Since no theoretical foundations for proving the convergence of Graph Shift Algorithm have been reported, we provide a generic framework consisting of three key GS components to fit the Zangwill's convergence theorem. We show that the sequence set generated by the GS procedures always terminates at a local maximum, or at worst, contains a subsequence which converges to a local maximum of the similarity measure function. What is more, a theoretical framework is proposed to apply our proof to a more general case.
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