Selected work

Representative Papers

Concatenated Matrix SVD: Compression Bounds, Incremental Approximation, and Error-Constrained Clustering

Jan 12, 2026arXiv.org

This work addresses the issue of uncontrolled reconstruction errors in SVD-based compression of large collections of matrices when heuristic grouping is employed prior to concatenation. To overcome this limitation, the authors propose a theory-driven compressive clustering framework grounded in spectral analysis of horizontally concatenated matrices. They establish, for the first time, a globally provable upper bound on SVD reconstruction error and derive two novel spectral bounds based on a lower bound for singular value growth. Building upon these theoretical guarantees, they design three clustering algorithms with explicit error control, integrated with incremental approximate SVD to efficiently estimate compression error without explicitly forming the full concatenated matrix. The resulting approach achieves a favorable balance among speed, accuracy, and scalability, significantly enhancing the reliability and practicality of SVD compression in applications such as multi-view learning, signal processing, and neural network compression.

1 citationsRead paper

Perturbation Analysis of Singular Values in Concatenated Matrices

Mar 11, 2025arXiv.org

This work investigates the impact of matrix concatenation operations on singular value spectra, aiming to bridge a theoretical gap in the structural stability of SVDs under concatenation. Addressing the central question—“How are the singular values of a concatenated matrix determined by those of its constituent submatrices?”—we extend Weyl’s inequality to block-wise concatenation for the first time, establishing a quantitative analytical framework grounded in matrix perturbation theory and norm inequalities. We derive computable upper bounds on singular value deviations and rigorously prove that dominant singular values remain stable when the operator norms of the submatrices are comparable. This result provides theoretical guarantees and principled design guidance for low-rank approximation, robust matrix clustering, and compression algorithms.

1 citationsRead paper

Convergence Analysis of Nyström Subsampling in Covariate Shift Adaptation for Misspecified case

Jun 20, 2026

This work addresses the convergence challenge in unsupervised domain adaptation under covariate shift when the target function lies outside the reproducing kernel Hilbert space (i.e., the misspecified setting). By integrating Tikhonov regularization with Nyström subsampling projection, the paper establishes, for the first time, a high-probability excess risk upper bound for Nyström-type domain adaptation methods in this misspecified regime. Leveraging source conditions, effective dimension estimates, and approximation of the Radon–Nikodym derivative, the proposed approach achieves the same convergence rate as in the well-specified setting, requiring only a minimal number of additional samples even when the Radon–Nikodym derivative is unknown.

0 citationsRead paper

Recent publications

Latest Papers

Convergence Analysis of Nyström Subsampling in Covariate Shift Adaptation for Misspecified case

Jun 20, 2026

This work addresses the convergence challenge in unsupervised domain adaptation under covariate shift when the target function lies outside the reproducing kernel Hilbert space (i.e., the misspecified setting). By integrating Tikhonov regularization with Nyström subsampling projection, the paper establishes, for the first time, a high-probability excess risk upper bound for Nyström-type domain adaptation methods in this misspecified regime. Leveraging source conditions, effective dimension estimates, and approximation of the Radon–Nikodym derivative, the proposed approach achieves the same convergence rate as in the well-specified setting, requiring only a minimal number of additional samples even when the Radon–Nikodym derivative is unknown.

0 citationsRead paper

Concatenated Matrix SVD: Compression Bounds, Incremental Approximation, and Error-Constrained Clustering

Jan 12, 2026arXiv.org

This work addresses the issue of uncontrolled reconstruction errors in SVD-based compression of large collections of matrices when heuristic grouping is employed prior to concatenation. To overcome this limitation, the authors propose a theory-driven compressive clustering framework grounded in spectral analysis of horizontally concatenated matrices. They establish, for the first time, a globally provable upper bound on SVD reconstruction error and derive two novel spectral bounds based on a lower bound for singular value growth. Building upon these theoretical guarantees, they design three clustering algorithms with explicit error control, integrated with incremental approximate SVD to efficiently estimate compression error without explicitly forming the full concatenated matrix. The resulting approach achieves a favorable balance among speed, accuracy, and scalability, significantly enhancing the reliability and practicality of SVD compression in applications such as multi-view learning, signal processing, and neural network compression.

1 citationsRead paper

Perturbation Analysis of Singular Values in Concatenated Matrices

Mar 11, 2025arXiv.org

This work investigates the impact of matrix concatenation operations on singular value spectra, aiming to bridge a theoretical gap in the structural stability of SVDs under concatenation. Addressing the central question—“How are the singular values of a concatenated matrix determined by those of its constituent submatrices?”—we extend Weyl’s inequality to block-wise concatenation for the first time, establishing a quantitative analytical framework grounded in matrix perturbation theory and norm inequalities. We derive computable upper bounds on singular value deviations and rigorously prove that dominant singular values remain stable when the operator norms of the submatrices are comparable. This result provides theoretical guarantees and principled design guidance for low-rank approximation, robust matrix clustering, and compression algorithms.

1 citationsRead paper