Distributed Nonnegative Matrix Factorization for Big Data
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Solution Overview
Problem
Existing nonnegative matrix factorization and completion (NMFC) methods are not accurate and scalable for large problems due to their non-convex formulation and underlying inverse problems, which makes them inefficient for handling large-scale data matrices.
Innovation Solution
The system employs an efficient greedy and distributed process for NMFC (GD-NMFC) by partitioning a large-scale data matrix into smaller submatrices, using rank-one ADMM for parallel optimization, and concatenating solutions to form low-rank matrix factors, eliminating the matrix inverse problem and enabling faster convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing NMFC methods are used to handle large-scale data matrices, then the problem formulation is straightforward, but the computational complexity increases and scalability deteriorates
Solution Approach 1:
The patent divides the large-scale data matrix into multiple smaller submatrices that can be processed in parallel across different computing nodes. This segmentation approach allows the system to handle large problems by breaking them into manageable chunks, improving both processing speed and scalability while reducing the computational burden on individual nodes
Solution Approach 2:
The patent introduces a distributed computing dimension by implementing NMFC across multiple processing nodes rather than a single node. This dimensional transformation from centralized to distributed processing enables the system to scale horizontally, handling larger data matrices efficiently by leveraging parallel computation resources
2Measurement precision
If existing NMFC methods are used for large problems, then the non-convex formulation is maintained, but accuracy and scalability worsen
Solution Approach 1:
By segmenting the large-scale matrix factorization problem into smaller subproblems that can be solved independently in parallel, the system maintains solution accuracy while achieving scalability. Each submatrix factorization contributes to the overall solution, allowing accurate computation to be distributed across multiple nodes without sacrificing precision
3Productivity
If matrix inverse problems are solved in existing NMFC methods, then the factorization is achieved, but computational efficiency deteriorates due to the inverse problem
Solution Approach 1:
The patent extracts and eliminates the computationally expensive matrix inverse operations from the NMFC algorithm by reformulating the problem to avoid explicit inversion. This extraction of the problematic inverse computation step replaces it with more efficient operations that maintain factorization accuracy while dramatically improving convergence speed and reducing algorithmic complexity
Data Source
AI summary
Systems and methods are disclosed for operating a machine, by receiving training data from one or more sensors; training a machine learning module with the training data by: partitioning a data matrix into smaller submatrices to process in parallel and optimized for each processing node; for each submatrix, performing a greedy search for rank-one solutions; using alternating direction method of multipliers (ADMM) to ensure consistency over different data blocks; and controlling one or more actuators using live data and the learned module during operation.