1. Covington, Paul, Jay Adams, and Emre Sargin. "Deep neural networks for youtube recommendations." Proceedings of the 10th ACM Conference on Recommender Systems. ACM, 2016.
For online prediction，we adopt Approximate Nearest Neighbor(ANN) to directly recall top N mostly likely watch video. However, our ANN system currently only supports cosin sorting, not by inner product sorting, which leads to big effect difference.
As a result, we sliently modify user and video vectors by a SIMPLE-LSH conversion\[[4](#References)\], so that inner sorting is equivalent to cosin sorting after conversion.
Details as follows:
For video vector, $$\mathbf{v}\in \mathbb{R}^N$$, we have $$\left \|\mathbf{v} \right \|\leqslant m$$. The modified video vector $$\tilde{\mathbf{v}}\in \mathbb{R}^{N+1}$$,
For user vector, $$\mathbf{u}\in \mathbb{R}^N$$, The modified user vector $$\tilde{\mathbf{u}}\in \mathbb{R}^{N+1}$$,
$$\tilde{\mathbf{u}} = [\mathbf{u}_{norm}; 0]$$，in which $$\mathbf{u}_{norm}$$ is normalized $$\mathbf{u}$$，
When online predicting, For a $$\mathbf{u}$$, we need recall $$\mathbf{v} by inner product sorting. After conversion, $$\mathbf{u}\rightarrow \tilde{\mathbf{u}}, \mathbf{v}\rightarrow \tilde{\mathbf{v}}$$, the order of inner prodct sorting is unchanged. Since $$\left \|\tilde{\mathbf{u}} \right \|$$ and $$\left \|\tilde{\mathbf{v}} \right \|$$ are both equal to 1, $$cos(\tilde{\mathbf{u}} ,\tilde{\mathbf{v}}) = \tilde{\mathbf{u}}\cdot \tilde{\mathbf{v}}$$, which makes cosin-supported-only ANN system works. And in order to retain precision, we find that $\tilde{\mathbf{v}} = [\mathbf{v}; \sqrt{m^2 -\left \|\mathbf{\mathbf{v}} \right \|^2}]$$ is also equivalent.
## References
1. Covington, Paul, Jay Adams, and Emre Sargin. "Deep neural networks for youtube recommendations." Proceedings of the 10th ACM Conference on Recommender Systems. ACM, 2016.
