Combining Entropy Measures for Anomaly Detection.

Area of Science:

• Machine Learning
• Data Science
• Information Theory

Background:

• Combining diverse data sources, often represented as similarity or kernel matrices, is a common challenge in data analysis.
• Existing methods may require complex model selection when integrating information from various sources.

Purpose of the Study:

• To propose a new class of methods for anomaly detection that combines multiple local entropy kernels into a single Mercer kernel.
• To avoid the need for model selection during the information combination process.
• To develop a robust framework for outlier detection using information geometry.

Main Methods:

• Generating a single Mercer kernel from a set of local entropy kernels.
• Utilizing Information Geometry to study information combination schemes and their behavior with increasing data size.
• Embedding data into a variety derived from positive definite kernel matrices.
• Applying a modified one-class Support Vector Machine for outlier detection.

Main Results:

• Successfully produced a single Mercer kernel from multiple sources, simplifying anomaly detection.
• Demonstrated the effectiveness of the proposed methodology on both real and artificial datasets.
• Provided theoretical insights into information combination within an Information Geometry context.

Conclusions:

• The proposed method offers an effective and model-selection-free approach to anomaly detection by combining diverse information sources.
• The use of Information Geometry provides a robust theoretical foundation for kernel combination strategies.
• The methodology is validated and applicable to various real-world and synthetic problems.