Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering with Instance-level Constraints
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Semi-supervised graph clustering: a kernel approach
Machine Learning
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
The power of convex relaxation: near-optimal matrix completion
IEEE Transactions on Information Theory
Matrix completion from a few entries
IEEE Transactions on Information Theory
Flexible constrained spectral clustering
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Robust Low-Rank Subspace Segmentation with Semidefinite Guarantees
ICDMW '10 Proceedings of the 2010 IEEE International Conference on Data Mining Workshops
Fixed point and Bregman iterative methods for matrix rank minimization
Mathematical Programming: Series A and B
Learning Spectral Embedding for Semi-supervised Clustering
ICDM '11 Proceedings of the 2011 IEEE 11th International Conference on Data Mining
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Learning data representation is a fundamental problem in data mining and machine learning. Spectral embedding is one popular method for learning effective data representations. In this paper we propose a novel framework to learn enhanced spectral embedding, which not only considers the geometrical structure of the data space, but also takes advantage of the given pairwise constraints. The proposed formulation can be solved by an iterative eigenvalue thresholding (IET) algorithm. Specially, we convert the problem of learning spectral embedding with pairwise constraints into the one of completing an "ideal" kernel matrix. And we introduce the spectral embedding of graph Laplacian as the auxiliary information and cast it as a small-scale positive semidefinite (PSD) matrix optimization problem with nuclear norm regularization. Then, we develop an IET algorithm to solve it efficiently. Moreover, we also present an effective semi-supervised clustering (SSC) approach with learned spectral embedding (LSE). Finally, we validate the proposed IET algorithm and LSE approach by extensive experiments on real-world data sets.