Perceptual Space: Predicting Odorant Perceived Similarity

The data set contains 144 odorants from  Dravniek's atlas of odor character profiles . Their perceptual descriptors are reduced to 4 dimensions by principal component analysis (PCA) and their first two principal components are displayed here. When two odorants are selected the euclidean distance between their coordinates is displayed. This distance corresponds to the perceived similarity of the odorants, see Khan et. al., 2007.

How can I add more data
To add an additional odorant which does not appear in this list use these instructions:
if A is a centered matrix (I.e. that its columns all average to zero) and COEFF and SCORE are given by the matlab command
[COEFF,SCORE]=princomp(A)
then
A=SCORE*COEFF'

A matrix A is centered with the commands
MEANA=mean(A)
A=A – repmat(MEAN,size(A,1),1)

Given a new odorant which we want to compare to the existing data and find its distances the procedure is as follows:

1)    rate the dravnieks descriptors of the odor (ideally the mean of 30 subjects) and represent it in a row vector v of length 144 (the ratings and statistics procedure are described in Dravnieks).
2)    Subtract from v the mean of the columns in A so that it is in the same coordinate system as the data analyzed previously. The command is
vCentered=v -MEAN
3)    next find the vector u of PC scores of the vector v by finding its representation in terms of the PC vectors. The command is u=vCenteres/COEFF'

4)    the first 4 components of u are the ones we use for the distance to the other vectors in the matrix. To find the distance to odor number 7 from the list in database. Download the attached csv file and take the coordinates for the 4 PC's for odor 7 and take the distance to the first 4 coordinates of u.

Attach the matrix COEFF' and the vector MEAN for the dravnieks raw data matrix.