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Ridge Estimation with Nonlinear Transformations
Zheng Zhai, Hengchao Chen, Zhigang Yao
Ridge estimation is an important manifold learning technique. The goal of this paper is to examine the effects of nonlinear transformations on the ridge sets. The main result prove…
Bounded Projection Matrix Approximation with Applications to Community Detection
Zheng Zhai, Hengchao Chen, Qiang Sun
Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded co…
Gradient descent in matrix factorization: Understanding large initialization
Hengchao Chen, Xin Chen, Mohamad Elmasri +1
Gradient Descent (GD) has been proven effective in solving various matrix factorization problems. However, its optimization behavior with large initial values remains less understo…
Statistical Analysis of Karcher Means for Random Restricted PSD Matrices
Hengchao Chen, Xiang Li, Qiang Sun
Non-asymptotic statistical analysis is often missing for modern geometry-aware machine learning algorithms due to the possibly intricate non-linear manifold structure. This paper s…
Quadratic Matrix Factorization with Applications to Manifold Learning
Zheng Zhai, Hengchao Chen, Qiang Sun
Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF)…