Social Media Mining: An Introduction

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

254 Recommendation in Social Media

Table 9.2. An User-Item Matrix

Lion King Aladdin Mulan

John 3 0 3

Joe 5 4 0

Jill 1 2 4

Jorge 2 2 0

k-dimensional item spaceVkT. This way, we can compute the most similar

neighbors based on distances in thisk-dimensional space. The similarity in

thek-dimensional space can be computed using cosine similarity or Pearson

correlation. We demonstrate this via Example9.3.

Example 9.3. Consider the user-item matrix, in Table 9.2. Assuming this

matrix is X, then by computing the SVD of X=U VT,^1 we have

U=

⎡

⎢⎢

⎣

− 0. 4151 − 0. 4754 − 0 .7679 0. 1093

− 0 .7437 0.5278 0. 0169 − 0. 4099

− 0. 4110 − 0 .6626 0. 6207 − 0. 0820

− 0 .3251 0.2373 0.1572 0. 9018

⎤

⎥⎥

⎦ (9.27)

=

⎡

⎢⎢

⎣

8. 0265 0 0

04. 3886 0

002. 0777

000

⎤

⎥⎥

⎦ (9.28)

VT =

⎡

⎣

− 0. 7506 − 0. 5540 − 0. 3600

0 .2335 0. 2872 − 0. 9290

− 0 .6181 0.7814 0. 0863

⎤

⎦ (9.29)

Considering a rank 2 approximation (i.e., k= 2 ), we truncate all three

matrices:

Uk=

⎡

⎢⎢

⎣

− 0. 4151 − 0. 4754

− 0 .7437 0. 5278

− 0. 4110 − 0. 6626

− 0 .3251 0. 2373

⎤

⎥⎥

⎦ (9.30)

(^) k=

[

8. 0265 0

04. 3886

]

(9.31)

VkT =

[

− 0. 7506 − 0. 5540 − 0. 3600

0 .2335 0. 2872 − 0. 9290

]

. (9.32)