Cross-Disorder Multiway Feature Ranking with Persistent Homology
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Solution Overview
Problem
Existing methods for analyzing multiway interactions in data sets, particularly in cross-disorder medical diagnostics, are computationally expensive and memory-intensive, making it difficult to identify interpretable features with significant biological or phenotypic pathways.
Innovation Solution
A computer-implemented method using harmonic homology to rank feature vectors by magnitude, based on persistent homology barcodes and harmonic representatives, to select a subset of significant feature vectors that impact a given condition, reducing computational load.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If statistical tools are used to identify the weight of each factor in multiway interactions, then measurement precision is improved, but computational cost and memory usage increase significantly
Solution Approach 1:
The patent extracts only the most significant features from the multiway data using persistent homology barcodes, rather than analyzing all features with traditional statistical tools. This extraction approach identifies critical features while avoiding the computational burden of comprehensive statistical analysis of every factor.
Solution Approach 2:
The patent transforms the data representation by converting multiway data into persistent homology barcodes, changing the parameter space from traditional statistical measurements to topological features. This parameter transformation enables feature identification with reduced computational requirements while maintaining measurement precision.
2Measurement precision
If statistical tools are used to identify the weight of each factor in multiway interactions, then measurement precision is improved, but memory usage increases significantly
Solution Approach 1:
The patent extracts only the essential topological features represented by persistent homology barcodes, discarding redundant data. This extraction reduces the quantity of data that needs to be stored in memory while preserving the critical information needed for accurate feature weight measurement.
Solution Approach 2:
Instead of starting with all data and filtering out unimportant features through memory-intensive statistical analysis, the patent inverts the approach by directly computing topological invariants that inherently capture only the significant structural features, thereby reducing memory requirements from the outset.
3Measurement precision
If all feature vectors are analyzed to determine their impact on the outcome, then measurement precision is improved, but productivity decreases due to computational expense
Solution Approach 1:
The patent applies partial action by analyzing only the subset of features that are identified as significant through persistent homology barcodes, rather than performing exhaustive analysis on all features. This partial analysis achieves sufficient measurement precision for identifying impactful features while dramatically improving analysis speed and productivity.
Solution Approach 2:
The patent performs preliminary action by first computing persistent homology barcodes to identify significant features before conducting detailed impact analysis. This preliminary filtering step prepares the data in advance, enabling faster and more efficient subsequent analysis of only the relevant features.
4Measurement precision
If traditional methods are used to handle complex interplay of features, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent substitutes traditional statistical mechanical systems with topological data analysis methods. By replacing conventional statistical tools with persistent homology computations, the system handles complex feature interplays through topological invariants, reducing computational system complexity while maintaining or improving measurement precision.
Solution Approach 2:
The patent changes the parameter representation from traditional statistical features to topological features encoded in persistent homology barcodes. This parameter transformation simplifies the computational model for handling complex interplays, reducing device complexity while preserving the ability to measure feature relationships accurately.
Data Source
AI summary
A computer-implemented method includes receiving at a processor an input set of multiway data. The method determines a set of persistent homology barcodes based on the multiway data 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 for a boundary of the multiway data is computed. The method obtains a harmonic representative by computing a projection of the representative cycle to an orthogonal complement and generates a set of feature vectors using the harmonic representative. Each feature vector has a magnitude corresponding to an impact that feature has on a given condition. The method then ranks the feature vectors by feature vector magnitude.