Eigenvectors and Factor Analysis

Now here is the point where I have to drag in a little bit of real math. We associate the complex spectrum of a linear device with a fourier transform, in which a pair of numbers is given for each frequency. But strictly speaking the fourier transform is no more and no less than a scheme for representing a mathematical function in terms of sine and cosine waves. (A cosine wave is just a sine wave phase-shifted 90 degrees.)

These wave forms are just a convenient set of eigenvectors or coordinate axes, which just happen to be useful for electrical signals because of Maxwell's equations. But any spectrum can be represented more or less well by any set of orthogonal functions, and that means we can look around for some functions more appropriate for our data.

A good example of this goes back a couple of years to some researchers who used factor analysis to come up with a good set of eigenvectors for comparing pictures of human faces. The principal eigenvector or best-single- coordinate-axis is simply an average human face, totally unmemorable, just the most typical human face, the average face.

Using that axis alone you have a single number which only says how typical a face is; a large positive number would describe a very ordinary face, and a large negative number an unusual face. Other coordinate axes are other eigenvectors, some of which describe squashed, twisted, or other orthogonal forms of extreme ugliness -- oops, I mean extremely distinctiveness in character.

Since these coordinate axes are facelike, you can look at them, seeing what I recognize as archetypical faces -- indeed when Jung was writing about archetypes I see him as writing about eigenvectors. And, of course, the archetypes Jung was most concerned about were archetypes of personality, and the Myers-Briggs personality types are derived from Jung's work.

In psychology the use of factor analysis, (which is really just the extraction of eigenvectors from autocorrelation matrices generated from personality test scores) is very old news, having been used for decades.

But here is what is wrong about factor analysis and what is why we have so many different theories of personality instead of just a useful toolkit. Almost all psychologists using factor analysis have viewed the extracted eigenvectors as somehow real, like the ideals of Platonic philosophy which Plato considered as much more real that anything in our world, the world of illusion.

But when computer science people use the extraction of eigenvectors it is not because of any underlying reality attributed to them, but simply as a form of data-compression. Both the JPEG and MPEG data compression standards, used for compressing still images and moving pictures (respectively), make use of the extraction of eigenvectors.

The basic idea can be seen in the use of archetypical faces: instead of having to produce an image which might contain millions of pixels to describe a face as a picture, you simply compare any face you want to describe with the archetypical faces (which are eigenvectors of the matrix etc. etc) and since pictures of real faces were used in generating the matrix, the face you want to describe will resemble more-or-less (or differ more-or-less from) the archetypical faces.

You can say your face is a 64% match with one archetype, a 32% match with another, and so on, so that you can produce a very accurate description of a human face by using only half a dozen or so numbers, instead of the millions of pixel values otherwise required. You can compress the millions of pixels to very few numbers, then at any time your can reconstruct the original image with very little loss of detail.

But no computer scientist would go on record as thinking that the archetypical faces are more real than our own (tragically flawed) visages. No one would say God used those archetypes when designing the face of Adam or Eve.

Similarly, I say the INTP or ESFJ or any other personality description does not relate to any underlying Platonic reality -- they are just data compression, to be used when useful. Oh, all right, sure, there are a few Platonists in the computer science community -- we have just about the same number of metaphysicians and lunatics as any other community. But my point really is that eigenvectors or archetypes are not part of Science, they are part of Technology. (Forgive the capital letters, they are part of the Platonic Archetype of this argument, so my hands are tied.)

Copyright © 1998 Douglas P. Wilson       

Copyright © 2009   Douglas Pardoe Wilson

Other relevant content:

New: Social Technology through Diagrams

New: Social Techs novel online

New: Social Technology Blog

New: Social Technology Wiki

Please see these web pages:

The main Social Technology page.

Find Compatibles , the key page, with the real solution to all other problems explained

Technological Fantasies , a page about future technology

Social Tech a page about Social Technology, technology for social purposes.  I think I was the first person to use this phrase on the Internet, quite a long time ago.

Roughly corresponding to these web pages are the following blogs :

Social Technology the main blog, hosted on this site, with posts imported from the following blogger.com blogs, which still exist and are useable.

Find Compatibles devoted to matching people with friends, lovers, jobs, places to live and so on, but doing so in ways that will actually work, using good math, good algorithms, good analysis.

Technological Fantasies devoted to future stuff, new ideas, things that might be invented or might happen, such as what is listed above and below.

Sex-Politics-Religion is a blog about these important topics, which I have been told should never be mentioned in polite conversation.  Alright that advice does seem a bit dated, but many people are still told not to bring up these subjects around the dinner table.

I believe I was the first person on the Internet to use the phrase Social Technology -- years before the Web existed.

Those were the good old days, when the number of people using the net exceeed the amount of content on it, so that it was easy to start a discussion about such an upopular topic.  Now things are different.  There are so many web pages that the chances of anyone finding this page are low, even with good search engines like Google.   Oh, well.

By Social Technology I mean the technology for organizing and maintaining human society.  The example I had most firmly in mind is the subject of  Find Compatibles , what I consider to be the key page, the one with the real solution to all other problems explained.

As I explained on my early mailing lists and later webpages, I find that social technology has hardly improved at all over the years.   We still use representative democracy, exactly the same as it was used in the 18th century.  By contrast, horse and buggy transporation has been replaced by automobiles and airplanes, enormous changes.

In the picture below you will see some 18th century technology, such as the ox-plow in the middle of the picture.  How things have changed since then in agricultural technology.  But we still use chance encounters, engagements and marriages to organize our home life and the raising of children.  

I claim that great advances in social technology are not only possible but inevitable.  I have written three novels about this, one preposterously long, 5000 pages, another merely very very long, 1500 pages.  The third is short enough at 340 pages to be published some day.  Maybe.  The topic is still not interesting to most people.   I will excerpt small parts of these novels on the web sometime, maybe even post the raw text for the larger two.

This site includes many pages dating from 1997 to 2008 which are quite out of date.  They are included here partly to show the development of these ideas and partly to cover things the newer pages do not.  There will be broken links where these pages referenced external sites.  I've tried to fix up or maiintain all internal links, but some will probably have been missed.   One may wish to look at an earlier version of this page , rather longer, and at an overview of most parts of what can be called a bigger project.

Type in this address to e-mail me.  The image is interesting.  See Status of Social Technology

Copyright © 2007, 2008, 2009, Douglas Pardoe Wilson

I have used a series of e-mail address over the years, each of which eventually became out of date because of a change of Internet services or became almost useless because of spam.  Eventually I stuck with a Yahoo address, but my inbox still fills up with spam and their spam filter still removes messages I wanted to see.  So I have switched to a new e-mail service.  Web spiders should not be able to find it, since it is hidden in a jpeg picture.   I have also made it difficult to reach me.  The picture is not a clickable link.  To send me e-mail you must want to do so badly enough to type this address in.  That is a nuisance, for which I do apologize, but I just don't want a lot of mail from people who do not care about what I have to say.



Copyright © 2009   Douglas Pardoe Wilson