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Extended Data Figure 6: Persistence across dimensions#
import plot and data loading dependencies#
[1]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
from persim import plot_diagrams
[2]:
data = pd.read_hdf("../data/EDFigure6.h5")
CEBRA rat dataset toplogy analysis#
For each dimension of CEBRA-Behavior embedding from the rat hippocampus dataset, we obtained Betti number by applying persistent co-homology. The colored dots are lifespans observed in hypothesis based CEBRA-Behavior. To rule out noisy lifespans, we set a threshold (colored diagonal lines) as maximum lifespan based on 500 seeds of shuffled-CEBRA embedding for each dimension. We obtained circular coordinate from the first cocycle from persistent co-homology analysis and map it to position.
[3]:
def plot_barcode(topology_dgms, shuffled_max, ax, label_vis):
plot_diagrams(
topology_dgms,
ax=ax,
legend=False,
)
ax.plot(
[
-0.5,
2,
],
[-0.5 + shuffled_max[0], 2 + shuffled_max[0]],
color="C0",
linewidth=3,
alpha=0.5,
)
ax.plot(
[
-0.5,
2,
],
[-0.5 + shuffled_max[1], 2 + shuffled_max[1]],
color="orange",
linewidth=3,
alpha=0.5,
)
ax.plot(
[-0.50, 2],
[-0.5 + shuffled_max[2], 2 + shuffled_max[2]],
color="green",
linewidth=3,
alpha=0.5,
)
ax.set_xlabel("Birth", fontsize=15)
ax.set_xticks([0, 1, 2])
ax.set_xticklabels([0, 1, 2])
ax.tick_params(labelsize=13)
if label_vis:
ax.set_ylabel("Death", fontsize=15)
else:
ax.set_ylabel("")
def plot_polar(radial_angle, label, ax, first, last):
r = np.ones(1000)
r_ind = label[:, 1] == 1
l_ind = label[:, 2] == 1
right = ax.scatter(
radial_angle[r_ind], r[r_ind], s=5, c=label[r_ind, 0], cmap="cool"
)
left = ax.scatter(
radial_angle[l_ind], r[l_ind], s=5, c=label[l_ind, 0], cmap="viridis"
)
ax.set_yticklabels([])
ax.set_xticks(np.pi / 180.0 * np.linspace(0, 360, 8, endpoint=False))
if first:
ax.set_xticklabels(
[
"",
"45$^\circ$",
"90$^\circ$",
"135$^\circ$",
"180$^\circ$",
"225$^\circ$",
"270$^\circ$",
"315$^\circ$",
]
)
if last:
ax.set_xticklabels(
[
"0$^\circ$",
"45$^\circ$",
"90$^\circ$",
"135$^\circ$",
"",
"225$^\circ$",
"270$^\circ$",
"315$^\circ$",
]
)
if not first and not last:
ax.set_xticks(np.pi / 180.0 * np.linspace(0, 360, 9))
ax.set_xticklabels(
[
"",
"45$^\circ$",
"90$^\circ$",
"135$^\circ$",
"",
"225$^\circ$",
"270$^\circ$",
"315$^\circ$",
"",
]
)
ax.tick_params(labelsize=11)
return right, left
def plot_position_angle(radial_angle, position, ax, yax_label=False):
r_ind = position[:, 1] == 1
l_ind = position[:, 2] == 1
def _to_deg(rad):
return rad * 180 / np.pi
ax.scatter(_to_deg(radial_angle[r_ind]), position[r_ind, 0] * 100, s=1, c="black")
ax.scatter(_to_deg(radial_angle[l_ind]), position[l_ind, 0] * 100, s=1, c="gray")
ax.set_xlabel("Radial angle [$^\circ$]", fontsize=15)
if yax_label:
ax.set_ylabel("Position [cm]", fontsize=15)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.tick_params(labelsize=13)
ax.set_xticks([0, 90, 180, 270, 360])
ax.set_xticklabels([0, 90, 180, 270, 360])
def display_labels_flag(i):
if i == 0:
first = True
last = False
label_vis = True
elif i == 4:
first = False
last = True
label_vis = False
else:
first = False
last = False
label_vis = False
return first, last, label_vis
[4]:
behavior_topology = data["behavior"]
max_dims_behavior = data["shuffled-max"]
circular_coord = data["circular_coord_analysis"]
dims = [3, 8, 16, 32, 64]
fig = plt.figure(figsize=(15, 11), dpi=300)
subfigs = fig.subfigures(
3,
1,
)
barcode_axs = subfigs[0].subplots(1, 5, sharey=True)
polar_axs = subfigs[1].subplots(1, 5, sharey=True, subplot_kw={"projection": "polar"})
position_axs = subfigs[2].subplots(1, 5, sharey=True)
for i, d in enumerate(dims):
first, last, label_vis = display_labels_flag(i)
barcode_ax = barcode_axs[i]
barcode_ax.set_title(f"Dimension {d}", fontsize=20, y=1.2)
plot_barcode(
behavior_topology[d]["dgms"], max_dims_behavior[d], barcode_ax, label_vis
)
polar_ax = polar_axs[i]
right, left = plot_polar(
circular_coord["circular_coord"][0][d],
circular_coord["position"],
polar_ax,
first,
last,
)
position_ax = position_axs[i]
plot_position_angle(
circular_coord["circular_coord"][0][d],
circular_coord["position"],
position_ax,
label_vis,
)
barcode_legend = [
Line2D([0], [0], ls="--", color="k"),
Line2D([0], [0], markerfacecolor="C0", marker="o", color="w", markersize=6),
Line2D([0], [0], markerfacecolor="C1", marker="o", color="w", markersize=6),
Line2D([0], [0], markerfacecolor="C2", marker="o", color="w", markersize=6),
]
position_legend = [
Line2D([0], [0], markerfacecolor="black", marker="o", color="w", markersize=6),
Line2D([0], [0], markerfacecolor="gray", marker="o", color="w", markersize=6),
]
subfigs[0].legend(
barcode_legend,
["$\infty$", "$H_0$", "$H_1$", "$H_2$"],
frameon=False,
bbox_to_anchor=[0.98, 0.7],
fontsize=15,
)
cax_r = polar_axs[-1].inset_axes([1.2, 0.1, 0.05, 1])
cax_l = polar_axs[-1].inset_axes([1.3, 0.1, 0.05, 1])
r_bar = subfigs[1].colorbar(right, ax=polar_axs, cax=cax_r)
l_bar = subfigs[1].colorbar(left, ax=polar_axs, cax=cax_l)
r_bar.set_ticks([])
l_bar.set_ticks([0, 1.5], fontsize=15)
l_bar.set_label("position [cm]", rotation=0, y=-0.1, fontsize=12)
subfigs[2].legend(
position_legend,
["right", "left"],
frameon=False,
bbox_to_anchor=[0.98, 0.4],
fontsize=15,
)
[4]:
<matplotlib.legend.Legend at 0x7f29a55799a0>
