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where <math>\boldsymbol{X}</math> is the set of all type 3 objects, <math>\boldsymbol{p(x)}</math> is the fuzzy membership vector of object <math>\boldsymbol{x}</math>, <math>\mathcal{N}(x)</math> is the set of nearest neighbors of <math>\boldsymbol{x}</math>, and <math>w_{\boldsymbol{xy}}</math> (<math>\sum_{\boldsymbol{y\in \mathcal{N}(x)}}w_{\boldsymbol{xy}}=1</math>) are the coefficients reflecting the relative proximities of the nearest neighbors.
The NAE can be minimized by solving the following linear equations with unique solution which is the unique global minimum of NAE with value zero:
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