Robust Anomaly Detection via Tensor Pseudoskeleton Decomposition
Bowen Su
TL;DR
The paper tackles anomaly detection in high-dimensional tensor data by framing it as a tensor robust PCA problem. It introduces a Tensor Pseudoskeleton Decomposition within the TRPCA framework to decompose the observed tensor $\mathcal{T}$ into a low Tucker-rank component $\mathcal{L}^\star$ and a sparse anomaly tensor $\mathcal{S}^\star$, where $\mathcal{T} = \mathcal{L}^\star + \mathcal{S}^\star$ and $\mathcal{L}^\star = \mathcal{R} \times_{i=1}^n (\mathcal{C}_i \mathcal{U}_i^\dagger)$. The method alternates between updating $\mathcal{S}$ via a decaying hard-thresholding rule and updating $\mathcal{L}$ through mode-wise QR-based subspace identification followed by projection, achieving reduced per-mode complexity $O(d_i r_i^2 + r_i^3)$. Theoretical guarantees are provided under $\mu$-incoherence and sampling conditions, including contraction bounds and a characterization of the required sampling size. Empirically, the approach demonstrates superior anomaly detection performance and faster runtimes on a real-world spatiotemporal NYC taxi dataset, validating its robustness and scalability for large-scale tensor data.
Abstract
Anomaly detection plays a critical role in modern data-driven applications, from identifying fraudulent transactions and safeguarding network infrastructure to monitoring sensor systems for irregular patterns. Traditional approaches, such as distance, density, or cluster-based methods, face significant challenges when applied to high dimensional tensor data, where complex interdependencies across dimensions amplify noise and computational complexity. To address these limitations, this paper leverages Tensor Chidori pseudoskeleton decomposition within a tensor-robust principal component analysis framework to extract low Tucker rank structure while isolating sparse anomalies, ensuring robustness to anomaly detection. We establish theoretical results regarding convergence, and estimation error, demonstrating the stability and accuracy of the proposed approach. Numerical experiments on real-world spatiotemporal data from New York City taxi trip records validate the effectiveness of the proposed method in detecting anomalous urban events compared to existing benchmark methods. Our results suggest that tensor pseudoskeleton decomposition may offer potential for enhancing anomaly detection in large-scale, high-dimensional data.