Anomaly Detection via Moving Window Functional Component Analysis
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Solution Overview
Problem
Existing anomaly detection techniques are not effective for functional data, such as time-series data, and demand high computational resources, limiting their applicability and efficiency.
Innovation Solution
The implementation of Moving Window Functional Component Analysis (MWFPCA) for anomaly detection, which computes discretized covariance functions and performs eigenanalysis on time-series data within sliding windows to detect anomalies based on angle changes between eigenfunctions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing anomaly detection techniques are applied to functional data, then anomaly detection capability is provided, but computational resources required increase significantly
Solution Approach 1:
The patent divides the time-series data into overlapping time windows and applies functional component analysis separately to each window. This segmentation allows the system to process functional data in manageable segments rather than attempting to analyze the entire dataset at once, significantly reducing computational resource requirements while maintaining anomaly detection capability.
Solution Approach 2:
The patent implements a dynamic sliding window approach where the analysis window moves through the time-series data incrementally. This dynamic processing enables real-time anomaly detection on streaming functional data with reduced computational burden compared to static batch processing of the entire dataset.
2Measurement precision
If comprehensive anomaly detection is performed on time-series data, then detection accuracy is improved, but time required for processing increases
Solution Approach 1:
The patent performs preliminary centering and scaling of the functional data before applying functional component analysis. These preprocessing steps are computed once for the entire dataset, and subsequent anomaly detection windows reuse these precomputed values, significantly reducing processing time for each detection step while maintaining detection accuracy.
Solution Approach 2:
The patent focuses computational effort on detecting deviations from the mean function rather than performing exhaustive analysis of all possible anomalies. By concentrating on the most significant variations captured by the first few principal components, the system achieves practical detection accuracy with substantially reduced processing time.
3Productivity
If functional component analysis is applied to streaming data, then real-time detection is enabled, but computational complexity increases
Solution Approach 1:
The patent segments the streaming data into overlapping time windows and applies functional component analysis to each segment independently. This segmentation transforms the complex problem of real-time analysis of entire streaming datasets into simpler, repeated analyses of smaller windows, reducing computational complexity while enabling real-time detection capability.
Solution Approach 2:
The patent transforms the time-series data into the functional domain by representing it as smooth functions through centering and scaling operations. This parameter transformation simplifies the mathematical operations required for anomaly detection in the functional domain compared to operating directly on raw time-series data, thereby reducing computational complexity.
Data Source
AI summary
Functions representing sequences of values of a time-series dataset measured within a particular time period are accessed. For a current time window of the time period, a first discretized covariance function is computed that represents a relationship between each value measured within the current time window. Eigenanalysis of the first covariance function is performed to estimate first eigenfunctions. The current time window is incremented to obtain a subsequent time window that overlaps a majority of the current time window at a shared window region. A second discretized covariance function is computed for the subsequent time window and eigenanalysis is performed to estimate second normalized eigenfunctions. An angle change is computed between a portion of the first normalized eigenfunctions and a corresponding portion of the second normalized eigenfunctions located within the shared window region. Based on the angle change, an anomaly detection output is generated.