Hierarchical Robust PCA for Scalable Data Quality Monitoring in Multi-level Aggregation Pipelines
Preetam Kumar Ojha
TL;DR
The paper tackles data quality monitoring in big data pipelines with multi-level aggregation by introducing Hierarchical Robust PCA (HrPCA), which extends Robust PCA to decompose data at each hierarchical level into low-rank components $L_i$ and sparse residuals $S_i$, yielding a total reconstruction $\hat{X} = \sum_{i=1}^k L_i$ and residual $S = X - \hat{X}$. Anomalies are detected via row-wise $\ell_2$ norms of $S$ after applying Truncated SVD to each level. The approach supports interpretability through eigenvector backtracking, correlating anomalies with dominant eigenmodes and contributing features to enable root-cause localization across the hierarchy. Experimental results on synthetic hierarchical data show HrPCA can outperform traditional rule-based checks, particularly at lower levels, while highlighting the need for multilevel fusion as signals dilute at higher levels; this method offers practical, scalable DQ auditing and diagnostic capabilities for complex data pipelines.
Abstract
Data quality (DQ) remains a fundamental concern in big data pipelines, especially when aggregations occur at multiple hierarchical levels. Traditional DQ validation rules often fail to scale or generalize across dimensions such as user interactions, sessions, profiles, accounts, and regions. In this paper, we present a novel application of Hierarchical Robust Principal Component Analysis (HrPCA) as a scalable, unsupervised anomaly detection technique tailored to DQ monitoring in multi-level aggregation pipelines. We propose a modular framework that decomposes the data at each hierarchical level into low-rank representations and sparse residuals, allowing the detection of subtle inconsistencies, outliers, and misalignments in the aggregated data. We evaluated our approach using synthetic hierarchical datasets with controlled anomalies and demonstrated how HrPCA outperforms traditional rule-based methods in detecting data corruption and rollup inconsistencies.