Anomaly Detection Using Persistent Homology on Weighted Graphs
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Solution Overview
Problem
Existing data analysis approaches using sparse structure learning for anomaly detection in time-series data only determine 'normal' or 'anomaly' without identifying the occurrence of failures or distinguishing between true anomalies and erroneous detections, leading to low reliability and inability to detect anomalies in advance.
Innovation Solution
A detection program that generates weighted graph structure data from time-series data using partial correlation based on a precision matrix, applies persistent homology transformation to detect anomalies by analyzing the distribution of data points in a persistence diagram.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If sparse structure learning is used to determine anomaly in time-series data, then anomaly detection capability is provided, but reliability is low due to inability to distinguish true anomalies from erroneous detections
Solution Approach 1:
The patent transforms the anomaly detection problem from traditional statistical dimensions to topological dimensions by constructing persistence diagrams. Instead of analyzing time-series data directly, the method creates weighted graphs from the data and applies persistent homology to generate topological signatures. This dimensional transformation enables more reliable anomaly detection by capturing structural properties that are invariant to noise and transformation, thereby distinguishing true anomalies from erroneous detections.
Solution Approach 2:
The patent introduces persistence diagrams as an intermediary representation between raw time-series data and anomaly detection results. The persistence diagram serves as a mediator that captures essential topological features while filtering out noise. By analyzing the distribution of data points in the persistence diagram rather than directly in the time domain, the method achieves higher reliability in distinguishing genuine anomalies from false positives.
2Reliability
If traditional anomaly detection methods are used, then binary classification of normal or anomaly is provided, but ability to detect anomalies in advance is lost
Solution Approach 1:
The patent performs preliminary transformation of time-series data into persistence diagrams that capture the topological structure of the data. By pre-computing these topological representations and establishing baseline distributions, the system can quickly detect anomalies by comparing new data against the baseline without performing complex analysis at detection time. This preliminary action enables early anomaly detection while minimizing computational time loss.
3Measurement precision
If weighted graph structure data with partial correlation is generated, then topological features are captured, but computational complexity increases
Solution Approach 1:
The patent segments the computational process into distinct stages: constructing weighted graphs from time-series data, computing persistence diagrams from these graphs, and analyzing the distribution of points in the persistence diagram. This segmentation allows each stage to be optimized independently and enables parallel processing where applicable, reducing overall computational complexity while maintaining precise topological feature extraction.
Data Source
AI summary
A non-transitory computer-readable recording medium stores a detection program for causing a computer to execute a process. In the process, the computer generates weighted graph structure data for a plurality of pieces of time-series data, with a partial correlation specified based on a matrix calculated by solving an optimization problem about a precision matrix for the plurality of pieces of time-series data, as a weight of a side in a graph; and detects a sign of an anomaly, based on distribution of data points in a predetermined region in a persistence diagram obtained by a persistent homology transformation for the weighted graph structure data.