# Principal Coordinates Analysis

Principal coordinates analysis (PCO) is another ordination method, also known as Metric Multidimensional Scaling.

The PCO routine finds the eigenvalues and eigenvectors of a matrix containing the distances or similarities between all data points. The Euclidean distance gives results similar to PCA. An additional 24 distance measures are available - these are explained under “Similarity and distance measures”. The eigenvalue, giving a measure of the variance accounted for by the corresponding eigenvector (coordinate) is given for each coordinate. The percentages of variance accounted for by these components are also given.

The similarity/distance values are raised to the power of *c* (the "Transformation exponent") before eigenanalysis. The standard value is *c*=2. Higher values (4 or 6) may decrease the "horseshoe" effect (Podani & Miklos 2002).

The *scatter plot* allows you to see all your data points (rows) plotted in the coordinate system given by the PCO. The "Eigenvalue scaling" option scales each axis using the square root of the eigenvalue (recommended). The minimal spanning tree option is based on the selected similarity or distance index in the original space.

Missing data is supported by pairwise deletion (not for the Raup-Crick, Rho or user-defined indices).

#### References

Davis, J.C. 1986. Statistics and Data Analysis in Geology. John Wiley & Sons.

Podani, J. & I. Miklos. 2002. Resemblance coefficients and the horseshoe effect in principal coordinates analysis. *Ecology* 83:3331-3343.