as np
|
|
from graph_tool.all import *
|
|
|
|
from src import centrality
|
|
from src import plot
|
|
from src import fitting
|
|
|
|
|
|
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)
|
|
# 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 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 sub_spatial_graph(adata, percentage):
|
|
sub_adata = np.array([])
|
|
distance_of_center = 0.5 * percentage
|
|
for point in adata:
|
|
if point[0] > 0.5 - distance_of_center and point[0] <= 0.5 + distance_of_center:
|
|
if point[1] > 0.5 - distance_of_center and point[1] <= 0.5 + distance_of_center:
|
|
sub_adata = np.append(sub_adata, [point[0], point[1]])
|
|
|
|
sub_adata = sub_adata.reshape(sub_adata.shape[0] // 2, 2)
|
|
return spatial_graph(sub_adata)
|
|
|
|
|
|
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 plot_graph_diff(G, c, fig, ax, name, cmap=plt.cm.plasma):
|
|
pos = G.vp["pos"]
|
|
x = []
|
|
y = []
|
|
distance_of_center = 0.5 * percentage
|
|
for v in G.vertices():
|
|
ver = pos[v]
|
|
if ver[0] > 0.5 - distance_of_center and ver[0] <= 0.5 + distance_of_center:
|
|
if ver[1] > 0.5 - distance_of_center and ver[1] <= 0.5 + distance_of_center:
|
|
x.append(ver[0])
|
|
y.append(ver[1])
|
|
|
|
sc = ax.scatter(x, y, s=1, cmap=cmap, c=c) # map closeness values as color mapping on the verticies
|
|
ax.set_title(name)
|
|
fig.colorbar(sc, ax=ax)
|
|
|
|
|
|
def apply(g, seed, weight, convex_hull, ax, method, method_name):
|
|
# calculate centrality values
|
|
vp = None
|
|
if method_name == "Betweenness":
|
|
vp, ep = method(g, weight=weight)
|
|
elif method_name == "Eigenvector":
|
|
ep, vp = method(g, weight=weight)
|
|
elif method_name == "Hits":
|
|
ep, vp, hub_centrality = method(g, weight=weight)
|
|
else:
|
|
vp = method(g, weight=weight)
|
|
vp.a = np.nan_to_num(vp.a) # correct floating point values
|
|
|
|
# generate model based on convex hull and associated centrality values
|
|
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)
|
|
|
|
# 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
|
|
if ax is not None:
|
|
plot.quantification_plot(ax, quantification, d_curve, C_curve, method_name, aic_opt)
|
|
|
|
# normalization
|
|
min_val, max_val = vp.a.min(), vp.a.max()
|
|
vp.a = (vp.a - min_val) / (max_val - min_val)
|
|
|
|
return vp
|
|
|
|
|
|
def apply_corrected(g, seed, weight, convex_hull, ax, method, method_name):
|
|
# calculate centrality values
|
|
vp = None
|
|
ep = None
|
|
if method_name == "Betweenness":
|
|
vp, ep = method(g, weight=weight)
|
|
elif method_name == "Eigenvector":
|
|
ep, vp = method(g, weight=weight)
|
|
elif method_name == "Hits":
|
|
ep, vp, hub_centrality = method(g, weight=weight)
|
|
else:
|
|
vp = method(g, weight=weight)
|
|
vp.a = np.nan_to_num(vp.a) # correct floating point values
|
|
|
|
# normalization
|
|
# min_val, max_val = vp.a.min(), vp.a.max()
|
|
# vp.a = (vp.a - min_val) / (max_val - min_val)
|
|
|
|
# generate model based on convex hull and associated centrality values
|
|
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)
|
|
|
|
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
|
|
if ax is not None:
|
|
plot.quantification_plot(ax, quantification, d_curve, C_curve, method_name, aic_opt)
|
|
|
|
vp = centrality.correct(g, vp, m_opt, c0_opt, b_opt)
|
|
# normalization
|
|
min_val, max_val = vp.a.min(), vp.a.max()
|
|
vp.a = (vp.a - min_val) / (max_val - min_val)
|
|
|
|
return vp
|
|
|
|
#
|
|
# - 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 `vp`
|
|
vp, ep = betweenness(g, weight=weight)
|
|
|
|
plot.graph_plot(fig_graph, ax_graph, g, vp, convex_hull, f"Pointcloud (seed: {seed})")
|
|
fig_graph.savefig("model_prediction_graph_original_betweenness_5000.svg", format='svg')
|
|
|
|
# normalization
|
|
min_val, max_val = vp.a.min(), vp.a.max()
|
|
vp.a = (vp.a - min_val) / (max_val - min_val)
|
|
vp_betweenness_original = vp
|
|
|
|
for percentage in np.arange(0.1, 1, 0.1, dtype=float):
|
|
print(f"Percentage: {percentage:.0%}")
|
|
g_sub, weight_sub = sub_spatial_graph(points, percentage)
|
|
g_sub = GraphView(g_sub)
|
|
convex_hull = centrality.convex_hull(g_sub)
|
|
# draw subgraph
|
|
fig_sub = plt.figure(figsize=(25, 12))
|
|
ax1, ax2 = fig_sub.subplots(1, 2)
|
|
vp, ep = betweenness(g_sub, weight=weight_sub)
|
|
plot.graph_plot(fig_sub, ax1, g_sub, vp, convex_hull, f"{percentage:.0%} of Pointcloud (seed: {seed})")
|
|
|
|
min_val, max_val = vp.a.min(), vp.a.max()
|
|
vp.a = (vp.a - min_val) / (max_val - min_val)
|
|
|
|
vp_betweenness_corrected = apply_corrected(g_sub, seed, weight_sub, convex_hull, None, betweenness, "Betweenness")
|
|
plot.graph_plot(fig_sub, ax2, g_sub, vp_betweenness_corrected, convex_hull, f"{percentage:.0%} of Pointcloud with applied prediction")
|
|
fig_sub.savefig(f"model_prediction_subgraph_betweenness_5000_{percentage * 100:.0f}_percent.svg", format='svg')
|
|
|
|
distance_of_center = 0.5 * percentage
|
|
|
|
sub_keys = iter(g_sub.vertices())
|
|
keys = iter(g.vertices())
|
|
|
|
scores = []
|
|
raw_sub_scores = []
|
|
sub_scores = []
|
|
raw_diff_scores = []
|
|
diff_scores = []
|
|
|
|
for sub_key in sub_keys:
|
|
key = next(keys)
|
|
position = g.vp["pos"][key]
|
|
while not (position[0] > 0.5 - distance_of_center and position[0] <= 0.5 + distance_of_center and position[1] > 0.5 - distance_of_center and position[1] <= 0.5 + distance_of_center):
|
|
key = next(keys)
|
|
position = g.vp["pos"][key]
|
|
# NOTE print corresponding position (which are identical)
|
|
# position = g.vp["pos"][key]
|
|
# sub_position = g_sub.vp["pos"][sub_key]
|
|
# print(f"position: {position} | sub_position: {sub_position}")
|
|
|
|
# calculate for betweenness
|
|
value = vp_betweenness_original[key]
|
|
pre_prediction = vp[sub_key]
|
|
sub_value = vp_betweenness_corrected[sub_key]
|
|
|
|
scores.append(value)
|
|
raw_sub_scores.append(pre_prediction)
|
|
sub_scores.append(sub_value)
|
|
raw_diff_scores.append(value - pre_prediction)
|
|
diff_scores.append(value - sub_value)
|
|
|
|
median_score = np.median(scores)
|
|
median_raw_sub_score = np.median(raw_sub_scores)
|
|
median_sub_score = np.median(sub_scores)
|
|
print(f"\tmedian score: {median_score}")
|
|
print(f"\tmedian raw_sub_score: {median_raw_sub_score}")
|
|
print(f"\tmedian sub_score: {median_sub_score}")
|
|
print(f"\tmedian delta (score - raw_sub_score): {(median_score - median_raw_sub_score)}")
|
|
print(f"\tmedian delta (score - sub_score): {(median_score - median_sub_score)}")
|
|
print("")
|
|
|
|
max_value_score = np.max(scores)
|
|
max_value_raw_sub_score = np.max(raw_sub_scores)
|
|
max_value_sub_score = np.max(sub_scores)
|
|
print(f"\tmax value score: {max_value_score}")
|
|
print(f"\tmax value raw_sub_score: {max_value_raw_sub_score}")
|
|
print(f"\tmax value sub_score: {max_value_sub_score}")
|
|
print(f"\tmax value delta (score - raw_sub_score): {(max_value_score - max_value_raw_sub_score)}")
|
|
print(f"\tmax value delta (score - sub_score): {(max_value_score - max_value_sub_score)}")
|
|
print("")
|
|
|
|
min_value_score = np.min(scores)
|
|
min_value_raw_sub_score = np.min(raw_sub_scores)
|
|
min_value_sub_score = np.min(sub_scores)
|
|
print(f"\tmin value score: {min_value_score}")
|
|
print(f"\tmin value raw_sub_score: {min_value_raw_sub_score}")
|
|
print(f"\tmin value sub_score: {min_value_sub_score}")
|
|
print(f"\tmin value delta (score - raw_sub_score): {(min_value_score - min_value_raw_sub_score)}")
|
|
print(f"\tmin value delta (score - sub_score): {(min_value_score - min_value_sub_score)}")
|
|
print("")
|
|
|
|
fig = plt.figure(figsize=(35, 10))
|
|
plot_graph_ax, plot_sub_graph_ax, plot_sub_graph_before_ax = fig.subplots(1, 3)
|
|
|
|
plot_graph_diff(g, scores, fig, plot_graph_ax, "Original Graph (region of sub graph)")
|
|
plot_graph_diff(g, diff_scores, fig, plot_sub_graph_ax, "Differences after correction of sub graph compared to original graph", plt.cm.seismic)
|
|
plot_graph_diff(g, vp.a, fig, plot_sub_graph_before_ax, "Sub Graph (extracted region of original graph) without correction")
|
|
|
|
fig.savefig(f"model_prediction_subgraph_betweenness_5000_{percentage * 100:.0f}_percentage_diff.svg", format='svg')
|