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Nonconvex Sparse Spectral Clustering by Alternating Direction Method of Multipliers and Its Convergence Analysis
Canyi Lu, Jiashi Feng, Zhouchen Lin +1
Spectral Clustering (SC) is a widely used data clustering method which first learns a low-dimensional embedding of data by computing the eigenvectors of the normalized Laplacia…
Convergence Rates Analysis of The Quadratic Penalty Method and Its Applications to Decentralized Distributed Optimization
Huan Li, Cong Fang, Zhouchen Lin
In this paper, we study a variant of the quadratic penalty method for linearly constrained convex problems, which has already been widely used but actually lacks theoretical justif…
Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization
Canyi Lu, Jiashi Feng, Yudong Chen +3
This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA (Candes et al. 2011) to the tensor case. Our model is based on a new ten…
Faster and Non-ergodic O(1/K) Stochastic Alternating Direction Method of Multipliers
Cong Fang, Feng Cheng, Zhouchen Lin
We study stochastic convex optimization subjected to linear equality constraints. Traditional Stochastic Alternating Direction Method of Multipliers and its Nesterov's acceleration…
Provable Accelerated Gradient Method for Nonconvex Low Rank Optimization
Huan Li, Zhouchen Lin
Optimization over low rank matrices has broad applications in machine learning. For large scale problems, an attractive heuristic is to factorize the low rank matrix to a product o…