Solution 6 Computational Intelligence Lab 2016

(see Master Solution from the lecture assistants (VPN needed))

Problem 1

1)

a)

${\frac {\partial }{\partial x_{i}}}H=-2\sum _{j}\left(m_{ij}-\langle x_{i},y_{j}\rangle \right)\cdot y_{j}$

${\frac {\partial }{\partial y_{j}}}H=-2\sum _{i}\left(m_{ij}-\langle x_{i},y_{j}\rangle \right)\cdot x_{i}$

b)

${\frac {\partial H_{ij}}{\partial x_{i}}}=-2\left(m_{ij}-\langle x_{i},y_{j}\rangle \right)\cdot y_{j}$

${\frac {\partial H_{ij}}{\partial y_{j}}}=-2\left(m_{ij}-\langle x_{i},y_{j}\rangle \right)\cdot x_{i}$