Hi Angelo D'Ambrosio, first and foremost, I’m sorry for the late late response. I found out about your question while replying to another one. Regarding your question, both of them are geometric distances, but the main difference is that the Euclidean Distance is just a straight-line distance between two points in a plane. Therefore the result is founded just in the subtraction of each corresponding pair of elements in between vectors. Meanwhile, the cosine similarity finds the angle between those vectors by operating with the whole vectors and their magnitudes. However, two vectors ‘pointing’ in the same direction, but one ‘shorter’ than the other, will have the same magnitude and in terms of similarity, they might be completely different things. That’s why when finding the adjusted cosine similarity, we subtract to both vectors the mean of their element to have that into account. Hope this answer your question, and sorry again for the delay. Cheers.