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Similarity (geometry), the property of sharing the same shape; Matrix similarity, a relation between matrices; Similarity measure, a function that quantifies the similarity of two objects Cosine similarity, which uses the angle between vectors; String metric, also called string similarity; Semantic similarity, in computational linguistics
A similarity (also called a similarity transformation or similitude) of a Euclidean space is a bijection f from the space onto itself that multiplies all distances by the same positive real number r, so that for any two points x and y we have ((), ()) = (,), where d(x,y) is the Euclidean distance from x to y. [16]
Similarity is an equivalence relation on the space of square matrices. Because matrices are similar if and only if they represent the same linear operator with respect to (possibly) different bases, similar matrices share all properties of their shared underlying operator: Rank; Characteristic polynomial, and attributes that can be derived from it:
Similarity measures play a crucial role in many clustering techniques, as they are used to determine how closely related two data points are and whether they should be grouped together in the same cluster. A similarity measure can take many different forms depending on the type of data being clustered and the specific problem being solved.
3. Often used for denoting other types of similarity, for example, matrix similarity or similarity of geometric shapes. 4. Standard notation for an equivalence relation. 5. In probability and statistics, may specify the probability distribution of a random variable.
However, in the Philosophical Investigations the separate word Ähnlichkeit has been translated as 'similarity' (§§11,130,185,444) and on two occasions (§§9,90) it is given as 'like'. The German family-word is common, and it is found in Grimm's dictionary ; a rare occurrence of 'family likeness' has been noted in a lecture by J. F. Moulton ...
Semantic similarity is a metric defined over a set of documents or terms, where the idea of distance between items is based on the likeness of their meaning or semantic content [citation needed] as opposed to lexicographical similarity. These are mathematical tools used to estimate the strength of the semantic relationship between units of ...
Homophily (from Ancient Greek ὁμός (homós) 'same, common' and φιλία (philía) 'friendship, love') is a concept in sociology describing the tendency of individuals to associate and bond with similar others, as in the proverb " birds of a feather flock together ". [1]