Could anybody explain how can we ensure the output v_u[0] and v_m[0] , v_u[1] and v_m[1] … is describe same feature, just like mentioned in the last lecture, v_u[0] describe user like romance is 4.9 and v_m[1] describe movie romance feature is 4.5

Hi @Peixin_Guo ,

The example given in the video was just for illustrative purposes to describe how a neural network can produce vectors v_{u} and v_{m}.

It may not be possible to interpret what each individual number in these vectors represents, you can be confident that they represent the preferences of the user e.g v_{u} and features of movie e.g v_{m} , computed from the features of the user_{j} and the movie_{i} . By taking the dot product of these vectors, we can predict how a user_{j} will rate a movie_{i}. Furthermore, the dot product of the vectors represents how similar the preferences of a user_{j} and the features of a movie_{i} are. When the dot product is higher, it suggests that the user_{j} preferences match more closely with the features of the movie_{i} . As a result, the user_{j} is more likely to enjoy the movie_{i} and give it a higher rating.

Regards,

Mujassim

Thank you for your answers,

but I still don’t know if v_u[0] and v_m[-1] describe the same feature, they should have multiplied, but now because of the dot production, they can’t match with each other and multiply correctly, in instead of v_u[0] match and dot multiply v_m[0] ( maybe they just describe totally different thing, v_u[0] is describe romance, v_m[0] is describe action ), v_u[1] match and dot multiply v_m[1] incorrectly. This condition is possible, right? Although we can’t explain the output of the neuron network, but it is possible that v_u[0] and v_m[-1] describe the same feature indeed, but because of the Mismatched position and the priciple of dot product, it didn’t be got very good use of.

If, for instance, you consider that v_{u}[0] captures how much do the user_{j} likes romance movies and v_{m}[0] captures how much is this an action movie, and let’s say v_{u}[0] and v_{m}[-1] describe the same feature, such as about romance. However, due to the way dot product works, instead of multiplying romance with romance (v_{u}[0] * v_{m}[-1]), it will get multiplied by romance with action (v_{u}[0] * v_{m}[0]). This might result in a smaller dot product, indicating that user_{j} is less likely to enjoy movie_{i} due to inappropriate choices of these vectors. Alternatively, it might be another case where multiplying romance with action may indicate strong representations. I suggest that you do not go into detail about what each number describes, as it is just for illustrative purposes. Just consider that if you are able to come up with appropriate numbers for these vectors, then the resulting dot product will be a good prediction.