-------- Original Message --------
Subject: Re: PCA with VERY large number of landmarks?
Date: Tue, 4 Oct 2011 15:44:17 -0400
From: Dean Adams <[email protected]>
To: [email protected]
Adam,
The short answer is 'yes', but perhaps with some computational
challenges. PCA is a desriptive statistical approach, so many of the
issues related to Rao's curse of dimensionality are less applicable (in
terms of hypothesis testing based on sparse, high-dimensional data).
However, the issue you will face is one of computation time. The
standard implementation of PCA involves an eigen-analysis of the
covariance matrix. Your covariance matrix will be 15,000 X 15,000 cells,
which will take a very long time to decompose. In fact, depending on the
computational power available, things may simply hang on this step
entirely.
An alternative means of getting to the same place would be to use
Principal Coordinates Analysis. In PCoA, one obtains the matrix of
pairwise distances between objects. This matrix is then double-centered,
and the eigen-decomposition is performed on this matrix. For the data
type you described, PCoA will obtain results identical to PCA on the
same data (see Gower 1966 for relationship between distance matrices and
covariance matrices in relation to PCA and PCoA).
Hope this helps.
Dean
--
Dr. Dean C. Adams
Associate Professor
Department of Ecology, Evolution, and Organismal Biology
Department of Statistics
Iowa State University
Ames, Iowa
50011
www.public.iastate.edu/~dcadams/
phone: 515-294-3834
On 10/4/2011 2:27 PM, morphmet wrote:
-------- Original Message --------
Subject: PCA with VERY large number of landmarks?
Date: Mon, 3 Oct 2011 21:48:03 -0400
From: Adam Douglas Yock <[email protected]>
To: [email protected]
Hello,
I am new to the field of morphometrics and have a (potentially very
ignorant) question.
I have images that contain a deformable body and a rigid body. The
images are rigidly registered to align the rigid bodies. The
deformable bodies are described by ~5,000 points which are matched
across each image. I believe my data is then comprised of the 3D
coordinates of the ~5,000 points of the deformable body depicted in
each image.
Can I treat these points as landmarks and perform a very
high-dimensional (~15,000-D) PCA? Is there any "curse of
dimensionality" with this method?
I appreciate your help.
Adam
[email protected] <mailto:[email protected]>
