clustering of singular value

Question

let us consider following graph of singular values

i want to make some kind of clustering of these data,namely to seperate main components from non main components,let say signal components from noise components,i would like to do like this(any software matlab,etc is great,better matlab)let us start like this ,first do linear regression with first point,then do regression analysis with first two point and so on,point is that one want to create two group,in first group coefficients of regression lines should be close to each other, also in another group regression coefficients should be close to each other,but regression coefficients in one group must be highly different then coefficients in another group,that means that we should find such point which separate this group optimally, in other word i should stop regression analysis at some point which well separate two group,and another regression will start after this stop point till other rest points,please help me how to do it programaticaly

Answer 1

The plots shown are cumulative plots - clustering of these values may be significantly easier if you consider their individual values, not their cumulative values.

We can suggest many different clustering algorithms for these values, but with only one sample it is difficult to determine what methods will be most successful. Some questions to consider are:

• Do you know how any clusters you want?
• Do you know absolute thresholds for these clusters?
• Will the values always be arranged into these groups of similar values?

Clustering is highly dependent on the behavior of the data over the larger dataset that you would like to be clustering within.

Finally, without knowing the purpose of the data, we are not able to comment on appropriate segmentations of this data that would yield good results for your application. In some cases, the first singular value may be enough, while in others, throwing away any of the eigenvectors in your transformation could be detrimental.