Social Media Mining: An Introduction

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CUUS2079-09 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:28

9.4 Evaluating Recommendations 263

Considering a neighborhood of size 2, the most similar users to Jill are

John and Jane:

N(Jill)={John,Jane}. (9.67)

We also know that friends of Jill are

F(Jill)={Joe,Jane,Jorge}. (9.68)

We can use Equation9.55to predict the missing rating by taking the

intersection of friends and neighbors:

rJill,Mulan=r ̄Jill+

sim(Jill,Jane)(rJane,Mulan−r ̄Jane)

sim(Jill,Jane)

= 2. 33 +(4− 2 .75)= 3. 58. (9.69)

Similarly, we can utilize Equation9.56to compute the missing rating.

Here, we take Jill’s two most similar neighbors: Jane and Jorge.

rJill,Mulan=r ̄Jill+

sim(Jill,Jane)(rJane,Mulan−r ̄Jane)

sim(Jill,Jane)+sim(Jill,Jorge)

+

sim(Jill,Jorge)(rJorge,Mulan−r ̄Jorge)

sim(Jill,Jane)+sim(Jill,Jorge)

= 2. 33 +

0 .72(4− 2 .75)+ 0 .54(1− 1 .75)

0. 72 + 0. 54

= 2 .72 (9.70)

9.4 Evaluating Recommendations

When a recommendation algorithm predicts ratings for items, one must

evaluate how accurate its recommendations are. One can evaluate the (1)

accuracy of predictions, (2) relevancy of recommendations, or (3) rankings

of recommendations.

9.4.1 Evaluating Accuracy of Predictions

When evaluating the accuracy of predictions, we measure how close pre-

dicted ratings are to the true ratings. Similar to the evaluation of supervised

learning, we often predict the ratings of some items with known ratings (i.e.,

true ratings) and compute how close the predictions are to the true ratings.

One of the simplest methods, mean absolute error (MAE), computes the

average absolute difference between the predicted ratings and true ratings,

MAE=

∑

ij|rˆij−rij|

n

, (9.71)