Slope One

Slope One takes the average ratings between two items, and adds another Users ratings to it
This is done for each pair of items
For multiple users, the individual averages are summed with a weight based on the number of
For users with several ratings, the predictions are combined using a weighted average

Example

Customer	Item A	Item B	Item C
John	5	3	2
Mark	3	4	Didn’t rate it
Lucy	Didn’t rate it	2	5

I.e for Item A and B: $a v g_{A B} = \frac{( 5 - 3 ) + ( 3 - 4 )}{2} = 0.5$ $R (A)_{A B} = a vg + R (B) = 0.5 + 2 = 2.5$

I.e for Item A and C: $a v g_{A B} = \frac{5 - 2}{1} = 3$ $R (A)_{A C} = a vg + R (B) = 3 + 5 = 8$

I.e Rating for Item A. With $U_{A B}$ being the number of users who rated both A and B, and $U_{A C}$ the number of users who rated both A and C.

R (A) = \frac{U _{A B} * R ( A ) _{A B} + U _{A C} * R ( A ) _{A C}}{U _{A B} + U _{A C}} = \frac{2 * 2.5 + 1 * 8}{2 + 1} = \frac{13}{3} = 4.33