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I'm sorry that the PCO ver.1.0 has a mistake in its calculation process.
If you have ever downloaded and installed PCO ver.1.0 on you computer,
please replace it by the current version of PCO (i.e., PCO ver.2.0).
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PCO ver.2.0: MS-DOS program for principal coordinate analysis
A small MS-DOS program for conducting principal co-ordinate analysis proposed
by Gower (1966).
This program is written by C language based on Tanaka and Tarumi (1995).
pco.zip (47kb)
This file contains the following files:
- pco.exe ... Executable file of PCO
- pco.c, matrix.c ... source files (C language)
- infile.dat ... sample input file (tab delimited text format)
- outfile.csv ... sample output file (CSV format)
Extract all files contained in "pco.zip", and copy them into
a folder which locates anywhere you want.
An example of folder name）
c:\Apps\pco
- Open a MS-DOS command prompt window.
- type
cd [the folder (directory) name which you install pco files]
- type
pco [input file name] [output file name]
- That's all! Please enjoy PCO analysis!
A screen shot of the MS-DOS command prompt window)
Input file is a tab delimeted text format which has a data structure described
in the following.
You can input these data by MS-Excel, and save it as a tab delimeted text
format file.
-----------------------------
[the number of samples]
[similarity (s) between the 1st and 1st samples] [s between the 1st and 2nd samples] ... [s between the 1st and n-th samples][s between the 2nd and 1st samples] ... [s bewteen 2nd and nth samples]
[s between the n-th and 1st samples] ...
[s between n-th and n-th samples]
----------------------------
You can obtain a similarity matrix from your distance matrix in several
ways. For example, you can calculate similarity between the i-th and j-th
samples (the i x j th element of similarity matrix) as follows.
e_ij = -d_ij^2 / 2
e_ii = 0
where d_ij^2 means the squared distance between the i and j th samples
(the i x j th element of squared distance matrix) (Tanaka and Tarumi 1995,
P188).
If you can directly obtain the similarity matrix, please use it directly
in PCO analysis (for example, it is a case of the Nei's genetic similarity
matrix).
-------Caution-------
Please input a "Similarity" (not "Distance") matrix!
--------------------
A screen shot of data input work on Excel)
The output file is formated as a csv (camma separated value) file.
Its contents are as follows:
---------------------------------------
[SIMILARITY MATRIX]
,0.000000,-1.000000,-5.000000,-17.000000,-20.000000,-25.000000,-13.000000,-9.000000
,-1.000000,0.000000,-4.000000,-16.000000,-25.000000,-32.000000,-20.000000,-16.000000
,-5.000000,-4.000000,0.000000,-4.000000,-13.000000,-20.000000,-16.000000,-20.000000
,-17.000000,-16.000000,-4.000000,0.000000,-9.000000,-16.000000,-20.000000,-32.000000
,-20.000000,-25.000000,-13.000000,-9.000000,0.000000,-1.000000,-5.000000,-17.000000
,-25.000000,-32.000000,-20.000000,-16.000000,-1.000000,0.000000,-4.000000,-16.000000
,-13.000000,-20.000000,-16.000000,-20.000000,-5.000000,-4.000000,0.000000,-4.000000
,-9.000000,-16.000000,-20.000000,-32.000000,-17.000000,-16.000000,-4.000000,0.000000
[DOUBLE CENTERING MATRIX]
,10.000000,12.000000,4.000000,-4.000000,-10.000000,-12.000000,-4.000000,4.000000
,12.000000,16.000000,8.000000,0.000000,-12.000000,-16.000000,-8.000000,0.000000
,4.000000,8.000000,8.000000,8.000000,-4.000000,-8.000000,-8.000000,-8.000000
,-4.000000,0.000000,8.000000,16.000000,4.000000,0.000000,-8.000000,-16.000000
,-10.000000,-12.000000,-4.000000,4.000000,10.000000,12.000000,4.000000,-4.000000
,-12.000000,-16.000000,-8.000000,0.000000,12.000000,16.000000,8.000000,0.000000
,-4.000000,-8.000000,-8.000000,-8.000000,4.000000,8.000000,8.000000,8.000000
,4.000000,0.000000,-8.000000,-16.000000,-4.000000,0.000000,8.000000,16.000000
[EIGEN VALUE],PCO1,PCO2,PCO3,PCO4,PCO5,PCO6,PCO7,PCO8
,58.246211,41.753789,0.000000,0.000000,0.000000,-0.000000,-0.000000,-0.000000
[CONTRIBUTION],PCO1,PCO2,PCO3,PCO4,PCO5,PCO6,PCO7,PCO8
,0.582462,0.417538,0.000000,0.000000,0.000000,-0.000000,-0.000000,-0.000000
[CONTRIBUTION],PCO1,PCO2,PCO3,PCO4,PCO5,PCO6,PCO7,PCO8
,0.582462,0.417538,0.000000,0.000000,0.000000,-0.000000,-0.000000,-0.000000
[EIGEN VECTOR],PCO1,PCO2,PCO3,PCO4,PCO5,PCO6,PCO7,PCO8
,-0.374131,0.210324,-0.000000,0.000000,0.000000,0.000000,0.000000,0.903211
,-0.520188,0.075635,-0.023405,0.509192,0.000000,-0.057395,-0.637367,-0.233087
,-0.292113,-0.269379,-0.830017,-0.331105,0.000000,0.198909,-0.024201,-0.058272
,-0.064038,-0.614392,0.268143,-0.062099,0.707107,0.107478,-0.132401,0.116543
,0.374131,-0.210324,-0.320687,0.753554,0.000000,0.263075,0.185208,0.203951
,0.520188,-0.075635,-0.239004,-0.120162,-0.000000,-0.535427,-0.557773,0.233087
,0.292113,0.269379,0.082212,-0.202726,0.000000,0.760360,-0.461200,0.058272
,0.064038,0.614392,-0.268143,0.062099,0.707107,-0.107478,0.132401,-0.116543
[PCO SCORE],PCO1,PCO2,PCO3,PCO4,PCO5,PCO6,PCO7,PCO8
,-2.855339,1.359057,-0.000000,0.000000,0.000000,0.000000,0.000000,0.000000
,-3.970030,0.488733,-0.000000,0.000000,0.000000,0.000000,0.000000,0.000000
,-2.229382,-1.740649,-0.000000,-0.000000,0.000000,0.000000,0.000000,0.000000
,-0.488733,-3.970030,0.000000,-0.000000,0.000000,0.000000,0.000000,0.000000
,2.855339,-1.359057,-0.000000,0.000000,0.000000,0.000000,0.000000,0.000000
,3.970030,-0.488733,-0.000000,-0.000000,-0.000000,0.000000,0.000000,0.000000
,2.229382,1.740649,0.000000,-0.000000,0.000000,0.000000,0.000000,0.000000
,0.488733,3.970030,-0.000000,0.000000,0.000000,0.000000,0.000000,0.000000
------------------------------------------
[SIMILARITY MATRIX] is a similarity matrix inputted by a user.
[DOUBLE CENTERING MATRIX] is a double centering matrix A. When the i x
j th element of the similarity matrix is indicated as e_ij,
The i x j th element of the double centering matrix is calculated as
a_ij = e_ij - e_i. - e_.j + e_..
where e_ij is the i x j th element of the similarity matrix. e_i., e_.j,
and e_.. are the averages of elements of i th row, j th colum, and overall
of the similarity matrix, respectively.
[EIGEN VALUE] are the eigen values of matrix A
[CONTRIBUTION] and [CUMULATIVE CONTRIBUTION] are the contribuitons and
cumulative contribution of eigen vectors of matrix A, respectively.
[EIGEN VECTOR] are the eigen vector of matrix A
[PCO SCORE] are the score of the principal coordinate obtained from your
similarity matrix!
You can visualize the location of each sample on a principal co-ordinate
plane using this matrix. The i x j th element of this matrix corresponds
to the j th co-ordinate value of the i th sample. For example, the 1st,
2nd, and 3rd samples locate on (-2.85, 1.36), (-3.97, 0.49), (-2.23, -1.74)
on the 1st and 2nd principal co-ordinate plane, respectively. Cumulative
contribution reaches 1.0 at the 2nd co-ordinate, indicated all the information
contained in the similarity matrix is explained by the 1st and 2nd principal
co-ordinates.
Gower, J.C. (1966) Some distance properties of latent root and vector
methods used in multivariate analysis. Biometrika 53: 325-38.
Tanaka and Tarumi （1995） Handbook of statistical analysis for Windows (in
Japanese)．Kyoritu-shuppan, Tokyo．
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