Similarity measure
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.
Manhattan distance is commonly used in GPS applications, as it can be used to find the shortest route between two addresses.
For example, edit distance is frequently used for natural language processing applications and features, such as spell-checking.
Jaro distance is commonly used in record linkage to compare first and last names to other sources.
Both provide a quantification of similarity for two probability distributions on the same domain, and they are mathematically closely linked.
The Bhattacharyya distance does not fulfill the triangle inequality, meaning it does not form a metric.
The Hellinger distance does form a metric on the space of probability distributions.
It is commonly used in recommendation systems and social media analysis[citation needed].
The Sørensen–Dice coefficient is commonly used in biology applications, measuring the similarity between two sets of genes or species[citation needed].
It involves partitioning a set of data points into groups or clusters based on their similarities.
One of the fundamental aspects of clustering is how to measure similarity between data points.
A similarity measure can take many different forms depending on the type of data being clustered and the specific problem being solved.
Another commonly used similarity measure is the Jaccard index or Jaccard similarity, which is used in clustering techniques that work with binary data such as presence/absence data [3] or Boolean data; The Jaccard similarity is particularly useful for clustering techniques that work with text data, where it can be used to identify clusters of similar documents based on their shared features or keywords.
Manhattan distance, also known as Taxicab geometry, is a commonly used similarity measure in clustering techniques that work with continuous data.
When dealing with mixed-type data, including nominal, ordinal, and numerical attributes per object, Gower's distance (or similarity) is a common choice as it can handle different types of variables implicitly.
In spectral clustering, a similarity, or affinity, measure is used to transform data to overcome difficulties related to lack of convexity in the shape of the data distribution.
[6] The choice of similarity measure depends on the type of data being clustered and the specific problem being solved.
If working with binary data such as the presence of a genomic loci in a nuclear profile, the Jaccard index may be more appropriate.
It observes a user's perception and liking of multiple items.
Recommender systems are observed in multiple online entertainment platforms, in social media and streaming websites.
[citation needed] Similarity matrices are used in sequence alignment.
Nucleotide similarity matrices are used to align nucleic acid sequences.
Because there are only four nucleotides commonly found in DNA (Adenine (A), Cytosine (C), Guanine (G) and Thymine (T)), nucleotide similarity matrices are much simpler than protein similarity matrices.
A later refinement was to determine amino acid similarities based on how many base changes were required to change a codon to code for that amino acid.
This model is better, but it doesn't take into account the selective pressure of amino acid changes.
PAM matrices are labelled based on how many nucleotide changes have occurred, per 100 amino acids.
At long evolutionary distances, for example PAM250 or 20% identity, it has been shown that the BLOSUM matrices are much more effective.
The BLOSUM series were generated by comparing a number of divergent sequences.
The BLOSUM series are labeled based on how much entropy remains unmutated between all sequences, so a lower BLOSUM number corresponds to a higher PAM number.
