Quote from: 2112 on May 14, 2018, 05:54:09 PM

Before you read this I really urge you to revert the title of this thread to the original. It was much better at eye-catching, even if somewhat poetic in its approach to mathematics. But finding the right way to exaggerate is helping in creating great art (and science.)

I totally agree, that's what I had in mind when I put the original title, so I restored the title. In any case eigenvectors do form a basis of the eigenspace so it should not be a big abuse.

Quote from: 2112 on May 14, 2018, 05:54:09 PM

Quote from: sncc on May 14, 2018, 05:07:09 PM

Right maybe orthonormal basis in general vector space should be more precise here for an analogy. As you noted my point is how to find out such a basis or analogous merit senders in the entire merit network space. It would be well-defined problem if it is e.g. some general vector space in mathematics as we could basically follow the Gram-Schmidt orthogonalization process for given liner independent vectors to construct a good basis. This process is not clear for the merit network space, but at least the visualization provides an intuitive approach.

To orthonormalize you'll have to both normalize and orthogonalize. The open question is how to normalize merit transfers? This "normalized merit" would have to meet the conditions of being a https://en.wikipedia.org/wiki/Lebesgue_measure , preferably of the order 2, which is an equivalent of the most common https://en.wikipedia.org/wiki/Euclidean_distance measure, also known as https://en.wikipedia.org/wiki/Root_mean_square in statistics.

In the SVD article there's a mention of open source algorithm used by Netflix to find similarities between films and user's tastes with the help of star ratings. I never had a Netflix account, but I believe the users assign films star ratings in the range 1-5 or 1-10. So they get normalization almost for free.

Quote from: sncc on May 14, 2018, 05:07:09 PM

I am not sure how the least square method works for resolving the issue, as it is not clear to me what we should minimize or fit to find out independent merit senders, but you seem to have some idea?

I was trying to make a funny reference to https://en.wikipedia.org/wiki/Ordinary_least_squares , a form of https://en.wikipedia.org/wiki/Regression_analysis . Perhaps you were trying to intuit some form of https://en.wikipedia.org/wiki/Correlation_clustering ?

Please do continue your research.

I have never heard about the Netflix ratings but there should be some earlier works on this kind of issue. Actually I think more important part is to define an analogous concept of orthogonality or linear independence for merit senders since if we have a well-defined orthogonal or linear independent set of merit senders, that's ok and we can use them as basis even without thinking about normalization. I think minimizing correlation or overlap of sent merit networks could be used as an analogous concept of orthogonalization. That should be a well-defined process. To compare two merit senders we can check the accounts they merited and see how many percentage of accounts are overlapping. We can then try to choose a set of merit senders whose overlap is minimized, and yet merits they sent can cover the entire forum as much as possible. We can then take into account number of posts, and allow more merit senders with overlap for dense region in the network space.

Quote from: Jet Cash on May 14, 2018, 06:21:05 PM

Would it be possible to see how many awards of 10 merits have been given to people with a current status of 'member', and which of the larger merit awarders are making awards that are predominantly single merits.

I haven't taken rank data from the forum so at this moment I cannot do this analysis. I think other statisticians in the forum can do this easily, and I will also think about that.