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Concept
Similarity measure
Summary
In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Though, in more broad terms, a similarity function may also satisfy metric axioms.
Cosine similarity is a commonly used similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions.
Different types of similarity measures exist for various types of objects, depending on the objects being compared. For each type of object there are various similarity measurement formulas.
Similarity between two data points
There are many various options available when it comes to finding similarity between two data points, some of which are a combination of other similarity methods. Some of the methods for similarity measures between two data points include Euclidean distance, Manhattan distance, Minkowski distance, and Chebyshev distance. The Euclidean distance formula is used to find the distance between two points on a plane, which is visualized in the image below. Manhattan distance is commonly used in GPS applications, as it can be used to find the shortest route between two addresses. When you generalize the Euclidean distance formula and Manhattan distance formula you are left with the Minkowski distance formula, which can be used in a wide variety of applications.
Euclidean distance
Manhattan distance
Minkowski distance
Chebyshev distance
Similarity between strings
For comparing strings, there are various measures of string similarity that can be used. Some of these methods include edit distance, Levenshtein distance, Hamming distance, and Jaro distance.
Official source
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