confusing regarding to kmeans clulstering for data correlation 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?
You will not get what you seek this way, but you are on the right path. Use the correlation between two instruments as a measure of similarity, and then perform spectral clustering with this measure as the kernel.

Basically, you will start with your correlation matrix $R$, and build the corresponding Laplacian matrix $L$. The eigen vectors corresponding to the smallest eigen values of $L$ will give you a projection space in which you can perform k-means clustering.

This technique is efficient if you have a good similarity measure, but only works for reasonably sized datasets (because you need the eigen decomposition of the $n \times n$ matrix).