Network Source Inference via Non-Negative Matrix Factorization
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Solution Overview
Problem
Current methods for inferring network dynamics and their sources are limited by the need for assumptions about network processes and are computationally complex, making it difficult to accurately identify influential agents in real-world networks.
Innovation Solution
A system that uses non-negative matrix factorization (NMF) on a signal matrix representing time-evolving states of network agents to learn dictionary atoms, allowing for dimensionality reduction and identification of influential source agents without assuming underlying processes, and can be scaled for large datasets by applying dictionary learning to submatrices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If linear and non-linear systems theory are used to model network dynamics, then understanding of network processes is improved, but computational complexity increases and assumptions about underlying processes are required
Solution Approach 1:
The patent replaces complex systems theory approaches with matrix factorization techniques from linear algebra. Instead of using linear and non-linear differential equations to model network dynamics, the invention uses non-negative matrix factorization (NMF) to decompose the network state matrix into basis matrices, thereby substituting a computationally tractable mathematical framework for the previously used complex systems theory while maintaining the ability to identify influential agents.
Solution Approach 2:
The patent changes the fundamental parameters and assumptions of the modeling approach. Rather than assuming specific dynamic processes (such as linear or non-linear diffusion models), the invention works directly with observed network state data and uses matrix factorization to discover the underlying structure. This parameter change eliminates the need for strong assumptions about the underlying processes while reducing computational complexity.
2Adaptability or versatility
If graph Fourier transform is used to represent network dynamics, then signal processing on graphs is improved, but the assumption that graph attributes are smooth with respect to network structure limits applicability to real-world dynamics
Solution Approach 1:
The patent inverts the traditional graph signal processing approach. Instead of assuming smoothness of graph attributes and applying graph Fourier transform accordingly, the invention starts with arbitrary (non-smooth) graph attributes and uses matrix factorization to discover the underlying structure. This inversion of the smoothness assumption allows the method to handle real-world dynamics that do not conform to smooth graph signal properties.
Solution Approach 2:
The patent introduces dynamics by allowing the basis matrices to capture temporal evolution of network states. Rather than using static graph Fourier transforms, the invention uses time-varying matrix factorizations where the basis matrices evolve over time, enabling the model to adapt to dynamic real-world network processes while maintaining mathematical tractability.
3Measurement precision
If wavelet transforms are designed to reflect underlying processes, then representation accuracy is improved, but the requirement for superficial understanding of processes makes design difficult and limits general applicability
Solution Approach 1:
The patent implements self-service by allowing the matrix factorization process to automatically discover the appropriate basis functions from the data itself. Instead of requiring manual design of wavelet transforms based on superficial understanding of underlying processes, the invention lets the algorithm learn the relevant patterns directly from observed network states, thereby eliminating the need for expert knowledge in transform design while maintaining high representation accuracy.
Data Source
AI summary
Described is a system for inferring network dynamics and their sources within the network. During operation, a vector representation is generated based on states of agents in a network. The vector representation including attribute vectors that correspond to the states of the agents in the network. A matrix representation is then generated based on the changing states of agents by packing the attribute vectors at each time step into an attribute matrix. Time-evolving states of the agents are learned using dictionary learning. Influential source agents in the network are then identified by performing dimensionality reduction on the attribute matrix. Finally, in some aspects, an action is executed based on the identity of the influential source agents. For example, marketing material may be directed to a source agent's online account, or the source agent's online account can be deactivated or terminated or some other desired action can be taken.