Euclidean Distance Limitation

One of the Euclidean distance limitations I will try to explain. Let’s consider 3 data points v1, v2, and v3. These points are shown in the attached picture.

When Euclidean distance is calculated between vectors v1, v2, and v2, v3, the distances are the same. In this case, we don’t know which vectors are nearby. So, in this case, we can use cosine similarity. Cosine similarity calculations are shown in the picture. As per calculation, we can say that the cosine of v1 and v2 is close to 1, so the angle (v1&v2) is smaller compared to the angle between v2 and v3. We can say v1 and v2 vectors are nearby.

Thank You for reading.