Auto-regressive processes explained by self-organized maps. Application to the detection of abnormal behavior in...

Area of Science:

• Data Science
• Machine Learning
• Time Series Analysis

Background:

• Auto-regressive (AR) processes are fundamental in time series analysis.
• Understanding temporal dynamics and detecting anomalies in AR processes is crucial for industrial applications.
• Self-Organized Maps (SOMs) offer a visualization technique but their application to time-dependent processes requires further investigation.

Purpose of the Study:

• To analyze the temporal evolution of AR processes using SOMs.
• To investigate how SOMs capture time-dependent information from AR processes.
• To develop a probabilistic framework for understanding neuron transitions in SOMs for AR process analysis.

Main Methods:

• Utilizing Self-Organized Maps (SOM) to model the time evolution of an auto-regressive (AR) process.
• Developing a probabilistic interpretation of neuron transitions within the SOM.
• Identifying regions on the SOM that represent expected future states of the AR process.

Main Results:

• Demonstrated that SOMs can effectively capture the temporal information inherent in AR processes.
• Characterized expected transitions between SOM neurons based on probabilistic analysis.
• Successfully identified regions on the map indicative of the AR process's expected trajectory.
• Developed and validated an anomaly detection method based on these theoretical findings.

Conclusions:

• The proposed method effectively characterizes AR process dynamics using SOMs.
• The probabilistic framework provides insights into temporal dependencies within the SOM.
• The anomaly detection approach is applicable to real-world industrial processes, enabling the identification of structural or parameter changes.