I am trying to think through my process before doing any real coding. However, got really confused easily.
Say I have 100 instruments and I know their price movements every day for a year. So I can create a movement matrix
A =[[I1-1, I2-1, .... I100-1], (I1-1 is price for instrument 1 on day 1) [I1-2, I2-2, .... I100-2], .... [I1-365, I-2365, .... I100-365] ]
Then for each instrument, I can calculate a price movement correlation between other instruments for the whole year.
C =[C1-2, C1-3,...C1-100,C2-3,....C99-100] (C1-2 is the price movement correlation between instrument 1 and 2 for the whole year)
Then I would like to apply a K-Means clustering algorithm to classify the correlation into say 10 categories. So in theory, I created 10 categories that the prices turned to move together.
However, the more I think about it, the more it is not correct. For example, if this is my Correlation result:
C =[0.35, 0.59,...0.88(C1-100),0.48,....0.99(C99-100)]
isn't it K-Means clustering may classify C1-100, C99-100 in one cluster, and C1-2, C1-3, C2-3 in another cluster.
When I read that, it means instrument 1,100, 99 in one category, and instrument 1,2,3 in another category. But I would like each instrument only available in one category, so looks like there is a hole in my idea or maybe my idea is totally wrong?