Comment 8 for bug 448705

One of the problems seems to be apparmor, which disallows initializing the databases required for akonadi in the user dir!
A workaround is to turn off apparmor as root:
/etc/init.d/apparmor stop

then run (as user):

mysql_install_db --datadir=$HOME/.local/share/akonadi/db_data/

Also, you have to adjust /etc/apparmor.d/usr.sbin.mysqld-akonadi to include the following lines:

  /etc/mysql/my.cnf r,
  /etc/mysql/conf.d/ r,
  /etc/mysql/conf.d/** r,
  /sys/devices/system/cpu/ r,

and then restart apparmor as root:

/etc/init.d/apparmor start

Now, the mysql database for akonadi seems to be started properly... Now, I only have to figure out how to make nepomuk registered at the D-Bus...