# C3_W2 content-based filtering, dot product comment on slides

Hi,
In C3_W2, for content-based filtering, on the slides with TensorFlow code example I see following comment, were dot product is calculated, says it calculated the vector similarity, but I think it’s not what dot product does:

In the practical lab notebook, the comment is correctly fixed.
I just want to highlight this mismatch as the comment on slides makes a confusion.

And btw → Fantastic course, thank you!!

I have not worked that assignment, but I would interpret that as just a “riff” on the idea of cosine similarity. Note that another way to express the dot product between two vectors is:

v \cdot w = |v||w|cos(\theta)

Where \theta is the subtended angle between the two vectors. It is common (e.g. when dealing with word embeddings) to compute the cosine similarity as:

cos(\theta) = \displaystyle \frac {v \cdot w}{|v||w|}

So maybe the language there is a bit approximate, but you could say that the magnitude and sign of v \cdot w are in a sense a measure of the similarity of v and w.

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Wow, you are right. Especially that vu, vm are normalized, so it’s exactly same! Thank you!

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