Adds points for new objects to a principal coordinates analysis.

### Option

`PRINT` = string tokens |
Printed output required (`coordinates` , `residuals` ); default `*` i.e. no printing |
---|

### Parameters

`NEWDISTANCES` = matrices |
Squared distances of the new objects from the original points |
---|---|

`LRV` = LRVs |
Latent roots and vectors from the `PCO` analysis |

`CENTROID` = diagonal matrices |
Centroid distances from the `PCO` analysis |

`COORDINATES` = matrices |
Saves the coordinates of the additional points in the space of the original points |

`RESIDUALS` = matrices or variates |
Saves the residuals of the new objects from that space |

### Description

The input to `ADDPOINTS`

is specified by the first three parameters. The `NEWDISTANCES`

parameter specifies an *s*×*n* matrix containing squared distances of the *s* new units from the *n* old units. The `LRV`

and `CENTROID`

parameters specify structures defining the configuration of old units; these have usually been produced by a `PCO`

statement.

The `PRINT`

option controls the printed output with settings:

`coordinates` |
to print the coordinates of the new points; |
---|---|

`residuals` |
to print the residual distances of the new units from the coordinates in the space of the old units. |

The other parameters can be used to save the results: the `COORDINATES`

parameter allows you to specify an *s*×*k* matrix to save the coordinates for the new units, and the residuals can be saved in an *s*×1 matrix using the `RESIDUALS`

parameter. The value *k* is determined by the dimensionality of the input coordinates from the preceding `PCO`

statement.

Option: `PRINT`

.

Parameters: `NEWDISTANCES`

, `LRV`

, `CENTROID`

, `COORDINATES`

, `RESIDUALS`

.

### See also

Commands for: Multivariate and cluster analysis.

### Example

" Genstat example PCO-1: Principal coordinates analysis. The data for this example (Nathanson J A 1971. An aplication of multivariate analysis in astronomy. Applied Statistics 20, 239-249) gives squared distances amongst ten types of galaxy: those of an elliptical shape, eight different kinds of spiral galaxy , and irregularly-shaped galaxies. The spiral types vary from those which are mailnly made up of a central core (coded as types SO and SBO) to those that are extremely tenuous (Sc and SBc). This example forms an ordination of the ten galaxy types. " " Declare the symmetric data matrix " SYMMETRIC [ROWS=!T(E,SO,SBO,Sa,SBa,Sb,SBb,Sc,SBc,I)] Galaxy READ Galaxy 0 1.87 0 2.24 0.91 0 4.03 2.05 1.51 0 4.09 1.74 1.59 0.68 0 5.38 3.41 3.15 1.86 1.27 0 7.03 3.85 3.24 2.25 1.89 2.02 0 6.02 4.85 4.11 3.00 2.13 1.71 1.45 0 6.88 5.70 5.12 3.72 3.01 2.97 1.75 1.13 0 4.12 3.77 3.86 3.93 3.27 3.77 3.52 2.79 3.29 0 : PRINT Galaxy CALCULATE Galaxy = -Galaxy/2 " Carry out the principal coordinates analysis, printing out the latent roots and trace, the principal coordinate scores, the distances of each unit from their overall centroid, and the matrix of inter-unit distances. " PCO [PRINT=roots,scores,centroid,distances] Galaxy " Carry out the analysis once again, printing information for the 8 smallest roots only. " PCO [PRINT=residuals,centroid; NROOTS=8; SMALLEST=yes] Galaxy " Create two different data matrices: Gname8 - which holds the data corresponding to the eight spiral galaxies. This is created from taking row 2 to column 2, to row 9, column 9 of the symmetric matrix Galaxy. Corresponding row labels are supplied. Gname2 - which holds the data corresponding to the elliptical and irregularly-shaped galaxies. This is created from taking the values in the Galaxy matrix from row 1, columns 2 to 9, and row 10, columns 2 to 9. Again, appropriate labels are supplied. " TEXT Gname8; !T(SO,SBO,Sa,SBa,Sb,SBb,Sc,SBc) & Gname2; !T(E,I) SYMMETRIC [ROWS=Gname8] G8 CALCULATE G8 = Galaxy$[!(2...9)] MATRIX [ROWS=Gname2; COLUMNS=Gname8] G2 CALCULATE G2 = Galaxy$[!(1,10); !(2...9)] " Transform the matrix back to the original scale. " CALCULATE G2 = -2*G2 PRINT G2; FIELDWIDTH=7 " Perform the analysis for the eight spiral galaxies, saving the latent vectors in the LRV structure L8, and the centroid distances in the diagonal matric C8. Their is no need to declare these structures in advance since the PCO will do this automatically. " PCO [PRINT=roots,scores] G8; LRV=L8; CENTROID=C8 " Now add the points for the elliptical and irregularly shaped galaxies to the principal coordinate analysis. " ADDPOINTS [PRINT=coordinates,residuals] G2; LRV=L8; CENTROID=C8