# jackmaney/ucc

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#Universal Correlation Coefficient

At the 2011 Joint Statistical Meetings, Nuo Xu of the University of Alabama at Birmingham presented a paper--coauthored with Xuan Huang also of UAB and Samuel Huang at the University of Cincinatti--in which a Universal Correlation Coefficient is defined and developed. This coefficient measures the degree of dependency (but not the form of dependency) for two discrete random variables.

This R package implements the algorithm described in the paper presented at the above talk.

##Example

``````library(ucc)
``````

We first grab 1,000 random `x` values between 0 and 1:

``````set.seed(1234) #for reproducability
x <- runif(1000)
``````

We then make these points close to fitting on a curve (with a bit of randomly-generated noise):

``````dat <- data.frame(x=x,y=exp(x)*cos(2*pi*x) + rnorm(1000,-0.1,0.1))
``````

If you plot these data points, you'll see that there's an obvious (contrived) relationship, albeit not a linear relationship. Predictably, the Pearson Correlation coefficient (ie the covariance divided by the product of standard deviations) does not reveal a linear relationship

``````cor(dat\$x,dat\$y)  # equals 0.2666508
``````

The Universal Correlation Coefficient briefly described above measures the degree of dependency independent of the form of dependency.

``````ucc(dat)\$ucc    # equals 0.9057609
``````

Check out the R documentation for more details about the algorithm, or a description on my homepage for a more informal (albeit long-winded) version.

##Install

• Clone the repository:

``````  git clone https://github.com/jackmaney/ucc.git ~/ucc
``````

(of course, feel free to use a different directory than `~/ucc`, if you'd like)

• In the parent directory of the repository (ie `~` if you cloned to `~/ucc`), run the following

``````  R CMD build ucc
``````

This will generate a `tar.gz` file.

• Run the following:

``````  R CMD INSTALL ucc_<x.y.z>.tar.gz
``````

where `<x.y.z>` is the latest version number of the `ucc` library.

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