In the K-nearest neighbor (KNN) algorithm, distance metrics are used to determine the similarity or dissimilarity between data points. The most commonly used distance metrics include:
Euclidean Distance: This is the straight-line distance between two points in Euclidean space. For example, in a 2D space, the Euclidean distance between points A(1,2) and B(4,6) is calculated as the square root of [(4-1)^2 + (6-2)^2].
Manhattan Distance: Also known as city block distance, it is the sum of the absolute differences of their Cartesian coordinates. For instance, the Manhattan distance between the same points A(1,2) and B(4,6) would be |4-1| + |6-2| = 3 + 4 = 7.
Minkowski Distance: This is a generalization of both Euclidean and Manhattan distances. It is defined as the pth root of the sum of the absolute differences raised to the power p. When p=1, it becomes Manhattan distance, and when p=2, it becomes Euclidean distance.
Cosine Similarity: Although not a distance metric in the strict sense, cosine similarity measures the cosine of the angle between two vectors in a multi-dimensional space. It is often used in text mining and information retrieval.
Hamming Distance: This metric is used for categorical or binary data and is defined as the number of positions at which the corresponding symbols are different.
For applications involving large datasets or real-time processing, cloud-based solutions like Tencent Cloud can provide the necessary computational resources to handle the KNN algorithm efficiently.