Case Amplification

#
높은 weight는 강조하고, 낮은 weight는 더 낮추도록 변환.



#
Case amplification refers to a transform applied to the weights used in the basic collaborative filtering prediction. The transform emphasizes high weights and punishes low weights:

\[ { w }_{ i,j }^{ ' }\quad =\quad w_{ i,j }\quad \cdot \quad { \left| { w }_{ i,j } \right| }^{ \rho -1 } \]

where ρ is the case amplification power, ρ ≥ 1, and a typical choice of ρ is 2.5. Case amplification reduces noise in the data. It tends to favor high weights as small values raised to a power become negligible. If the weight is high, for example,  \({w}_{i, j} \) = 0.9, then it remains high ( \({0.9}^{2.5}\) ≈ 0.8); if it is low, for example, \({w}_{i, j} \) = 0.1, then it will be negligible ( \({0.1}^{2.5}\) ≈ 0.003).

(Xiaoyuan Su and Taghi M. Khoshgoftaar, A survey of collaborative filtering techniques, Journal Advances in Artificial Intelligence archive Volume 2009)



#
의도에 따라서 적당이 이용하면 될것 같음.

 왼쪽부터 \(  y={x}^{1}, y={x}^{1.5}, y={x}^{2}, y={x}^{2.5}, y={x}^{3}     \)