Gamification of Workplace Activities - Smart Information Systems: Computational Intelligence for Real-Life Applications - page 260

Fig. 9.7 Matrix factorization. Approximate the user-design matrix S by low-rank matrices X and Y

Fig. 9.8 A simplified illustration of the latent factor space generated by matrix factorization. The
latent factors refer to the preferences indicated by the x -and y -axis. The six users and seven design
elements of Table 9.8 are embedded into the factor space. According to Bartle's player typology
[ 2 ], users fall into one of the four categories achiever, explorer, socializer ,and killer . Similarly, the
features of the design elements refer to characteristics of the user categories

in order to complete matrix S .
To learn the embeddings into the factor space

k , we need to solve the following

R

basic problem:

s ug −

x u y g 2

( P ) : min

x ∗ ,

,

y

∗

) ∈ P ( u , g

where P is the set of all pairs ( u , g ) for which s ug is known.