The mean angular distance among objects and its relationships with Kohonen artificial neural networks

Area of Science:

• Artificial Intelligence
• Data Science
• Analytical Chemistry

Background:

• Kohonen artificial neural networks are effective for classifying multidimensional objects.
• Interpreting the organization of objects within Kohonen maps can be challenging.
• Existing methods may not fully leverage the spatial relationships between objects.

Purpose of the Study:

• Introduce a novel metric, Mean Angular Distance Among Objects (MADO), for enhanced interpretation of Kohonen maps.
• Demonstrate the utility of MADO in analyzing multidimensional object classification.
• Apply MADO to a real-world dataset for discovering hidden patterns in air quality data.

Main Methods:

• Developed the Mean Angular Distance Among Objects (MADO) metric, calculated as the cosine of mean centered vectors.
• Expressed MADO in matrix form for scalable analysis of multiple objects.
• Utilized simulated examples to establish the relationship between MADO and Kohonen map organization.
• Applied MADO to a large dataset from an air quality monitoring campaign.

Main Results:

• MADO provides a quantifiable method to interpret object arrangements in Kohonen maps.
• Simulated data confirmed the correlation between MADO values and Kohonen map structures.
• Analysis of air quality data revealed a distinct subgroup of objects deviating from the general trend.
• This subgroup was successfully linked to an unidentified sulfur dioxide (SO2) source.

Conclusions:

• MADO is a valuable tool for understanding multidimensional data organization in Kohonen maps.
• The metric facilitates the discovery of anomalies and hidden patterns within complex datasets.
• The application in analytical chemistry highlights MADO's potential for environmental monitoring and source identification.