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I have a morphometric dataset of 430 fish, with 27 various "shape" measurements, for example: total length, head length, fin distances, etc.

My goal is multi-fold: (BIG GOAL: cluster by "shape")

Hypotheses:

H0a: No groups can be found in the dataset

H0b: No groups can be imposed on the dataset

H1: Pre-specified well defined groups do “not” a priori exist; though the characteristics of the data can be used to assign entities into artificial groups by morphometric "shape" characteristics (independent of and/or secondary to size) (i.e. Cluster analysis)

H2: Pre-specified well defined groups “do” exist; pre-specified a prioi “expert knowledge” (validated stock origins based on DNA chemistry) well-defined groups exist. Dependent relationships between one set of discriminating variables (morpho-variables, date) and a single grouping variable (DNA stock origin) can be made to define the relationship between dependent and independent variables.

Where I need your help. I would like to run non-hierarchical cluster analysis. If I were to run the analysis on the morphometric variables I have, the clustering would likely be driven purely by size. When I say "size" I mean length.

In multivariate morphometrics, if PCA is run and all the variables load eveningly in the same direction on PC1, typically that PC1 component can be thought of as a "size or length" component and that component is typically "cleaved" from the analysis (not my language, but lit). And the rest of the analysis can be run on the other PC scores.

I'm not totally familar with what "cleave" means. But I guess my overall questions comes down to:

Can I run a PCA on the dataset, get PC1-PCn indidividual unit PC scores, and run cluster analysis on those new PC scores >PC1, i.e. PC2, PC3,... and identify "shape" groups that are relatively independent of size.

I do know I have a number of assumptions I have to meet, or stay within reason with, for distribution, outliers, etc..

If you need more clarity on my objectives, I can provide more information.

Thank you!!

Image below is example of fish with morphometric measurements: enter image description here

Tyler Gagne
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  • You might be interested in reading this: [Examples of PCA where PCs with low variance are “useful”](http://stats.stackexchange.com/a/101490/7290). – gung - Reinstate Monica Jul 12 '16 at 21:05
  • Are these distances two-dimensional, as suggested by the image, or three-dimensional? – whuber Jul 12 '16 at 21:07
  • An approach that I think might be useful would be to standardize measurements of each fish individually. Rather than recording the actual dimensions, you calculate ratios of different lengths for each fish in isolation. Clustering this resultant dataset can then help you group together fishes that have similar ratios, ié shapes. – Arun Jose Jul 13 '16 at 09:13
  • @gung excellent link! Do you have the code you used to produce those two scatterplots from the crab data? – Tyler Gagne Jul 13 '16 at 15:08

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