Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Journal of Global Optimization
Learning Spectral Clustering, With Application To Speech Separation
The Journal of Machine Learning Research
Penalized Model-Based Clustering with Application to Variable Selection
The Journal of Machine Learning Research
Foundations and Trends® in Machine Learning
Survey of clustering algorithms
IEEE Transactions on Neural Networks
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Clustering analysis is widely used in many fields. Traditionally clustering is regarded as unsupervised learning for its lack of a class label or a quantitative response variable, which in contrast is present in supervised learning such as classification and regression. Here we formulate clustering as penalized regression with grouping pursuit. In addition to the novel use of a non-convex group penalty and its associated unique operating characteristics in the proposed clustering method, a main advantage of this formulation is its allowing borrowing some well established results in classification and regression, such as model selection criteria to select the number of clusters, a difficult problem in clustering analysis. In particular, we propose using the generalized cross-validation (GCV) based on generalized degrees of freedom (GDF) to select the number of clusters. We use a few simple numerical examples to compare our proposed method with some existing approaches, demonstrating our method's promising performance.