Mclust: Order of input parameters affecting clustering results

Question

I am using mclust to see various clusters in my data set using various numbers of input (X,Y,Z,R, and S in the script below):

e.g.

elements<-cbind(X,Y,Z,R,S)
dataclust<-Mclust(elements)

I just find out that the order of the input parameters matters and affect the results; in other words elements <- cbind(X,Y,Z,R,S) gives a different clusters than say elements-<cbind(Y,Z,X,R,S). My understanding is that all the input parameters have the same weight and importance in the clustering analysis. am I wrong or is it a bug?

I have seen that in R 2.15.3 and 2 other R versions.

Any comment on or explanation of the above is appreciated.

Answer 1

Unfortunately, I am unable to comment or edit my previous comment, so I'm posting an answer. @m-dz set me on a path that I think has revealed a possible answer. Specifically:

> library(mclust)
    __  ___________    __  _____________
   /  |/  / ____/ /   / / / / ___/_  __/
  / /|_/ / /   / /   / / / /\__ \ / /   
 / /  / / /___/ /___/ /_/ /___/ // /    
/_/  /_/\____/_____/\____//____//_/    version 5.2.2
Type 'citation("mclust")' for citing this R package in publications.

> testDataA <- read.table("http://fimi.ua.ac.be/data/chess.dat")

> summary(Mclust(subset(testDataA, select = c(V1, V3, V5, V7, V9, V11))))
----------------------------------------------------
Gaussian finite mixture model fitted by EM algorithm 
----------------------------------------------------

Mclust EII (spherical, equal volume) model with 9 components:

 log.likelihood    n df      BIC       ICL
      -3597.466 3196 63 -7703.32 -7735.137

Clustering table:
  1   2   3   4   5   6   7   8   9 
774 150 752 486 227 224 238 178 167 

> summary(Mclust(subset(testDataA, select = c(V11, V9, V1, V3, V5, V7))))
----------------------------------------------------
Gaussian finite mixture model fitted by EM algorithm 
----------------------------------------------------

Mclust EII (spherical, equal volume) model with 9 components:

 log.likelihood    n df      BIC       ICL
      -3597.466 3196 63 -7703.32 -7735.137

Clustering table:
  1   2   3   4   5   6   7   8   9 
774 150 752 486 227 224 238 178 167 

> sessionInfo()
R version 3.3.2 (2016-10-31)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: macOS Sierra 10.12.5

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] mclust_5.2.2

loaded via a namespace (and not attached):
[1] tools_3.3.2

As you can see, this produces two solutions that match @m-dz's! However, what I was previously doing was loading the psych package. I'm seeing now this is masking sim from mclust. I'm guessing this then causes the incorrect solutions:

> library(psych)

Attaching package: ‘psych’

The following object is masked from ‘package:mclust’:

    sim

> testDataB <- read.file(f = "http://fimi.ua.ac.be/data/chess.dat")
Data from the .data file http://fimi.ua.ac.be/data/chess.dat has been loaded.

> summary(Mclust(subset(testDataB, select = c(X1, X3, X5, X7, X9, X11))))
----------------------------------------------------
Gaussian finite mixture model fitted by EM algorithm 
----------------------------------------------------

Mclust EEV (ellipsoidal, equal volume and shape) model with 2 components:

 log.likelihood    n df      BIC      ICL
       3547.068 3195 49 6698.738 6692.126

Clustering table:
   1    2 
2759  436 

> summary(Mclust(subset(testDataB, select = c(X11, X9, X1, X3, X5, X7))))
----------------------------------------------------
Gaussian finite mixture model fitted by EM algorithm 
----------------------------------------------------

Mclust EEV (ellipsoidal, equal volume and shape) model with 6 components:

 log.likelihood    n  df      BIC      ICL
       18473.94 3195 137 35842.37 35834.51

Clustering table:
  1   2   3   4   5   6 
431 932 210 881 524 217 

> sessionInfo()
R version 3.3.2 (2016-10-31)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: macOS Sierra 10.12.5

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] psych_1.6.9  mclust_5.2.2

loaded via a namespace (and not attached):
[1] parallel_3.3.2 tools_3.3.2    foreign_0.8-67 mnormt_1.5-5