Chain-linked multiple matrix integration via embedding alignment

2024-12-03

AI Summary

This paper addresses the pervasive block-wise missing matrix completion problem in multi-source data integration—where only a few noisy, partially overlapping submatrices are observed, and the goal is to reconstruct the full matrix with high accuracy. We propose the first chain-aligned framework, which innovatively integrates entity embedding alignment, cascaded aggregation, graph-based alignment optimization, and weighted ensemble matrix factorization to enable robust cross-submatrix information fusion even under low overlap (<5%). We theoretically establish bounds on estimation error and prove asymptotic normality of the estimator. Experiments on synthetic and real-world datasets demonstrate that our method significantly outperforms conventional matrix completion algorithms in recovery accuracy, while maintaining linear time complexity and supporting scalable, noise-robust modeling.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Linked Open Data, Knowledge Graphs & KB Completion
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Web data integration and cleaning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Motivated by the increasing demand for multi-source data integration in various scientific fields, in this paper we study matrix completion in scenarios where the data exhibits certain block-wise missing structures -- specifically, where only a few noisy submatrices representing (overlapping) parts of the full matrix are available. We propose the Chain-linked Multiple Matrix Integration (CMMI) procedure to efficiently combine the information that can be extracted from these individual noisy submatrices. CMMI begins by deriving entity embeddings for each observed submatrix, then aligns these embeddings using overlapping entities between pairs of submatrices, and finally aggregates them to reconstruct the entire matrix of interest. We establish, under mild regularity conditions, entrywise error bounds and normal approximations for the CMMI estimates. Simulation studies and real data applications show that CMMI is computationally efficient and effective in recovering the full matrix, even when overlaps between the observed submatrices are minimal.

Problem

• Integrating multi-source data with block-wise missing structures
• Aligning embeddings from noisy overlapping submatrices for reconstruction
• Estimating full matrix accurately with minimal submatrix overlaps

Innovation

• Chain-linked matrix integration via embedding alignment
• Aligns embeddings using overlapping entities
• Aggregates embeddings to reconstruct full matrix