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Spectral Clustering (SC) is a widely used data clustering method which first learns a low-dimensional embedding U of

data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on U^⊤ to get the final clustering result. The sparse spectral clusteing method extends SC with a sparse regularization on U U^⊤ by using the block diagonal structure prior of U U^⊤ in the ideal case. However, encouraging U U^⊤ to be sparse leads to a heavily nonconvex problem which is challenging to solve. Lu propose a new method and considers to solve the nonconvex formulation of SSC which directly encourages U U^⊤ to be sparse by using a huber loss rather than ℓ₁ norm. Also the proposed ADMM method on solving this problem doesn't have a convergence guarantee when the penalty is the ℓ₁ norm. In this work, we proposed the model on nonconvex spectral clustering. In order to solve this model more efficiently and accurately, we proposed the ManPL algorithm by using the ingredients in manifold optimization and proximal linear method. Our analysis does not impose any assumptions on the iterates and thus is practical. Experimental analysis on several machine learning data sets verifies the effectiveness of our method.

There will be pizza.