Cosine similarity measures the angle between two vectors, which represents their similarity irrespective of their magnitude. This method is commonly used in natural language processing to find similarities between documents or words, making it useful for tasks like information retrieval.
Euclidean distance calculates the straight-line distance between two vectors. This method is useful for determining how far apart vectors are in vector space, helping in clustering tasks or measuring dissimilarity between text data.
Manhattan distance measures the distance between two points by summing the absolute differences of their coordinates. This method is often used in high-dimensional spaces and works well for finding nearest neighbors or classifying data points.