| CPC H03M 7/6011 (2013.01) [H03M 7/3066 (2013.01)] | 21 Claims |
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4. A numerical compression method for extracting derived, latent features from multidimensional (or multi-dimensionalizable) data sets, the method comprising:
identifying targets (variables, vectors, or data subsets) in multimodal, multidimensional, and/or multi-dimensionalizable data sets to find representations of the target in terms of the other modes, or data subgroupings, from the full data set;
extracting representations in the form of either dependent and/or independent variables of simple algebraic form and order, along with their integrals along varying dimensions or dependencies, and their derivatives with respect to each other (including temporal, spatial, partial, and/or “phase derivatives”);
using the extracted representations to discover parsimonious (or near parsimonious) representations of the input data, in the expression of simple differential-type equations; and encoding and storing the parsimonious representations for later retrieval, data reconstruction, analysis, and/or downstream use;
transforming extracted representations into digitized versions of numerical and symbolic representations;
extracting the deep relationships in the data encoded into families of differential-style equations and the coinciding residuals associated to the numerical approximations representing differential and integral forms;
generating computationally invertible mappings between the forward and reverse numerical and algebraic representations of the differential and integro-differential forms from the extracted representations;
training the representational numerical forms of the extracted representations to be substantially parsimonious, relative to user assigned constraints, limits, or in-built assumptions;
optimizing the representational numerical forms to balance the needs of the application at hand; and
storing the optimal representations for later use.
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