## Cosine Similarity Calculator

This tool computes the cosine similarity between two data sets and determines whether these are uncorrelated, orthogonal, or both.
Instructions

- Please enter two data sets of identical size and select how these are delimited.
- Check centered mode if you wish to center the sets by subtracting their means.
- In general, mean-centering data sets can change their cosine similarities.

Who can use it?

- Researchers, teachers, students, or anyone working with data sets.
- Users with a basic knowledge of cosine similarity measures.

Suggested Exercises

- What is the difference, if any, between orthogonal and uncorrelated sets?
- Does a cosine similarity of zero mean that sets are uncorrelated? Explain.
- Are the following orthogonal, uncorrelated, or both? Why?

Set A = [1,-5,3,-1]

Set B = [5,1,1,3]
- Pearson's Correlation Coefficient, r, is the cosine similarity between a pair of mean-centered variables. Because cosines are not additive, Pearson's r cannot be arithmetically averaged. Calculate Pearson's r from two data sets.

Recommended Readings

- Garcia, E. (2015). A Cosine Similarity Tutorial.
- Rodgers, J. L., Nicewander, W. A., Toothaker, L. (1984). Linearly Independent, Orthogonal, and Uncorrelated Variables. The American Statistician, Vol. 38, No. 2. Pp 133-134.