Cosine Similarity vs. Cosine Distance Explained with PyTorch Examples | Applications in Deep Learning
1. What is Cosine Similarity? Cosine similarity is a metric used to measure the similarity in direction between two vectors, regardless of their magnitude. It is widely used in tasks like text similarity analysis, sentence embedding comparison, and image embedding evaluation. The key idea is that the metric focuses on the angle (or direction) rather than the vector length. Formula: cos_sim(A, B) = (A · B) / (||A|| * ||B||) Here, A and B are input vectors, · denotes the dot product, and ||A|| is the norm (magnitude) of vector A. The cosine similarity value ranges from -1 to 1. A value close to 1 means the vectors are pointing in a similar direction, while a value close to -1 indicates they are pointing in opposite directions. 2. What is Cosine Distance? Cosine distance is derived from cosine similarity and represents the dissimilarity between vectors. It is defined as follows: cos_dist(A, B) = 1 - cos_sim(A, B) The cosine distance ranges from 0 to 2. A...