Definitions for

**"Similarity"**A numerical estimate of the difference between two people, groups of people, or concepts. Often used in perceptual mapping. Similar to correlation, but varies only between 0 and 1. A similarity of 0 means the two units had completely different responses; a similarity of 1 means they are exactly the same.

The relationship between two objects that have exactly the same shape but not necessarily the same size.

gestalt principle of grouping, stating that people will tend to group similar items together.

Similarity in biology refers to the relatedness of nucleic acid and amino acid sequences and protein structures. Similarity can be expressed in percent identity referring to the percentage of building blocks in any two or more sequences found in the same string or pattern. Similarity is used to infer homology, a term in evolutionary biology that indicates a common ancestry between sequences or structures, i.e., to modern genes or proteins, albeit not identical but highly similar (~72%) are evolutionarily related and have diverged and accumulated changes independently from each other after a speciation event. Similarities around 25% identity or lower can no longer indicate an evolutionary relationship.

Sequence identity between two nucleotide sequences. For example, 85% similarity means that 85 nucleotide positions out of 100 are identical in the two nucleotide sequences. Sequence similarity does not necessarily indicate that two sequences have common ancestry.

The extent to which nucleotide or protein sequences are related. The extent of similarity between two sequences can be based on percent sequence identity and/or conservation. In BLAST similarity refers to a positive matrix score.

Two triangles are similar if they have equal angles in which case their corresponding sides, say, a1, b1, c1 and a2, b2, c2, are proportional with a coefficient r: a1/a2 = b1/b2 = c1/c2 = r. Since side length could be looked at as the distances between the vertices, going from one triangle to another modifies these distances by a factor of r. Distances between other corresponding points in the triangles also change by the factor of r. This can be generalized. A similarity is such a transformation of the plane under which distance between any pair of points changes by the same factor. Similarity transformations play a central role in the Fractal Geometry and even more so in the theory of Iteration Function Systems (IFS). Consecutive Peano curves each consist of four images of itself each half the size of the whole. Similarity transformations are easily defined in spaces of higher dimensions.

a measure of how closely two items correspond, often on a scale of zero to 1. Typically this reflects closeness of query to a document (for retrieval), or a document to another document (for clustering). Similarity can be computed using a similarity measure (e.g., the cosine correlation) or an an inverse function of distance.

The similarity between two objects is a measure of how closely they resemble each other. Dissimilarity is the inverse of this, and this is related to the concept of distance.

a composition of a homothety and an isometry

"Lexical relations of words with related meaning. For example, gluttonous is similar to greedy."

(Also called similitude.) See dynamic similarity.

The quality or state of being similar; likeness; resemblance; as, a similarity of features.