Entropy Regularizer

Definition

$$h(S,\mathbf{X})=\frac{1}{2}|S|\log (2\pi e)+\frac{1}{2}\log \det (\mathbf{X}(S{)}^T\mathbf{X}(S)+{\sigma }^2\mathbf{I})$$

• $\mathbf{X}(S)$ 는 집합 $S$ 에 포함된 item 들의 feature vector 로만 이루어진 matrix 를 의미: $\mathbf{X}(S)\in {\mathbb{R}}^{d\times |S|}$

This definition of entropy regularizer is derived as the differential entropy of ratings based on the Probabilistic Matrix Factorization (PMF) model.

특징

• The value of entropy regularizer $h(S,\mathbf{X})$ is maximized if the feature vectors of movies in $S$ are orthogonal (most dissimilar).
• And it is minimized when the feature vectors are linearly dependent (most similar).

References

• Contextual Combinatorial Bandit and its Application on Diversified Online Recommendation

Related

References