## Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

For the discussion of math. Duh.

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tlbs
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### Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

If they don't, then they aren't really 29 dimensions now, are they?

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Lycur
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

Actually orthogonality is more than you need, all it takes is linear independence.

_MC_
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

So if you can prove linear dependence, would the next step be a lawsuit?

mike-l
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

_MC_ wrote:So if you can prove linear dependence, would the next step be a lawsuit?

Or use your knowledge to play the system and get lots of hot dates.
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Yakk
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

Discriminating elements of E-Harmony have no basis for rotating their expectations of what the measure of dependence between the dual relationship between components of ...
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

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tlbs
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

Lycur wrote:Actually orthogonality is more than you need, all it takes is linear independence.

My bad... it's been almost 30 years since my last linear algebra class. Perhaps, "orthonormal basis", would have been a better choice of words in the subject line.
Thanks for pointing that out. It made me look up the difference between orthogonal and orthonormal. Being an engineer I deal with orthogonality on a regular basis but rarely with orthonormality.

So, that brings up another question about those, "29 dimensions of compatibility". How does one show that the defining factor for each dimension is normalized in that dimension?

_MC_ wrote:So if you can prove linear dependence, would the next step be a lawsuit?

I have actually had that notion since I started pondering the original question. I was not happy with E-harmony last spring -- but I did get a refund, contrary to what many people were reporting on ratings sites.

orangeperson
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

tlbs wrote: Perhaps, "orthonormal basis", would have been a better choice of words in the subject line.
Thanks for pointing that out. It made me look up the difference between orthogonal and orthonormal.

They would only need to be linearly independent. For example, the vectors (1,1) and (0,1) are linearly independent: you can't have a*(0,1)=b*(1,1). They form a basis of the 2-dimensional plane, but are not orthogonal, much less orthonormal. To be orthogonal they would need to be perpendicular, to be orthonormal they would have to be orthogonal and have a size of one.
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BlackSails
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

I would guess that the 29 dimensions are linearly indpendant, but they do not span the entire set of all human qualities.

Random832
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

BlackSails wrote:I would guess that the 29 dimensions are linearly indpendant, but they do not span the entire set of all human qualities.

The question is if they span a set that is strictly better (i.e. a superset of) than those of competing sites.

BlackSails
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

Nah, the question is if they give better results. Having many dimensions, but not weighting them appropriately could give a worse measurement than a site that has fewer dimensions but uses statistical analysis to see which ones matter for relationships.

Eebster the Great
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

BlackSails wrote:I would guess that the 29 dimensions are linearly indpendant, but they do not span the entire set of all human qualities.

I doubt they are linearly independent. There is probably at least one question which is essentially a linear combination of previously asked questions (making said question technically worthless), given how proud they are of the large number of questions asked.

Dason
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

Eebster the Great wrote:I doubt they are linearly independent. There is probably at least one question which is essentially a linear combination of previously asked questions (making said question technically worthless), given how proud they are of the large number of questions asked.

But people can interpret questions differently so I don't think it's really a mathematical question. You might be able to predict the answer to question 25 with 95% accuracy using questions 11,17, and 19 but that extra 5% might tell you a lot of information you wouldn't get otherwise.
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Eebster the Great
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

Dason wrote:
Eebster the Great wrote:I doubt they are linearly independent. There is probably at least one question which is essentially a linear combination of previously asked questions (making said question technically worthless), given how proud they are of the large number of questions asked.

But people can interpret questions differently so I don't think it's really a mathematical question. You might be able to predict the answer to question 25 with 95% accuracy using questions 11,17, and 19 but that extra 5% might tell you a lot of information you wouldn't get otherwise.

Well, when you find somebody who DOES give an unexpected answer (which will happen frequently), it might tell you that that person has a different interpretation of the question (but you will never know what it is), or it might be that that person misunderstood the question, or didn't read carefully, or forgot the earlier questions, or didn't think about it for very long. To be honest, asking similar questions multiple times is not a useful way to gain new information about somebody.

That's why I hate most surveys.

antonfire
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

Surveys have such questions on there for a reason. For instance is not a bad idea to throw away the data from people who give incompatible answers to such questions, because they are probably not actually paying attention.
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gmalivuk
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

I imagine the individual questions aren't meant to be in only one dimension or another, but rather might count for a point or whatever in two or more dimensions. For comparison, consider the (much cooler) OkCupid matching scheme: They give you a match percentage based on how you answer questions in general, but you can also get it broken down into... *counts* 32 dimensions. You can compare yourself to other users to see who is more adventurous, aggressive, ambitious, into sports, arrogant, compassionate, geeky, capitalistic, progressive, giving, greedy, independent, indie, mathematical, kinky, moral, literary, loving, modern, optimistic, organized, pure, conservative, scientific, desiring of sex, sloppy, spiritual, emotional, thrifty, political, romantic, and well-mannered. So asking a question about math probably affects both your mathematical and your geeky "score", rather than trying to have a separate set of questions for each category.

Are those linearly independent? I don't know, but I suspect the answer is the same as for eHarmony. (And as suggested above, it's probably more a matter of different levels of correlation than actual linear dependence. Capitalism may correlate with greed, for example, but asking at least a few questions that try and separate the two gives you far more useful information than using one as a proxy for the other.)
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Eebster the Great
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### Re:http:/ Do E-Harmony's 29 Dimensions form an Orthogonal Ba

gmalivuk wrote:I imagine the individual questions aren't meant to be in only one dimension or another, but rather might count for a point or whatever in two or more dimensions. For comparison, consider the (much cooler) OkCupid matching scheme: They give you a match percentage based on how you answer questions in general, but you can also get it broken down into... *counts* 32 dimensions. You can compare yourself to other users to see who is more adventurous, aggressive, ambitious, into sports, arrogant, compassionate, geeky, capitalistic, progressive, giving, greedy, independent, indie, mathematical, kinky, moral, literary, loving, modern, optimistic, organized, pure, conservative, scientific, desiring of sex, sloppy, spiritual, emotional, thrifty, political, romantic, and well-mannered. So asking a question about math probably affects both your mathematical and your geeky "score", rather than trying to have a separate set of questions for each category.

Are those linearly independent? I don't know, but I suspect the answer is the same as for eHarmony. (And as suggested above, it's probably more a matter of different levels of correlation than actual linear dependence. Capitalism may correlate with greed, for example, but asking at least a few questions that try and separate the two gives you far more useful information than using one as a proxy for the other.)

Yeah, see, those are definitely not orthogonal. For instance, by some care ethics, compassion and morality are essentially synonymous. I have no idea what definition of "moral" OKCupid uses, but it is reasonable to say that it is dependent on compassion. Similarly, it is literally impossible to be both greedy and giving, or organized and sloppy. These are basically antonyms.

But are they linearly dependent? I'm not sure. The terms are vague enough that one could argue each is independent.

the tree
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

If it's not independent then it's dependent.

I'd like to think that none of them are independent, partially because some are nearly antonyms and partially because it'd be rubbish if you could be 100% on half of them.

Also there's no real origin point in OKCupids system - or at least not one that you get to know where it is - everyone's position is relative to someone else's.

gmalivuk
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### Re: Do E-Harmony's 29 Dimensions form an Orthogonal Basis?

There could still be an origin, though, since clearly there's some way that each question increments a number you have for one or more of those characteristics. So you can take the origin as zero for all those numbers, even if that point will change its distance from the population average over time as different people answer the questions.

Eebster the Great wrote:Yeah, see, those are definitely not orthogonal.

Well sure, but from about the first reply we've accepted that this discussion is really about linear independence rather than orthogonality or normality.
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