[Paper Review] Denoising individual bias for a fairer binary submatrix detection

Changlin Wan, Wennan Chang+3 more|arXiv (Cornell University)|Jul 31, 2020

Face and Expression Recognition6 references4 citations

TL;DR

This paper proposes BIND, a denoising framework that improves fairness and accuracy in binary submatrix detection by modeling heterogeneous row- and column-wise background noise in binary matrices. By estimating mixture distributions of pattern and background probabilities, BIND identifies and removes attributes likely from background noise, significantly enhancing state-of-the-art BMF and co-clustering methods on synthetic and real-world data.

ABSTRACT

Low rank representation of binary matrix is powerful in disentangling sparse individual-attribute associations, and has received wide applications. Existing binary matrix factorization (BMF) or co-clustering (CC) methods often assume i.i.d background noise. However, this assumption could be easily violated in real data, where heterogeneous row- or column-wise probability of binary entries results in disparate element-wise background distribution, and paralyzes the rationality of existing methods. We propose a binary data denoising framework, namely BIND, which optimizes the detection of true patterns by estimating the row- or column-wise mixture distribution of patterns and disparate background, and eliminating the binary attributes that are more likely from the background. BIND is supported by thoroughly derived mathematical property of the row- and column-wise mixture distributions. Our experiment on synthetic and real-world data demonstrated BIND effectively removes background noise and drastically increases the fairness and accuracy of state-of-the arts BMF and CC methods.

Motivation & Objective

• Address the fairness issue in binary matrix factorization (BMF) and co-clustering (CC) caused by heterogeneous, non-i.i.d. background noise in real-world data.
• Identify and remove binary attributes that are more likely due to individual-level biases (e.g., user activity or item popularity) rather than true underlying patterns.
• Develop a generalizable denoising framework that enhances existing BMF and CC methods without requiring algorithmic reimplementation.
• Provide rigorous mathematical derivations for the row- and column-wise mixture distributions of pattern and background probabilities in binary matrices.

Proposed method

• Model the observed binary matrix as a combination of true rank-1 patterns, a heterogeneous background matrix with row- and column-wise probabilities, and i.i.d. noise.
• Estimate the marginal probability of 1s in each row and column to infer the background distribution using empirical frequencies.
• Apply a quantile-based shift function to detect rows and columns with overrepresented 1s compared to their background, identifying potential true patterns.
• Use a thresholding mechanism to select high-signal rows and columns, forming a denoised submatrix for downstream BMF or CC analysis.
• Integrate the denoising step as a preprocessing layer that can be applied to any existing BMF or CC algorithm.
• Leverage mathematical properties of mixture distributions to justify the statistical validity of the denoising process.

Experimental results

Research questions

• RQ1 How does heterogeneous background noise—caused by individual-level biases such as user activity or item popularity—affect the fairness and accuracy of existing BMF and CC methods?
• RQ2 Can a data-driven denoising framework that models non-i.i.d. background distributions improve the detection of true rank-1 submatrices in binary matrices?
• RQ3 To what extent does the proposed BIND framework enhance the performance of state-of-the-art BMF and CC methods on both synthetic and real-world data?
• RQ4 How does the framework enable better interpretability and stability in real-world applications such as recommendation systems?

Key findings

• BIND increased the Jaccard index by an average of 2.6-fold across all synthetic data scenarios when compared to non-denoised baseline (τ=0).
• When combined with the LOM BMF method, BIND achieved an average 7.5-fold increase in Jaccard index for pattern detection, demonstrating significant accuracy gains.
• With the Biclust CC method, BIND improved the Jaccard index by an average of 2.6-fold, confirming consistent performance gains across different algorithmic paradigms.
• On Movielens data, the denoised region (I¹) showed the most stable user rating behavior with minimal dispersion across movie categories, indicating more coherent and interpretable user preferences.
• Users in the high-signal region (I¹) exhibited higher overall activity but lower category diversity, suggesting targeted recommendation potential.
• The framework effectively isolated true patterns from background noise, as evidenced by improved pattern recovery and reduced false positives in both synthetic and real-world settings.