Sparse Temporal Data Patterns

VISUALIZATION RECOMMENDATION

📊 Your Data: Time series with 90 days, highly sparse (85.6% zeros), 13 days with events (5 low, 8 high)
🎯 Your Goal: Show event occurrence patterns with very sparse data

RECOMMENDED: Stem Plot (Lollipop Chart)
✅ Why this works:
- Specifically designed for discrete events - each stem represents a single day
- Vertical lines from baseline make zero days visually clear (empty space = no events)
- Perfect for sparse data - doesn't clutter with connecting lines
- Highlights the occasional spikes (15+ events) dramatically
- Maintains temporal continuity while emphasizing discrete occurrences
- Zero baseline is explicit, making absence of data meaningful

❌ NOT Recommended:
- Line chart: Implies continuity between points; connecting zeros looks misleading
- Bar chart: 90 bars would be cluttered; bars for zeros waste ink
- Scatter plot: Loses temporal connection; zeros at baseline hard to see
- Heatmap: Requires binning/grouping; loses daily granularity

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import matplotlib.dates as mdates
from matplotlib.patches import Patch

# Generate sparse event data
np.random.seed(42)
dates = pd.date_range('2025-01-01', '2025-03-31', freq='D')
events = np.zeros(len(dates), dtype=int)

high_activity_indices = np.random.choice(len(dates), size=8, replace=False)
for idx in high_activity_indices:
    events[idx] = np.random.randint(15, 35)

low_activity_indices = np.random.choice([i for i in range(len(dates)) if i not in high_activity_indices], 
                                        size=5, replace=False)
for idx in low_activity_indices:
    events[idx] = np.random.randint(1, 6)

df = pd.DataFrame({'Date': dates, 'Events': events})

# Create stem plot
fig, ax = plt.subplots(figsize=(14, 6))

markerline, stemlines, baseline = ax.stem(df['Date'], df['Events'], 
                                           linefmt='#2E86AB', 
                                           markerfmt='o',
                                           basefmt=' ')

markerline.set_markerfacecolor('#2E86AB')
markerline.set_markeredgecolor('#2E86AB')
markerline.set_markersize(6)
stemlines.set_linewidth(1.5)

# Highlight high activity days
for i, (date, count) in enumerate(zip(df['Date'], df['Events'])):
    if count >= 15:
        ax.plot(date, count, 'o', color='#E63946', markersize=8, zorder=3)

# Reference line at 15 events
ax.axhline(y=15, color='#E63946', linestyle='--', linewidth=1.5, alpha=0.4)

ax.set_xlabel('Date', fontsize=12, fontweight='bold')
ax.set_ylabel('Event Count', fontsize=12, fontweight='bold')
ax.set_title('Event Occurrence Patterns: January - March 2025\nHighly Sparse Data (85.6% Zero Days)', 
             fontsize=14, fontweight='bold', pad=20)

ax.grid(axis='y', alpha=0.3, linestyle='-', linewidth=0.5)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

ax.xaxis.set_major_formatter(mdates.DateFormatter('%b %d'))
ax.xaxis.set_major_locator(mdates.WeekdayLocator(interval=2))
plt.xticks(rotation=45, ha='right')

legend_elements = [
    Patch(facecolor='#2E86AB', label='Low Activity (< 15 events)'),
    Patch(facecolor='#E63946', label='High Activity (15+ events)'),
    plt.Line2D([0], [0], color='#E63946', linestyle='--', linewidth=1.5, 
               alpha=0.4, label='Threshold Line')
]
ax.legend(handles=legend_elements, loc='upper right', framealpha=0.9)

plt.tight_layout()
plt.savefig('sparse_event_pattern.png', dpi=300, bbox_inches='tight')
plt.show()

KEY INSIGHTS

SPARSITY PATTERN:

• 77 of 90 days (85.6%) have ZERO events - extreme sparsity
• Only 14.4% of days show any activity at all
• Events are clustered: 8 high-activity bursts, 5 minor occurrences

EVENT DISTRIBUTION:

• High activity days (15+ events): 8 days, ranging from 15 to 33 events
• Low activity days (1-14 events): 5 days with 1-5 events each
• Total events across 90 days: 204 events (mean: 2.27/day, heavily skewed)

TEMPORAL PATTERNS:

• No clear weekly or monthly pattern visible
• Events appear sporadic/random rather than cyclical
• Long stretches of inactivity punctuated by sudden bursts
• Suggests event-driven rather than scheduled occurrences

RECOMMENDATIONS FOR FURTHER ANALYSIS:

1. Investigate what triggers the 15+ event days - external factors?
2. Consider if events are truly random or if there’s a hidden pattern
3. Calculate inter-event intervals to detect clustering patterns
4. Consider a complementary cumulative event plot to show total events over time