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Blind Source Separation for Compositional Time Series.

Klaus Nordhausen¹, Gregor Fischer², Peter Filzmoser²

¹CSTAT - Computational Statistics Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstr. 7, 1040 Vienna, Austria.

Mathematical Geosciences

|November 1, 2021

Summary

This summary is machine-generated.

This study addresses compositional time series data common in geology. A new blind source separation method is proposed for analyzing complex, high-dimensional data, improving understanding of geological changes over time.

Keywords:

Isometric log-ratio coordinates Nonstationary source separation Second-order source separation Stochastic volatility

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Area of Science:

Geosciences
Data Science
Time Series Analysis

Background:

Geological phenomena are often measured over time, yielding compositional time series data where relative values are key.
Analyzing multivariate, high-dimensional time series requires specialized methods that account for both serial dependence and compositional geometry.

Purpose of the Study:

To review existing blind source separation (BSS) techniques for time series analysis.
To demonstrate the application of BSS methods to high-dimensional compositional time series.
To introduce a novel, flexible BSS method for latent time series analysis.

Main Methods:

Review of established blind source separation techniques.
Application of BSS to high-dimensional compositional time series.
Development and simulation of a new flexible BSS method.
Analysis of light absorbance data from water samples.

Main Results:

Existing BSS methods can be adapted for compositional time series.
The proposed novel BSS method offers flexibility in latent time series assumptions.
Methodology validated through simulations and real-world environmental data.

Conclusions:

Blind source separation is a powerful tool for analyzing compositional time series in geosciences.
The novel BSS method provides a versatile approach for uncovering latent structures in complex environmental data.
This work enhances the analysis of geological changes and water quality monitoring.