TABLE 4.

Sample KCC Utility Functions

	$\mu ({\mathbf{m}}_{k,i})$	$U_{\mu }(\pi ,{\pi }_i)$	$f(\mathbf{b}\mathbf{l},{\mathbf{m}}_k)$
$U_c$	${\Vert {\mathbf{m}}_{k,i}\Vert }_2^2-{\Vert {\mathbf{P}}^{(i)}\Vert }_2^2$	${\sum }_{k=1}^K{p}_k+{\Vert {\mathbf{P}}_k^{(i)}\Vert }_2^2-{\Vert {\mathbf{P}}^{(i)}\Vert }_2^2$	${\sum }_{i=1}^r{w}_i{\Vert {\mathbf{b}}_{l,i}-{\mathbf{m}}_{k,i}\Vert }_2^2$
$U_H$	$(-H({\mathbf{m}}_{k,i}))-(-H({\mathbf{P}}^{(i)}))$	${\sum }_{k=1}^K{p}_k+(-H({\mathbf{P}}_k^{(i)}))-(-H({\mathbf{P}}^{(i)}))$	${\sum }_{i=1}^r{w}_{i}D({\mathbf{b}}_{l,i}\Vert {\mathbf{m}}_{k,i})$
$U_{\cos }$	${\Vert {\mathbf{m}}_{k,i}\Vert }_2-{\Vert {\mathbf{P}}^{(i)}\Vert }_2$	${\sum }_{k=1}^K{p}_k+{\Vert {\mathbf{P}}_k^{(i)}\Vert }_2-{\Vert {\mathbf{P}}^{(i)}\Vert }_2$	${\sum }_{i=1}^r{w}_i(1-\cos ({\mathbf{b}}_{l,i},{\mathbf{m}}_{k,i}))$
$U_{L_p}$	${\Vert {\mathbf{m}}_{k,i}\Vert }_p-{\Vert {\mathbf{P}}^{(i)}\Vert }_p$	${\sum }_{k=1}^K{p}_k+{\Vert {\mathbf{P}}_k^{(i)}\Vert }_p-{\Vert {\mathbf{P}}^{(i)}\Vert }_p$	${\sum }_{i=1}^r{w}_i(1-\frac{{\sum }_{j=1}^{K_i}{b}_{l,ij}{m_{k,i,j}}^{p-1}}{{\Vert {\mathbf{m}}_{k,i}\Vert }_p^{p-1}}$

Note: ${\mathbf{P}}_k^{(i)}={\mathbf{m}}_{k,i}=(p_{k1}^{(i)}∕p_{k+},\cdots ,p_{kj}^{(i)}∕p_{k+},\cdots ,p_{k{K}_i}^{(i)}∕p_{k+})$, ${\mathbf{P}}^{(i)}=(n_{+1}^{(i)}∕n,\cdots ,n_{+j}^{(i)}∕n,\cdots ,p_{+K_i}^{(i)}∕n)$.