50b6fbdc27
Analysis shows no significant correlation between conceptual depth and hop distance to letter nodes (r=0.281, p=0.113). Includes Python scripts, visualizations, and LaTeX paper. Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
109 lines
3.9 KiB
Python
109 lines
3.9 KiB
Python
"""
|
||
Plot correlation between minimum hops to letter nodes and conceptual depth.
|
||
"""
|
||
|
||
import json
|
||
import matplotlib
|
||
matplotlib.use('Agg') # Non-interactive backend
|
||
import matplotlib.pyplot as plt
|
||
import numpy as np
|
||
from scipy import stats
|
||
|
||
def load_slipnet(filepath):
|
||
with open(filepath, 'r') as f:
|
||
return json.load(f)
|
||
|
||
def main():
|
||
filepath = r'C:\Users\alexa\copycat\slipnet_analysis\slipnet.json'
|
||
data = load_slipnet(filepath)
|
||
|
||
# Extract data points (excluding letter nodes themselves)
|
||
names = []
|
||
depths = []
|
||
hops = []
|
||
is_unreachable = [] # Track which nodes are unreachable
|
||
|
||
for node in data['nodes']:
|
||
name = node['name']
|
||
depth = node['conceptualDepth']
|
||
path_info = node.get('minPathToLetter', {})
|
||
hop_count = path_info.get('hops')
|
||
nearest = path_info.get('nearestLetter')
|
||
|
||
# Skip letter nodes (hops 0)
|
||
if hop_count is not None and hop_count > 0:
|
||
names.append(name)
|
||
depths.append(depth)
|
||
hops.append(hop_count)
|
||
# Unreachable nodes have no nearestLetter
|
||
is_unreachable.append(nearest is None)
|
||
|
||
# Convert to numpy arrays
|
||
depths = np.array(depths)
|
||
hops = np.array(hops)
|
||
is_unreachable = np.array(is_unreachable)
|
||
|
||
# Compute correlation
|
||
correlation, p_value = stats.pearsonr(depths, hops)
|
||
spearman_corr, spearman_p = stats.spearmanr(depths, hops)
|
||
|
||
# Create the plot
|
||
fig, ax = plt.subplots(figsize=(10, 8))
|
||
|
||
# Scatter plot with jitter for overlapping points
|
||
jitter = np.random.normal(0, 0.08, len(hops))
|
||
|
||
# Plot reachable nodes in blue
|
||
reachable_mask = ~is_unreachable
|
||
ax.scatter(depths[reachable_mask], hops[reachable_mask] + jitter[reachable_mask],
|
||
alpha=0.7, s=100, c='steelblue', edgecolors='navy', label='Reachable')
|
||
|
||
# Plot unreachable nodes in red
|
||
if np.any(is_unreachable):
|
||
ax.scatter(depths[is_unreachable], hops[is_unreachable] + jitter[is_unreachable],
|
||
alpha=0.7, s=100, c='crimson', edgecolors='darkred', label='Unreachable (2×max)')
|
||
|
||
# Add labels to each point
|
||
for i, name in enumerate(names):
|
||
ax.annotate(name, (depths[i], hops[i] + jitter[i]), fontsize=8, alpha=0.8,
|
||
xytext=(5, 5), textcoords='offset points')
|
||
|
||
# Add trend line
|
||
z = np.polyfit(depths, hops, 1)
|
||
p = np.poly1d(z)
|
||
x_line = np.linspace(min(depths), max(depths), 100)
|
||
ax.plot(x_line, p(x_line), "r--", alpha=0.8, label=f'Linear fit (y = {z[0]:.3f}x + {z[1]:.2f})')
|
||
|
||
# Labels and title
|
||
ax.set_xlabel('Conceptual Depth', fontsize=12)
|
||
ax.set_ylabel('Minimum Hops to Letter Node (Erdos-style)', fontsize=12)
|
||
ax.set_title('Correlation: Conceptual Depth vs Hops to Nearest Letter\n'
|
||
f'Pearson r = {correlation:.3f} (p = {p_value:.4f}), '
|
||
f'Spearman rho = {spearman_corr:.3f} (p = {spearman_p:.4f})',
|
||
fontsize=11)
|
||
|
||
ax.legend(loc='upper left')
|
||
ax.grid(True, alpha=0.3)
|
||
max_hops = int(max(hops))
|
||
ax.set_yticks(range(1, max_hops + 1))
|
||
ax.set_ylim(0.5, max_hops + 0.5)
|
||
|
||
# Print statistics
|
||
print(f"Number of nodes with paths (excluding letters): {len(names)}")
|
||
print(f"\nPearson correlation: r = {correlation:.4f}, p-value = {p_value:.6f}")
|
||
print(f"Spearman correlation: rho = {spearman_corr:.4f}, p-value = {spearman_p:.6f}")
|
||
print(f"\nLinear regression: hops = {z[0]:.4f} * depth + {z[1]:.4f}")
|
||
|
||
print("\nData points:")
|
||
print(f"{'Node':<30} {'Depth':<10} {'Hops':<10}")
|
||
print("-" * 50)
|
||
for name, depth, hop in sorted(zip(names, depths, hops), key=lambda x: (x[2], x[1])):
|
||
print(f"{name:<30} {depth:<10.1f} {hop:<10}")
|
||
|
||
plt.tight_layout()
|
||
plt.savefig(r'C:\Users\alexa\copycat\slipnet_analysis\depth_hops_correlation.png', dpi=150)
|
||
print(f"\nPlot saved to: C:\\Users\\alexa\\copycat\\slipnet_analysis\\depth_hops_correlation.png")
|
||
|
||
if __name__ == '__main__':
|
||
main()
|