Partial-Order Hypergraph Encoding for Machine Learning
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Solution Overview
Problem
Existing hypergraph structures fail to capture ordering relationships among entities, leading to information loss and suboptimal performance in machine learning tasks, as they represent hyperedges as unordered sets without considering partial order relations.
Innovation Solution
The introduction of a Partial-Order Hypergraph (POH) structure that encodes partial order relations between entities using directed edges and logic rules, allowing for the representation of these relations as a set of matrices and the formulation of an objective function to obtain a prediction function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If hyperedges are represented as unordered sets of vertices, then the hypergraph structure is simple and easy to construct, but ordering relationships among entities are lost leading to information loss
Solution Approach 1:
The patent transforms the symmetric unordered set representation into an asymmetric ordered structure by introducing directed edges. Each directed edge from vertex u to vertex v within ahyperedge explicitly encodes the ordering relationship that u precedes v, thereby preserving ordering information while maintaining the hypergraph framework.
Solution Approach 2:
The patent adds a new dimensional aspect to the hypergraph by introducing directionality to edges. Instead of treating edges as undirected connections, the patent models them as directed edges with explicit source and destination vertices, creating a partial order structure that captures temporal or hierarchical relationships among entities.
2Reliability
If directed edges are added to represent partial order relations, then ordering relationships are captured, but the hypergraph structure becomes more complex
Solution Approach 1:
The patent applies partial ordering rather than complete ordering. Not all pairs of vertices within ahyperedge need to have explicit ordering relationships. The directed edges are added only where ordering information is available and relevant, avoiding the excessive complexity of fully ordering all elements while still capturing the essential partial order structure needed for the machine learning task.
3Loss of information
If partial order relations are encoded using logic rules and directed edges, then information loss is reduced, but the computational complexity increases
Solution Approach 1:
The patent replaces complex iterative optimization procedures with a more direct approach using matrix operations and convex optimization. The partial order hypergraph is represented using incidence matrices and adjacency matrices, allowing the learning problem to be formulated as a convex optimization problem that can be solved efficiently using standard algorithms, thereby reducing computational complexity compared to traditional iterative methods.
Data Source
AI summary
A machine learning method comprises: receiving input data comprising a set of feature variables each indicating features of a plurality of entities; encoding partial order relations between entities of the plurality of entities as a set of logic rules; constructing a hypergraph comprising a plurality of vertices representing the entities of the plurality of entities and a plurality of hyperlinks linking similar entities of the plurality of entities; adding directed edges to the hypergraph to represent partial order interactions between entities to form a partial order hypergraph; representing the partial order hypergraph as a set of matrices; forming an objective function using the logic rules and matrices of the set of matrices; minimizing the objective function to obtain a prediction function; and outputting an indication of the prediction function.