Outlier Detection in Functional Data Using Adjusted Outlyingness

Area of Science:

• Statistics
• Signal Processing
• Data Analysis

Background:

• Anomaly detection is crucial for data integrity and reliable analysis.
• Detecting outliers in functional data is challenging due to high dimensionality and subtle shape deformations.
• Conventional methods often discretize curves, losing important variations.

Purpose of the Study:

• To develop a novel framework for robust outlier detection in functional data.
• To address the challenges posed by the infinite dimensionality of functional data.
• To improve the accuracy and efficiency of anomaly identification in complex datasets.

Main Methods:

• Projecting functional data into a low-dimensional feature space using a tailored weighting scheme.
• Employing Mahalanobis distance for directional outlyingness detection under non-Gaussian assumptions.
• Utilizing a robustified bootstrap resampling method with data-driven threshold determination.

Main Results:

• The proposed framework demonstrated superior performance in simulations.
• Achieved higher true positive rates and lower false positive rates for various outlier types.
• Validated through practical applications in environmental, trajectory, and population data analysis.

Conclusions:

• The novel framework offers a versatile and effective solution for functional data outlier detection.
• The method enhances data cleaning and facilitates the discovery of anomalous events.
• Its cross-domain applicability highlights its practical utility in diverse scientific fields.