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Tikhonov regularisation utilises additional a-priori information to modify the objective surface, and thus is not a true least squares approach.

In the proposed method, a novel non local adaptive spatial constraint term is introduced to modify the objective function of GIFP_FCM.

Additionally taking into account the whitening transformation, we modify the objective function as follows: Jleft(W,b,mathrm{c}right)=frac{lambda }{M}{displaystyle sum_{n=1}^M}{leftVert {W}^Tsigma left(W{W}_{ZCAwhite}{x}^{(n)}+bright)+c-{W}_{ZCAwhite}{x}^{(n)}rightVert}_2^2+Sleft left{W,bright},{W}_{ZCAwhite}{x}^{(1)},dots, {W}_{ZCAwhite}{x}^{(M }right) (5).

These probability values have to be integrated into the EM algorithm and modify the objective function as outlined in Equation 9, where E symbolizes a vector containing the energy values of the conformers and p(E n ) depicts the probability of the n-th conformation.

For DeltaL, we modify the objective function of equation (1) by incorporating the prior probabilities of membership θ∗.

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It was necessary to modify the objectives and theoretical contents of the different subjects and also the learning methodology, considering the general chemical engineering skills and also the transferable skills reached by the students, according to the recommendations of the European Federation of Chemical Engineering EFCEE) for chemical engineering education in Bologna two-cycle degree system.

Outlier removal can also be integrated in the clustering directly by modifying the objective function [3].

The method has a good computational performance by modifying the membership instead of modifying the objective function.

Policies that best meet multiple objectives simultaneously are obtained by modifying the objective function of models (14) and (16), or/and by adding constraints.

They modified the objective function so that the FCM algorithm worked on distances to the Voronoi cell of the cluster rather than using distances to the cluster prototypes.

Ahmed et al.[12] modified the objective function of FCM to allow the labeling of a pixel to be influenced by the labels in its immediate neighborhood.

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