IEEE Trans Image Process - Efficient semidefinite spectral clustering via lagrange duality.

Tópicos

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Resumo

We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm approximation-based algorithm, the proposed algorithm can more accurately find the closest doubly stochastic approximation to the affinity matrix by considering the p.s.d. constraint. In this paper, SSC is formulated as a semidefinite programming (SDP) problem. In order to solve the high computational complexity of SDP, we present a dual algorithm based on the Lagrange dual formalization. Two versions of the proposed algorithm are proffered: one with less memory usage and the other with faster convergence rate. The proposed algorithm has much lower time complexity than that of the standard interior-point-based SDP solvers. Experimental results on both the UCI data sets and real-world image data sets demonstrate that: 1) compared with the state-of-the-art spectral clustering methods, the proposed algorithm achieves better clustering performance and 2) our algorithm is much more efficient and can solve larger-scale SSC problems than those standard interior-point SDP solvers.

Resumo Limpo

propos effici approach semidefinit spectral cluster ssc address frobenius normal posit semidefinit psd constraint spectral cluster compar origin frobenius norm approximationbas algorithm propos algorithm can accur find closest doubli stochast approxim affin matrix consid psd constraint paper ssc formul semidefinit program sdp problem order solv high comput complex sdp present dual algorithm base lagrang dual formal two version propos algorithm proffer one less memori usag faster converg rate propos algorithm much lower time complex standard interiorpointbas sdp solver experiment result uci data set realworld imag data set demonstr compar stateoftheart spectral cluster method propos algorithm achiev better cluster perform algorithm much effici can solv largerscal ssc problem standard interiorpoint sdp solver

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