Privacy-Preserving Matrix Factorization for Simultaneous Imputation and Fitting
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Solution Overview
Problem
Conventional methods cannot simultaneously perform imputation, fitting, and subspace analysis while ensuring privacy protection, particularly in compliance with regulations like GDPR, as they often result in loss of numerical values and are not suitable for mathematical calculations.
Innovation Solution
A privacy-preserving predicting method that involves obtaining predictor and response matrices, approximating them as products of nonnegative matrices, and using orthogonal projection, weight, and basis matrices to determine a cost function, allowing for simultaneous imputation, fitting, and subspace analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If information removal technology is used to protect privacy, then privacy protection is improved, but numerical values are lost and mathematical calculations cannot be performed
Solution Approach 1:
The patent introduces masked values as an intermediary representation that preserves the structural and relational properties of original data while removing sensitive information. These masked values serve as placeholders that maintain matrix dimensions and allow mathematical operations to proceed without exposing actual sensitive data, thus resolving the contradiction between privacy protection and numerical value preservation
Solution Approach 2:
The patent transforms the state of data from original sensitive values to masked placeholder values through a parameter change process. This transformation allows the data to maintain its functional properties for mathematical calculations while changing its informational content to protect privacy, enabling both privacy protection and mathematical operations to coexist
2Reliability
If conventional techniques are used for imputation, then privacy protection is improved, but simultaneous performance of imputation, fitting, and subspace analysis cannot be achieved
Solution Approach 1:
The patent merges three separate operations (imputation, fitting, and subspace analysis) into a single unified computational framework. By formulating all three operations as simultaneous matrix factorization tasks with orthogonal constraints, the system achieves them concurrently rather than sequentially, improving productivity while maintaining privacy protection through the use of masked values throughout the process
Solution Approach 2:
The patent creates a universal computational model that performs multiple functions simultaneously: it conducts imputation by estimating masked values, performs fitting by modeling relationships between variables, and executes subspace analysis by identifying latent structures. This multi-functional approach allows a single algorithm to handle all three tasks together, resolving the contradiction between privacy protection and operational efficiency
Data Source
AI summary
A provided method includes: obtaining a predictor matrix having at least one masked attribute; obtaining a response matrix; setting that the predictor matrix is approximated by a product of a basis matrix and a coefficient matrix; setting that the response matrix is approximated by a product of a weight matrix, a projection matrix and the predictor matrix; setting that the basis matrix, the coefficient matrix, the weight matrix, and the projection matrix are nonnegative; setting that the projection matrix, the weight matrix, or a product of the projection matrix and the predictor matrix is orthogonal, and thus setting a cost function; and calculating the basis matrix, the coefficient matrix, the weight matrix, and the projection matrix according to the cost function. Accordingly, operations of imputation, fitting, and subspace analysis can be performed.