Surrogate Ranking Operator for Network Node Analysis
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Solution Overview
Problem
Conventional methods for ranking nodes in a network require multiple recursive steps, consuming significant time and computational resources, and often need to be learned from empirical measurements, which can be inefficient and cumbersome.
Innovation Solution
The development of a surrogate ranking operator (SRO) inspired by quantum mechanics and quantum field theory, allowing for a single operational step to rank network nodes by multiplying a state vector representing the ranking criteria with a matrix that represents all paths in the network, thereby bypassing the need for recursive traversals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional link analysis algorithms (e.g., PageRank) are used to rank network nodes, then the ranking can be obtained based on network interconnections, but the process requires multiple recursive steps consuming significant time and computational resources
Solution Approach 1:
The patent pre-computes and stores the eigenvector corresponding to the largest eigenvalue of the network's adjacency matrix (or a normalized version thereof) during an offline phase. This pre-computed eigenvector captures the essential ranking information of the network structure. When ranking queries are made online, the system simply projects the query vector onto this pre-computed eigenvector, avoiding the need for iterative recursive computations at query time.
Solution Approach 2:
The patent replaces the mechanical iterative recursive process of conventional link analysis algorithms with a direct mathematical projection operation. Instead of repeatedly applying the adjacency matrix to converge to the principal eigenvector, the system uses the pre-computed eigenvector to directly compute rankings through vector projection, significantly reducing computational steps.
2Loss of information
If conventional link analysis algorithms are used to rank network nodes, then comprehensive network information can be utilized, but the computational intensity and resource consumption are high
Solution Approach 1:
The patent performs the computationally intensive eigenvector computation in advance during an offline phase, storing the result for efficient online query processing. This separates the heavy computational workload from the energy-constrained online operation, allowing comprehensive network information to be processed once rather than repeatedly for each query.
Solution Approach 2:
The patent creates a simplified representation (the principal eigenvector) that captures the essential ranking information of the entire network. This eigenvector serves as a compact copy or surrogate of the full network structure, enabling fast queries without repeatedly accessing or processing the complete network data.
3Measurement precision
If multiple recursive steps are performed to rank network nodes, then accurate rankings can be achieved, but the process becomes cumbersome and inefficient
Solution Approach 1:
The patent pre-computes the principal eigenvector that embodies the optimal ranking criteria, storing it for direct use in online queries. This eliminates the need for operators to execute multiple recursive steps, as the ranking computation reduces to a simple vector projection operation using the pre-computed eigenvector.
Solution Approach 2:
The patent extracts the essential ranking information from the complex network structure by computing the principal eigenvector, which captures the dominant pattern of node importance. This extracted eigenvector can be directly applied to ranking queries without needing to retain or process the full complexity of the original network structure.
Data Source
AI summary
An apparatus and method are provided for rapidly ranking network nodes according to input ranking criteria. The links (i.e., first-order paths) between nodes are expressed in a first-order path matrix, which is used to generate nth-order path matrices as nth powers of the first-order path matrix and summed as a power series to generate a surrogate ranking operator (SRO) representing as a single matrix operation a sum over paths of all orders. Thus, in contrast to conventional ranking methods that require multiple recursive steps to account for the interrelatedness of linked nodes, a ranking is produced by multiplying the SRO by a state vector representing the input ranking criteria.