Weighted Persistence Diagram Feature Extraction
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Solution Overview
Problem
Existing methods for extracting features from time series data using topological data analysis (TDA) face challenges in distinguishing between data sets due to the removal of information with short existence times, which can lead to inaccurate feature extraction, especially in cases with high-frequency components or small amplitudes.
Innovation Solution
A method that generates quasi-attractors from time series data, performs persistent homology conversion, and adjusts weights based on the existence and appearance times of holes in the persistence diagram to generate a weighted Betti sequence, allowing for more accurate feature extraction while maintaining the influence of data with short existence times.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Object-affected harmful factors
If data with short existence times is removed during feature extraction, then noise suppression is improved, but information loss occurs leading to reduced measurement precision
Solution Approach 1:
The patent applies local quality by differentiating the treatment of data points based on their local characteristics (existence time and appearance time). Instead of uniformly removing all short-duration features, the method selectively weights individual data points in the persistence diagram based on their specific temporal properties, preserving locally significant features while suppressing locally insignificant noise.
Solution Approach 2:
The patent changes parameters by introducing weight values that modify the influence of each data point based on its existence time and appearance time. This parameter transformation allows the system to dynamically adjust the contribution of each feature to the final Betti sequence, transforming fixed threshold-based noise removal into a flexible, parameter-driven weighting scheme that maintains precision while suppressing noise.
2Ease of operation
If all data points in the persistence diagram are treated equally, then processing simplicity is maintained, but feature differentiation capability is reduced
Solution Approach 1:
The patent implements local quality by assigning different weight values to different data points in the persistence diagram based on their individual characteristics (existence time and appearance time). This allows the system to differentiate between significant features and noise while maintaining a relatively simple processing framework that builds upon the existing persistent homology conversion process.
Data Source
AI summary
A method for extracting features, the method being implemented by a computer, the method includes generating attractors from time series data having a cyclic characteristic; generating a persistence diagram by performing persistent homology conversion for the attractors; changing a degree of influence with respect to individual items of data in the persistence diagram in accordance with a time of existence or an appearance time of a hole generated by performing the persistent homology conversion; and extracting features of the time series data from the changed persistence diagram in which the degree of influence has been changed.