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I have both a distance matrix and the original vectors, and am using MDS (Multidimensional Scaling) with R to generate vectors in more dimensions for the data.

With dimensionality reduction (for instance PCA) one can calculate the transformation with a portion of the data, and apply it to new elements. Is there an analog equivalent in MDS? The distance from the new points to all the original ones can be calculated, that's why I'm asking.

The reason I'm not directly using the original vectors with a dimensionality reduction technique is that there are mixed numeric and categorical variables, possibly some NAs and 1000 rows with 50 variables. Other methods (using imputation, trees, etc) were very slow. The daisy() function from cluster calculates the distance matrix quickly.

A large part of this question is the genuine doubt about if it's possible to train and apply MDS (even if it makes no sense to use it in this particular case), but if you have a suggestion for quickly converting categorical to numeric variables it'll be welcome (AFAIK only Multiple Correspondence Analysis can do this).

Alejandro Pulver
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  • possible duplicate of [Two broad categories of dimensionality reduction](http://stats.stackexchange.com/questions/142960/two-broad-categories-of-dimensionality-reduction) – Momo Mar 24 '15 at 18:53
  • "converting categorical to numeric variables": [optimal scaling](http://www.jstatsoft.org/v31/i04/paper) and Gifi methods? I am unsure about the question, though. You are talking about dimension reduction and prediction on new samples. Could you perhaps clarify? – chl Mar 24 '15 at 20:27
  • I was referring to the fact that if all my variables were numeric, I could use PCA or other "parametric" dimensionality reduction techniques to train the model and then predict on new samples. I didn't know about the distinction before Momo's answer. So I must either convert categorical variables to numeric, or use a "parametric" technique that supports both kinds of variables (which seems `homals` can do, though I haven't yet read it carefully). – Alejandro Pulver Mar 24 '15 at 23:07
  • Related: https://stats.stackexchange.com/questions/368331/project-new-point-into-mds-space – Sterling Aug 12 '21 at 02:26

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