DISTANCE CORRELATION Meaning and
Definition
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Distance correlation is a statistical measure that quantifies the association or relationship between two variables in a dataset, independent of any linear or nonlinear dependencies. It aims to capture both linear and nonlinear relationships that traditional correlation measures, such as Pearson's correlation coefficient, fail to detect.
In essence, distance correlation assesses how similar the paired distances between the observations of two variables are compared to what would be expected under independence. It measures the degree to which the relationship between the variables can be described by a monotonic or nonlinear function.
The calculation of distance correlation involves three main steps. Firstly, the pairwise Euclidean distances between observations of each variable are computed. Next, matrices are created from these distances, and the product of these matrices is obtained. Finally, a normalization process is applied to obtain the distance correlation coefficient.
Distance correlation ranges from 0 to 1, where a value of 0 implies no relationship, and a value of 1 indicates a perfect relationship. It is relatively unaffected by outliers, resistant to changes in scale, and can detect dependencies that linear correlation measures may overlook.
Distance correlation has applications in various fields, including finance, genetics, ecology, and computer science. It provides a valuable tool for exploring and identifying complex relationships between variables, especially when traditional correlation measures prove inadequate.
Etymology of DISTANCE CORRELATION
The term "distance correlation" is formed by combining the words "distance" and "correlation". The etymology of these individual words is as follows:
- Distance: The word "distance" originated from the Latin word "distantia", which means "a standing apart". It entered English in the 14th century and refers to the measure of space between two points or the extent of separation.
- Correlation: The word "correlation" comes from the Latin word "correlatus", which means "brought together". It entered English in the late 16th century and refers to a statistical measure that represents the relationship or association between two variables.
Therefore, the term "distance correlation" is a combination of these two words to create a statistical measure that quantifies the association between points based on their spatial separation or distance.
