I appreciate certain things; adore some. One of these is Bell Labs. The things they do in there, amazing. People work on Robotics and end up writing papers in Psychology. Such was the case a couple of decades back, when a publication (and a small book) came out of Bell Labs, which read 'Multi Dimensional Scaling'. Brilliance, I tell you.
The aim of MDS is simple: Get uncertainty closer to certainty. And when I talk about uncertainty, it's not the quantum world or probability in that sense. It's uncertainty in decisions; when you do not have enough parameters to evaluate, you try reaching a decision based on what you know, however limited it may be. A simpler way to put it would be: Identifying the similarities and the dissimilarities. The best part about this is the fact that people in Bell Labs introduced it in the field of Psychology and explained it's applications. It went on to be a part of Marketing, Data mining, Cognitive Sciences, Psychometrics, Operations Research, what not. A seminar was presented on this by one of the research students when I was there in the IISc Lab.
Take a simple example: I give you three cities, and the distances between any two of them (in pairs). These distances have been measured by an incorrect distance meter. Your job is to find out the actual distance between cities. In case of three cities, you just draw the triangle and get done with it! Now I increase the number of cities to four, and give you distances in pairs. Note that when we add a city, we add three more distances. Which means that for pin pointing the fourth city, three circles have to meet at a point. Which may not, and in most cases, will not be the case. Adding one more city making it five needs four circles to meet at a point, which is even more improbable. This goes on, where for a n city situation, n-1 circles need to meet at a point, for every city. Of course, we know that the distance meter is incorrect, otherwise all distances would be perfect. Hence, we optimize with a so called stress function, which is similar to standard deviation, to obtain pairs of distances, which agree to a reasonable extent with the incorrect meter, overall. We thus obtain how similar the distance meter is, to the actual distance between two cities.
The application of this in Psychology for instance, or psychometric tests is remarkable. Consider an example, where you write a psychometric test. There is no right/wrong in such tests, we know. However, after your responses are registered, an algorithm similar to MDS would be run, with your answers mapped to 'distances' in a certain way, to see how your answers vary from one another. It's like saying: Even if the distance meter is incorrect, MDS gives all distances with errors in distances of different pairs being similar. This however, is true only when the distance meter is uniformly incorrect. Similarly, it doesn't matter whether you're a baby or a terrorist. If you lie in certain questions, in which case you're not being uniformly a terrorist or a baby, the clash in responses gives a high relative error amongst all questions. In which case you get screwed. So never lie.
And Bell Labs rocks.
Update: Regarding the previous post, if you happened to think I was serious, and hence asked me to get a life, or cursed me, please please please, I was joking.
The aim of MDS is simple: Get uncertainty closer to certainty. And when I talk about uncertainty, it's not the quantum world or probability in that sense. It's uncertainty in decisions; when you do not have enough parameters to evaluate, you try reaching a decision based on what you know, however limited it may be. A simpler way to put it would be: Identifying the similarities and the dissimilarities. The best part about this is the fact that people in Bell Labs introduced it in the field of Psychology and explained it's applications. It went on to be a part of Marketing, Data mining, Cognitive Sciences, Psychometrics, Operations Research, what not. A seminar was presented on this by one of the research students when I was there in the IISc Lab.
Take a simple example: I give you three cities, and the distances between any two of them (in pairs). These distances have been measured by an incorrect distance meter. Your job is to find out the actual distance between cities. In case of three cities, you just draw the triangle and get done with it! Now I increase the number of cities to four, and give you distances in pairs. Note that when we add a city, we add three more distances. Which means that for pin pointing the fourth city, three circles have to meet at a point. Which may not, and in most cases, will not be the case. Adding one more city making it five needs four circles to meet at a point, which is even more improbable. This goes on, where for a n city situation, n-1 circles need to meet at a point, for every city. Of course, we know that the distance meter is incorrect, otherwise all distances would be perfect. Hence, we optimize with a so called stress function, which is similar to standard deviation, to obtain pairs of distances, which agree to a reasonable extent with the incorrect meter, overall. We thus obtain how similar the distance meter is, to the actual distance between two cities.
The application of this in Psychology for instance, or psychometric tests is remarkable. Consider an example, where you write a psychometric test. There is no right/wrong in such tests, we know. However, after your responses are registered, an algorithm similar to MDS would be run, with your answers mapped to 'distances' in a certain way, to see how your answers vary from one another. It's like saying: Even if the distance meter is incorrect, MDS gives all distances with errors in distances of different pairs being similar. This however, is true only when the distance meter is uniformly incorrect. Similarly, it doesn't matter whether you're a baby or a terrorist. If you lie in certain questions, in which case you're not being uniformly a terrorist or a baby, the clash in responses gives a high relative error amongst all questions. In which case you get screwed. So never lie.
And Bell Labs rocks.
Update: Regarding the previous post, if you happened to think I was serious, and hence asked me to get a life, or cursed me, please please please, I was joking.
6 comments:
Awesome stuff man!
Nice, I wonder why it is called multi_dimensional_ _scaling_ of all things, what is dimensional about it, and what is being scaled? Cool idea, though.
However, with regard to psychometric tests, I don't agree that even MDS could help. The problem, as I see it, is this: MDS assumes that there exists a 'correct' measure : for instance, in your distance example, what if I was not measuring distance between cities, but between buoys in a sea? There _is_ no one thing called the 'distance' between them, because they are constantly moving around. We'd then have to settle with something like the avg.
Again, in psychometry, who defines "the clash in responses" ? Oh whatever, we'll talk after the quiz :-)
Nice!
NICE,but i guess ur next blog is abt india loosing against bangladesh.............lol
Nice post. KV told me about it in class today.
Once, when I went to the library to mug my head off, I ended up reading a Handbook of Psychology, and I did read quite a lot about Psychometry. Yeah, there are no "standards", so to speak. But some of the crazy statistical methods they use go well above the head. I guess it's time I go read it up again.
Le le le...
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