Medoid
Encyclopedia
Medoids are representative objects of a data set
or a cluster with a data set whose average dissimilarity to all the objects in the cluster is minimal. Medoids are similar in concept to means
or centroids, but medoids are always members of the data set. Medoids are most commonly used on data when a mean or centroid cannot be defined such as 3-D trajectories or in the gene expression
context. The term is used in computer science
in data clustering
algorithms.
A common application of the medoid is the k-medoids
clustering algorithm, which is similar to the k-means algorithm but works when a mean or centroid is not definable. This algorithm basically works as follows. First, a set of medoids is chosen at random. Second, the distances to the other points are computed. Third, data are clustered according to the medoid they are most similar to. Fourth, the medoid set is optimized via an iterative process.
Note that a medoid is not equivalent to a median
or a geometric median
. A median
is only defined on 1-dimensional data, and it only minimizes dissimilarity to other points for a specific distance metric (Manhattan norm). A geometric median
is not necessarily a point from within the original dataset.
Data set
A data set is a collection of data, usually presented in tabular form. Each column represents a particular variable. Each row corresponds to a given member of the data set in question. Its values for each of the variables, such as height and weight of an object or values of random numbers. Each...
or a cluster with a data set whose average dissimilarity to all the objects in the cluster is minimal. Medoids are similar in concept to means
Means
Means was a Christian Post-hardcore/Melodic hardcore band from Regina, Saskatchewan. The band was formed in 2001 under the name of Means 2 An End as a 3-piece by main-songwriter/lyricist Matt Goud. They were originally from the small city of Dauphin, Manitoba. In 2003, they relocated to Regina, SK...
or centroids, but medoids are always members of the data set. Medoids are most commonly used on data when a mean or centroid cannot be defined such as 3-D trajectories or in the gene expression
Gene expression
Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product. These products are often proteins, but in non-protein coding genes such as ribosomal RNA , transfer RNA or small nuclear RNA genes, the product is a functional RNA...
context. The term is used in computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
in data clustering
Data clustering
Cluster analysis or clustering is the task of assigning a set of objects into groups so that the objects in the same cluster are more similar to each other than to those in other clusters....
algorithms.
A common application of the medoid is the k-medoids
K-medoids
The -medoids algorithm is a clustering algorithm related to the -means algorithm and the medoidshift algorithm. Both the -means and -medoids algorithms are partitional and both attempt to minimize squared error, the distance between points labeled to be in a cluster and a point designated as the...
clustering algorithm, which is similar to the k-means algorithm but works when a mean or centroid is not definable. This algorithm basically works as follows. First, a set of medoids is chosen at random. Second, the distances to the other points are computed. Third, data are clustered according to the medoid they are most similar to. Fourth, the medoid set is optimized via an iterative process.
Note that a medoid is not equivalent to a median
Median
In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...
or a geometric median
Geometric median
The geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher...
. A median
Median
In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...
is only defined on 1-dimensional data, and it only minimizes dissimilarity to other points for a specific distance metric (Manhattan norm). A geometric median
Geometric median
The geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher...
is not necessarily a point from within the original dataset.