Social Media Mining: An Introduction

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

264 Recommendation in Social Media

wherenis the number of predicted ratings,rˆijis the predicted rating, and

rijis the true rating. Normalized mean absolute error (NMAE) normalizes

MAE by dividing it by the range ratings can take,

NMAE=

MAE

rmax−rmin

, (9.72)

wherermaxis the maximum rating items can take andrminis the minimum.

In MAE, error linearly contributes to the MAE value. We can increase this

contribution by considering the summation of squared errors in the root

mean squared error (RMSE):

RMSE=

√√

√√^1

n

∑

i,j

(rˆij−rij)^2. (9.73)

Example 9.6.Consider the following table with both the predicted ratings

and true ratings of five items:

Item Predicted Rating True Rating

1 1 3

2 2 5

3 3 3

4 4 2

5 4 1

The MAE, NMAE, and RMSE values are

MAE=

| 1 − 3 |+| 2 − 5 |+| 3 − 3 |+| 4 − 2 |+| 4 − 1 |

5

= 2. (9.74)

NMAE=

MAE

5 − 1

= 0. 5. (9.75)

RMSE=

√

(1−3)^2 +(2−5)^2 +(3−3)^2 +(4−2)^2 +(4−1)^2

5

. (9.76)

= 2. 28.

9.4.2 Evaluating Relevancy of Recommendations

When evaluating recommendations based on relevancy, we ask users if

they find the recommended items relevant to their interests. Given a set

of recommendations to a user, the user describes each recommendation as