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The proposed method is flexible in adding extra constraints (e.g., passivity can be enforced on reduced order models) and modifying the objective function (e.g., frequency weights can be added to the minimization criterion).
To overcome this problem, an improved FCM with spatial constraints algorithm for image segmentation is presented in this paper, which is formulated by modifying the objective function and the membership function of the standard fuzzy c-means algorithm to enhance the noise immunity.
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.
These bounds can be useful in the optimization problem to demonstrate that a particular solution generated can solve the partitioning optimization problem by modifying the objective function of each path.
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In the proposed method, a novel non local adaptive spatial constraint term is introduced to modify the objective function of GIFP_FCM.
Tikhonov regularisation utilises additional a-priori information to modify the objective surface, and thus is not a true least squares approach.
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.
In particular, we modified the objective function to include the stream relevance weights and derived the necessary conditions to optimize all of the model parameters simultaneously.
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