Preheat oven to 180C/160C fan and grease and line a 9 inch square cake tin.
Whisk together the sugar, oil, yogurt and eggs in a large mixing bowl.
Sift together the flour, bicarbonate of soda, spices and salt.
Stir the dry ingredients into the wet, and fold in the grated swede.
Spoon into the prepared baking tin and bake in the centre of the oven for 25-30 minutes. A skewer inserted in the centre will come out clean when it's ready. Transfer to a wire rack to cool completely.
To prepare the frosting gently combine the cream cheese and icing sugar together. Ice the cake when it is completely cool and decorate with chopped crystalised ginger or chopped nuts, if desired.