Time Series Segmentation

Time Series Segmentation

Aeon provides algorithms to partition time series into regions with distinct characteristics, identifying change points and boundaries.

Segmentation Algorithms

Binary Segmentation

• BinSegmenter - Recursive binary segmentation
  • Iteratively splits series at most significant change points
  • Parameters: n_segments, cost_function
  • Use when: Known number of segments, hierarchical structure

Classification-Based

• ClaSPSegmenter - Classification Score Profile
  • Uses classification performance to identify boundaries
  • Discovers segments where classification distinguishes neighbors
  • Use when: Segments have different temporal patterns

Fast Pattern-Based

• FLUSSSegmenter - Fast Low-cost Unipotent Semantic Segmentation
  • Efficient semantic segmentation using arc crossings
  • Based on matrix profile
  • Use when: Large time series, need speed and pattern discovery

Information Theory

• InformationGainSegmenter - Information gain maximization
  • Finds boundaries maximizing information gain
  • Use when: Statistical differences between segments

Gaussian Modeling

• GreedyGaussianSegmenter - Greedy Gaussian approximation
  • Models segments as Gaussian distributions
  • Incrementally adds change points
  • Use when: Segments follow Gaussian distributions

Hierarchical Agglomerative

• EAggloSegmenter - Bottom-up merging approach
  • Estimates change points via agglomeration
  • Use when: Want hierarchical segmentation structure

Hidden Markov Models

• HMMSegmenter - HMM with Viterbi decoding
  • Probabilistic state-based segmentation
  • Use when: Segments represent hidden states

Dimensionality-Based

• HidalgoSegmenter - Heterogeneous Intrinsic Dimensionality Algorithm
  • Detects changes in local dimensionality
  • Use when: Dimensionality shifts between segments

Baseline

• RandomSegmenter - Random change point generation
  • Use when: Need null hypothesis baseline

Quick Start

from aeon.segmentation import ClaSPSegmenter
import numpy as np

# Create time series with regime changes
y = np.concatenate([
    np.sin(np.linspace(0, 10, 100)),      # Segment 1
    np.cos(np.linspace(0, 10, 100)),      # Segment 2
    np.sin(2 * np.linspace(0, 10, 100))   # Segment 3
])

# Segment the series
segmenter = ClaSPSegmenter()
change_points = segmenter.fit_predict(y)

print(f"Detected change points: {change_points}")

Output Format

Segmenters return change point indices:

# change_points = [100, 200]  # Boundaries between segments
# This divides series into: [0:100], [100:200], [200:end]

Algorithm Selection

• Speed priority: FLUSSSegmenter, BinSegmenter
• Accuracy priority: ClaSPSegmenter, HMMSegmenter
• Known segment count: BinSegmenter with n_segments parameter
• Unknown segment count: ClaSPSegmenter, InformationGainSegmenter
• Pattern changes: FLUSSSegmenter, ClaSPSegmenter
• Statistical changes: InformationGainSegmenter, GreedyGaussianSegmenter
• State transitions: HMMSegmenter

Common Use Cases

Regime Change Detection

Identify when time series behavior fundamentally changes:

from aeon.segmentation import InformationGainSegmenter

segmenter = InformationGainSegmenter(k=3)  # Up to 3 change points
change_points = segmenter.fit_predict(stock_prices)

Activity Segmentation

Segment sensor data into activities:

from aeon.segmentation import ClaSPSegmenter

segmenter = ClaSPSegmenter()
boundaries = segmenter.fit_predict(accelerometer_data)

Seasonal Boundary Detection

Find season transitions in time series:

from aeon.segmentation import HMMSegmenter

segmenter = HMMSegmenter(n_states=4)  # 4 seasons
segments = segmenter.fit_predict(temperature_data)

Evaluation Metrics

Use segmentation quality metrics:

from aeon.benchmarking.metrics.segmentation import (
    count_error,
    hausdorff_error
)

# Count error: difference in number of change points
count_err = count_error(y_true, y_pred)

# Hausdorff: maximum distance between predicted and true points
hausdorff_err = hausdorff_error(y_true, y_pred)

Best Practices

1. Normalize data: Ensures change detection not dominated by scale
2. Choose appropriate metric: Different algorithms optimize different criteria
3. Validate segments: Visualize to verify meaningful boundaries
4. Handle noise: Consider smoothing before segmentation
5. Domain knowledge: Use expected segment count if known
6. Parameter tuning: Adjust sensitivity parameters (thresholds, penalties)

Visualization

import matplotlib.pyplot as plt

plt.figure(figsize=(12, 4))
plt.plot(y, label='Time Series')
for cp in change_points:
    plt.axvline(cp, color='r', linestyle='--', label='Change Point')
plt.legend()
plt.show()