Mining Time Series Data

Mining Time-Series Data: Periodicity Analysis & Similarity Search

Time-series data mining involves extracting meaningful patterns from temporal data. Two critical techniques are Periodicity Analysis (identifying recurring patterns) and Similarity Search (finding matching subsequences). Below is a detailed breakdown of methods, algorithms, and applications.

---

1. Periodicity Analysis

Goal: Detect repeating patterns (e.g., daily sales spikes, weekly ECG cycles).

A. Key Concepts

• Period: Time interval after which a pattern repeats (e.g., 24 hours for daily trends).
• Seasonality: Regular periodic fluctuations (e.g., holiday sales surges).
• Cyclic Patterns: Non-fixed periods (e.g., economic cycles).

B. Methods for Periodicity Detection

Method	Description	Use Case
Fourier Transform	Converts time-series to frequency domain to identify dominant cycles.	ECG signal analysis
Autocorrelation	Measures self-similarity at different time lags.	Traffic flow analysis
Lomb-Scargle Periodogram	Detects periods in unevenly sampled data.	Astronomy light curves
Wavelet Analysis	Captures localized periodicity in non-stationary data.	Vibration sensor data

C. Example: Autocorrelation in Python

import pandas as pd
from statsmodels.graphics.tsaplots import plot_acf
 
# Load time-series data
data = pd.read_csv('sales.csv', parse_dates=['date'], index_col='date')
 
# Plot autocorrelation to detect periodicity
plot_acf(data['sales'], lags=50)  # Peaks at lag=7 → weekly pattern

---

2. Similarity Search in Time-Series

Goal: Find similar subsequences within or across time-series (e.g., matching ECG anomalies).

A. Key Challenges

• Time Warping: Sequences may vary in speed (e.g., walking vs. running).
• Noise: Sensor artifacts or missing data.
• Scale: Large datasets require efficient indexing.

B. Similarity Measures

Measure	Description	Pros & Cons
Euclidean Distance	Compares point-to-point distances.	Fast but inflexible to warping.
DTW (Dynamic Time Warping)	Aligns sequences non-linearly.	Handles warping but slower.
Shape-Based (SAX)	Symbolic Aggregate Approximation reduces dimensionality.	Scalable but loses granularity.
Pearson Correlation	Measures linear dependence.	Ignores magnitude, focuses on shape.

C. Algorithms for Similarity Search

Algorithm	Description	Library/Tool
k-NN with DTW	Finds k most similar sequences using DTW.	tslearn, dtaidistance
FastDTW	Optimized DTW with reduced complexity.	fastdtw
UCR Suite	State-of-the-art exact similarity search.	UCR Suite
TS-Clust	Clustering-based similarity search.	pyts

D. Example: DTW in Python

from dtaidistance import dtw
import numpy as np
 
# Two time-series sequences
series1 = np.array([1, 3, 5, 6, 8])
series2 = np.array([2, 4, 6, 7, 9])
 
# Compute DTW distance
distance = dtw.distance(series1, series2)
print(f"DTW Distance: {distance:.2f}")

---

3. Applications

A. Periodicity Analysis

• Retail: Detect weekly/monthly sales cycles.
• Healthcare: Identify circadian rhythms in vital signs.
• Energy: Forecast electricity demand peaks.

B. Similarity Search

• Finance: Find stock price patterns resembling past crashes.
• IoT: Match sensor fault signatures.
• Biometrics: Identify gait patterns for security.

---

4. Tools & Libraries

Task	Tool/Library	Key Feature
Periodicity Detection	statsmodels, astropy	Lomb-Scargle, autocorrelation
Similarity Search	tslearn, dtaidistance, UCR Suite	DTW, FastDTW
Visualization	matplotlib, plotly	Interactive time-series plots

---

5. Key Takeaways

1. Periodicity Analysis:

   • Use Fourier transforms for stationary data, wavelets for non-stationary.
   • Autocorrelation helps identify fixed intervals (e.g., seasonality).

2. Similarity Search:

   • DTW is gold standard for warped sequences but computationally heavy.
   • SAX balances speed and accuracy for large datasets.

3. Domain-Specific Tuning:

   • Normalize data for magnitude-invariant comparisons.
   • Use indexing (e.g., UCR Suite) for scalability.

# Pro Tip: Speed up DTW with lower-bounding (LB_Keogh)
from dtaidistance.dtw_ndim import lb_keogh
lb = lb_keogh(series1, series2, radius=3)

Mastering these techniques unlocks actionable insights from temporal data! 🚀