Constructing predictive setups using harmonic homology for disentangling multiway interactions

A computer system comprising:

• a processor and a non-transitory memory storing instructions for causing the computer system to perform the method of
• receiving at the processor an input set of multiway data, wherein the multiway data includes a numerical representation of each factor in a set of interconnected factors affecting an outcome, and wherein each factor has a codependency on at least one other factor in the set of interconnected factors;
• determining a set of persistent homology barcodes based on the multiway data using the processer;
• identifying at least a first significant persistent homology barcode in the set of persistent homology barcodes, returning a representative cycle of the first significant persistent homology and computing an orthonormal basis for a boundary of the multiway data;
• obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement;
• and
• determining a predictive setup for an experiment based on the harmonic representation and outputting the predictive setup for the experiment to a user.

A computer program product comprising:

• a non-transitory computer readable storage medium storing instructions for cause a computer system to perform operations comprising:
• receiving at a processor an input set of multiway data, wherein the multiway data includes a numerical representation of each factor in a set of interconnected factors affecting an outcome, and wherein each factor has a codependency on at least one other factor in the set of interconnected factors;
• determining a set of persistent homology barcodes based on the multiway data using the processer;
• identifying at least a first significant persistent homology barcode in the set of persistent homology barcodes, returning a representative cycle of the first significant persistent homology and computing an orthonormal basis for a boundary of the multiway data;
• obtaining a harmonic representative by computing a projection of the representative cycle to an orthogonal complement;
• and
• determining a predictive setup for an experiment based on the harmonic representation and outputting the predictive setup for the experiment to a user.