Publications (12)
Convergence analysis of a family of Zermelo-type iterations for the Bradley--Terry model
Ruijian Han, Ding Lu, Yiming Xu
Zermelo's algorithm is a classical method for computing the maximum likelihood estimator in the Bradley--Terry (BT) model, but its convergence can be slow in practice. To accelerat…
Variational Characterization of Monotone Nonlinear Eigenvector Problems and Geometry of Self-Consistent-Field Iteration
Zhaojun Bai, Ding Lu
This paper concerns a class of monotone eigenvalue problems with eigenvector nonlinearities (mNEPv). The mNEPv is encountered in applications such as the computation of joint numer…
Hidden Convexity of Fair PCA and Fast Solver via Eigenvalue Optimization
Junhui Shen, Aaron J. Davis, Ding Lu +1
Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outc…
Multi-scale prediction for robust hand detection and classification
Ding Lu, Yong Wang, Robert Laganiere +2
In this paper, we present a multi-scale Fully Convolutional Networks (MSP-RFCN) to robustly detect and classify human hands under various challenging conditions. In our approach, t…
An NPDo Approach for Principal Joint Block Diagonalization
Ren-Cang Li, Ding Lu, Li Wang +1
Matrix joint block-diagonalization (JBD) frequently arises from diverse applications such as independent component analysis, blind source separation, and common principal component…
Optimal Convergence Rate of Self-Consistent Field Iteration for Solving Eigenvector-dependent Nonlinear Eigenvalue Problems
Zhaojun Bai, Ren-Cang Li, Ding Lu
We present a comprehensive convergence analysis for Self-Consistent Field (SCF) iteration to solve a class of nonlinear eigenvalue problems with eigenvector-dependency (NEPv). Usin…
Effects of ion mobility and positron fraction on solitary waves in weak relativistic electron-positron-ion plasma
Ding Lu, Zi-Liang Li, Bai-Song Xie
Effects of ion mobility and positron fraction on solitary waves of envelop of laser field and potential of electrostatic field in weak relativistic electron-positron-ion plasma are…
Backward Stability of Explicit External Deflation for the Symmetric Eigenvalue Problem
Chao-Ping Lin, Ding Lu, Zhaojun Bai
A thorough backward stability analysis of Hotelling's deflation, an explicit external deflation procedure through low-rank updates for computing many eigenpairs of a symmetric matr…
Vacuum pair production of charged scalar bosons in time-dependent electric fields
Zi-Liang Li, Ding Lu, Bai-Song Xie
Based on the quantum mechanical scattering model, the dynamical assist effect and the multiple-slit interference effect in electron-positron pair production from vacuum are general…
Locally Unitarily Invariantizable NEPv and Convergence Analysis of SCF
Ding Lu, Ren-Cang Li
We consider a class of eigenvector-dependent nonlinear eigenvalue problems (NEPv) without the unitary invariance property. Those NEPv commonly arise as the first-order optimality c…
Eigenvalue backward errors of Rosenbrock systems and optimization of sums of Rayleigh quotient
Ding Lu, Anshul Prajapati, Punit Sharma +1
We address the problem of computing the eigenvalue backward error of the Rosenbrock system matrix under various types of block perturbations. We establish computable formulas for t…
Scalable Spectral Clustering with Group Fairness Constraints
Ji Wang, Ding Lu, Ian Davidson +1
There are synergies of research interests and industrial efforts in modeling fairness and correcting algorithmic bias in machine learning. In this paper, we present a scalable algo…