Attractor Reconstruction for Time-Series Feature Extraction
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Solution Overview
Problem
Existing data analysis techniques using topological data analysis (TDA) struggle to accurately extract features from time-series data due to limited data points, leading to deteriorated feature extraction performance.
Innovation Solution
The method involves reconstructing an attractor using time-series data with interpolated points at regular intervals, ensuring a consistent number of data points per timing, which stabilizes the Betti series and enhances feature extraction by increasing the density and clarity of the attractor shape in the phase space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of data points in time-series data is limited, then the data analysis process is simpler and faster, but the feature extraction performance deteriorates
Solution Approach 1:
The patent segments the time-series data by dividing each time point into multiple interpolated points at regular intervals. This segmentation increases the number of data points without adding new information, allowing the attractor to be reconstructed with higher density while maintaining the same underlying data content.
Solution Approach 2:
The patent performs preliminary interpolation of the time-series data before constructing the attractor. By pre-interpolating the data at regular intervals, the system prepares a denser dataset that stabilizes the Betti series and improves feature extraction accuracy before the actual analysis begins.
2Measurement precision
If the number of data points is increased through interpolation, then the attractor shape becomes clearer and Betti series stabilizes, but the data processing time increases
Solution Approach 1:
The patent applies periodic interpolation at regular intervals between data points. This periodic action creates a consistent pattern of interpolated points that stabilizes the Betti series and clarifies the attractor shape. The regularity of the interpolation pattern allows for efficient processing while achieving the desired enhancement in attractor clarity.
Data Source
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AI summary
A program causes a computer to execute a process, the process including determining numerical values indicating features at respective timings having a predetermined time interval with respect to time-series data to be analyzed, numbers of the numerical values at the respective timings being made same, and generating an attractor related to the time-series data based on the determined numerical values.