Skip to content

🔢 DFTSeriesDecomposition

🔢 DFTSeriesDecomposition

🟡 Intermediate ✅ Stable ⏱️ Time Series

🎯 Overview

The DFTSeriesDecomposition layer decomposes time series into seasonal and trend components using frequency-domain analysis. It extracts:

  1. Seasonal Component: Periodic patterns at specific frequencies
  2. Trend Component: Smooth, long-term variations

Based on the Discrete Fourier Transform (FFT) for extracting dominant frequencies.

🔍 How It Works

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
Input Time Series
       |
       V
FFT (Frequency Domain)
       |
       |---> Top-k Frequencies (Seasonal)
       |
       |---> Remaining (Trend + Noise)
       |
       V
Inverse FFT
       |
       |---> Seasonal Component
       |
       |---> Trend Component

💡 Why Use This Layer?

vs. Moving Average vs. STL DFT Advantage
Less precise More complex ✅ Explicit frequency
Misses patterns Slow ✅ FFT fast
Limited accuracy Hard tune ✅ Data-driven

📊 Use Cases

  • Periodic Pattern Detection: Identify exact frequencies
  • Multi-seasonal Data: Multiple seasonal periods
  • Spectral Analysis: Frequency domain insights
  • Denoising: Separate signal from noise
  • Anomaly Detection: Detect frequency shifts

🚀 Quick Start

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
import keras
from kerasfactory.layers import DFTSeriesDecomposition

# Create decomposition layer
dft_decomp = DFTSeriesDecomposition(top_k=5)

# Input time series
x = keras.random.normal((32, 100, 8))

# Decompose
seasonal, trend = dft_decomp(x)

print(f"Seasonal shape: {seasonal.shape}")  # (32, 100, 8)
print(f"Trend shape: {trend.shape}")        # (32, 100, 8)

# Verify: seasonal + trend ≈ original
reconstructed = seasonal + trend

🔧 API Reference

1
2
3
4
5
kerasfactory.layers.DFTSeriesDecomposition(
    top_k: int = 5,
    name: str | None = None,
    **kwargs: Any
)

Parameters

Parameter Type Default Description
top_k int 5 Number of top frequencies to retain
name str \| None None Optional layer name

Input Shape

  • (batch_size, time_steps, channels)

Output Shape

  • Tuple of (seasonal, trend) each with shape (batch_size, time_steps, channels)

💡 Best Practices

  1. Top-k Selection: Usually 3-10 for most applications
  2. Data Length: Longer series yield better frequency estimates
  3. Preprocessing: Normalize data before decomposition
  4. Combine: Use with trend analysis for multi-scale patterns
  5. Validation: Check seasonal patterns make domain sense

⚠️ Common Pitfalls

  • ❌ Small top_k: May miss important patterns
  • ❌ Large top_k: Too much noise/overfitting
  • ❌ Non-stationary data: Apply differencing first
  • ❌ Aliasing: Ensure proper sampling frequency

📚 References

  • Cooley, J.W. & Tukey, J.W. (1965). "An algorithm for the machine computation of complex Fourier series"
  • Zhou, H., et al. (2023). "TimeMixer: Decomposing Time Series for Forecasting"

Last Updated: 2025-11-04 | Keras: 3.0+ | Status: ✅ Production Ready