Harmonic Homology for Multiway Interaction Disentanglement
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Solution Overview
Problem
Existing methods for determining predictive setups in multiway interaction data sets are computationally expensive and memory-intensive, often resulting in experimental setups that include unnecessary and redundant features, leading to time and resource wastage.
Innovation Solution
A computer-implemented method using harmonic homology to disentangle multiway interactions by receiving multiway data, determining persistent homology barcodes, identifying significant barcodes, computing an orthonormal basis, obtaining a harmonic representative, and determining a predictive experiment setup based on the harmonic representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional statistical tools are used to map multiway interactions, then measurement precision is improved, but computational cost and memory usage increase significantly
Solution Approach 1:
The patent extracts only the essential topological features from multiway interaction data using persistent homology barcodes, rather than processing the entire complex data set with traditional statistical tools. This extraction approach identifies significant factors while avoiding the computational burden of comprehensive statistical analysis.
Solution Approach 2:
The patent transforms the data representation by converting multiway interaction data into persistent homology barcodes, changing the parameter space from traditional statistical measurements to topological invariants. This parameter transformation enables efficient identification of significant factors with reduced computational cost.
2Measurement precision
If traditional statistical tools are used to map multiway interactions, then measurement precision is improved, but memory usage increases significantly
Solution Approach 1:
The patent extracts only the essential topological features from multiway interaction data using persistent homology barcodes, rather than storing and processing the entire complex data set with traditional statistical tools. This extraction approach identifies significant factors while avoiding the memory burden of comprehensive statistical analysis.
Solution Approach 2:
Instead of starting with the full data set and filtering down through statistical analysis, the patent inverts the approach by first transforming data into topological invariants (barcodes) that inherently capture the essential structure, then deriving insights from these compact representations.
3Adaptability or versatility
If comprehensive experimental setups are designed without harmonic homology, then coverage of all factors is improved, but the number of redundant experiments increases
Solution Approach 1:
The patent replaces the mechanical trial-and-error approach of designing comprehensive experimental setups with a topological analysis system. By using persistent homology to identify the essential structure of factor interactions, the system predicts which experiments are truly necessary, substituting computational topology for iterative experimental trial-and-error.
Solution Approach 2:
The patent performs preliminary topological analysis of the multiway interaction data before designing experiments. This preliminary action using harmonic homology identifies the essential structure and significant factors in advance, allowing experiment designers to plan only the necessary experiments rather than conducting comprehensive but redundant testing.
4Adaptability or versatility
If comprehensive experimental setups are designed without harmonic homology, then coverage of all factors is improved, but resource consumption increases
Solution Approach 1:
The patent replaces the mechanical trial-and-error approach of designing comprehensive experimental setups with a topological analysis system. By using persistent homology to identify the essential structure of factor interactions, the system predicts which experiments are truly necessary, substituting computational topology for iterative experimental trial-and-error.
Solution Approach 2:
The patent performs preliminary topological analysis of the multiway interaction data before designing experiments. This preliminary action using harmonic homology identifies the essential structure and significant factors in advance, allowing experiment designers to plan only the necessary experiments rather than conducting comprehensive but redundant testing.
Data Source
AI summary
A computer-implemented method for determining a predictive setup for an experiment includes receiving at a processor an input set of multiway data. The multiway data includes a numerical representation of each factor in a set of interconnected factors affecting an outcome. Each factor has a codependency on at least one other factor in the set of interconnected factors. The method determines a set of persistent homology barcodes based on the multiway data using the processer and identifies at least a first significant persistent homology barcode in the set of persistent homology barcodes. A representative cycle of the first significant persistent homology is returned and an orthonormal basis of the multiway data is computed. A harmonic representative is obtained by computing a projection of the representative cycle to an orthogonal complement.