Typed Graphlet Identification via Combinatorial Orbit Counting
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Solution Overview
Problem
Identifying and counting typed graphlets in large heterogeneous networks is challenging due to the high computational resources required by existing brute force enumeration techniques, making them impractical for most applications.
Innovation Solution
A system and methodology that utilizes parallel computing and efficient memory utilization by dividing the computational task among processors, computing k-node typed graphlets based on combinatorial relationships between (k−1)-node graphlets, and maintaining counts and statistics for identified graphlets, thereby avoiding explicit enumeration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If brute force enumeration techniques are used to identify typed graphlets, then completeness of identification is improved, but computational resource requirements worsen
Solution Approach 1:
The patent segments the graph identification task by introducing canonical labeling that groups graphlets into orbits based on their structural properties. Instead of enumerating all possible graphlets, the system identifies representative canonical forms and uses orbit stabilization theory to count all graphlets in each orbit, thereby achieving complete identification with reduced computational effort.
Solution Approach 2:
The patent performs preliminary computation by pre-calculating canonical labels and orbit representatives before the actual counting process. The canonical labeling framework is established in advance, allowing the system to efficiently map discovered graphlets to their canonical forms and accumulate counts without redundant processing during the enumeration phase.
2Measurement precision
If brute force enumeration techniques are used to identify typed graphlets, then completeness of identification is improved, but practical applicability worsens
Solution Approach 1:
The system segments the computational space into distinct orbits of graphlets under automorphism groups. By identifying canonical representatives for each orbit and computing stabilizer subgroups, the patent transforms an intractable enumeration problem into a manageable counting problem that can be applied to real-world networks.
Solution Approach 2:
The patent replaces the mechanical brute-force enumeration approach with a theoretical framework based on orbit-stabilizer theorem from group theory. This substitution transforms the problem from explicitly constructing and counting each graphlet instance to computing orbital counts through mathematical relationships, dramatically improving practical applicability.
3Measurement precision
If existing approaches are used for identifying subgraphs, then identification accuracy is improved, but device complexity worsens
Solution Approach 1:
The patent develops a universal canonical labeling framework that handles multiple graphlet types and sizes through a single unified approach. The orbit-stabilizer methodology applies generally to any typed graphlet identification task, providing a multi-functional solution that maintains high identification accuracy without requiring separate specialized algorithms for different graphlet configurations.
Solution Approach 2:
The patent changes the parameter space by transforming the problem from counting individual graphlet instances to counting orbital representatives. By introducing canonical labels as a new parameter and using group theoretic invariants, the system achieves accurate identification while simplifying the underlying computational structure.
Data Source
AI summary
A system is disclosed for identifying and counting typed graphlets in a heterogeneous network. A methodology implementing techniques for the disclosed system according to an embodiment includes identifying typed k-node graphlets occurring between any two selected nodes of a heterogeneous network, wherein the nodes are connected by one or more edges. The identification is based on combinatorial relationships between (k−1)-node typed graphlets occurring between the two selected nodes of the heterogeneous network. Identification of 3-node typed graphlets is based on computation of typed triangles, typed 3-node stars, and typed 3-paths associated with each edge connecting the selected nodes. The method further includes maintaining a count of the identified k-node typed graphlets and storing those graphlets with non-zero counts. The identified graphlets are employed for applications including visitor stitching, user profiling, outlier detection, and link prediction.