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Uncertainty-Aware Seasonal-Trend Decomposition based on Loess

✨ Overview

This repository provides the code for Uncertainty-Aware Seasonal-Trend Decomposition Based on Loess (UASTL) by Krake et al. [1]. It describes the main method and additional visualization techniques.

The content is as follows:

│
├── figures   
│   └── fig_1.png               # Example figure for UASTL and correlation exploration
│   └── fig_1_cor.png           # Example figure for respective correlation matrix
│   └── fig_2.png               # Example figure for UASTL and sensitivity analysis
├── VIS    
│   ├── plot_distributionmtx.m  # Main visualization techniques
│   ├── plot_dist.m             # Helper
│   └── ...
├── loessmtx.m                  # Computation of loess matrix
├── uastl.m                     # Core of UASTL
└── main_demo.m                 # Main demo for UASTL

⚙️ Usage

This code was tested with MATLAB2023b.

Main functionality can be accessed via the function uastl:

Xhat = UASTL(X,p,opts)

This function uastl implements the method Uncertainty-Aware Seasonal-Trend Decomposition Based on Loess. The method is described in more detail in the related publication [1]. For a (discrete) Gaussian process X and periods p, this function computes an uncertainty-aware seasonal-trend decomposition that consists of trend, seasonal, and residual components. The global Gaussian distributed variable Xhat contains these components and the data as well as the associated global covariance matrix.

A demo of UASTL is presented in main_demo.m, where a simple (discrete) Gaussian process with moderate uncertainty is analyzed. The results are as follows:

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📖 References

[1] T. Krake, D. Klötzl, D. Hägele, and D. Weiskopf, "Uncertainty-Aware Seasonal-Trend Decomposition Based on Loess", In: currently under review.

👤 Authors

Tim Krake and Daniel Klötzl and David Hägele

License

Copyright 2024 Tim Krake & Daniel Klötzl & David Hägele

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.