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Consistency of Spectral Clustering on Hierarchical Stochastic Block Models
Lihua Lei, Xiaodong Li, Xingmei Lou
We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under su…
Nonconvex Matrix Completion with Linearly Parameterized Factors
Ji Chen, Xiaodong Li, Zongming Ma
Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice including collaborative filt…
Convex Relaxation Methods for Community Detection
Xiaodong Li, Yudong Chen, Jiaming Xu
This paper surveys recent theoretical advances in convex optimization approaches for community detection. We introduce some important theoretical techniques and results for establi…
Subspace Perspective on Canonical Correlation Analysis: Dimension Reduction and Minimax Rates
Zhuang Ma, Xiaodong Li
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by rec…
Convexified Modularity Maximization for Degree-corrected Stochastic Block Models
Yudong Chen, Xiaodong Li, Jiaming Xu
The stochastic block model (SBM) is a popular framework for studying community detection in networks. This model is limited by the assumption that all nodes in the same community a…
Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow
T. Tony Cai, Xiaodong Li, Zongming Ma
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal from noisy quadratic measurements , $j=1, \l…
Global testing against sparse alternatives in time-frequency analysis
T. Tony Cai, Yonina C. Eldar, Xiaodong Li
In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit…
Robust and computationally feasible community detection in the presence of arbitrary outlier nodes
T. Tony Cai, Xiaodong Li
Community detection, which aims to cluster nodes in a given graph into distinct groups based on the observed undirected edges, is an important problem in network data analy…