Seems straightforward. For each pair of series you need to calculate a correlation coefficient, r (using either levels or differences). Then find n pairs with lowest r.

The second question is not quite clear though. Some examples of your data are needed.

You only have to make an algorithm which selects the chronological series that checks the correlation criterion you want

Milad Cheraghzade

Seems straightforward. For each pair of series you need to calculate a correlation coefficient, r (using either levels or differences). Then find n pairs with lowest r.

The second question is not quite clear though. Some examples of your data are needed.

Now I see that you need not n pairs, but n time series. This becomes a bit more complicated.

Firstly you need to formulate the criteria:

You need to find n time series having min(max(abs(cor(s_i,s_j)))) for any i and j (i!=j), where s_i and s_j are time series i and j.

Yes, you need a special algorithm here. One very simple approach is to try all subsets, but this can take too long, so you can try iterative approaches.

Andrey Davydenko

Dear Andrey , thanks for your kind responses

The problem is pretty much straightforward. consider that we have a datasets X which includes 100 acceleration time histories. {X = [t1, t2, ... t100] (10 second data with sampling frequency of 100 Hz)}.

Now, I'm about to pick up the most non-correlated time series which is a fraction of the whole datasets (according to their characteristics).

What comes to my mind is that i conduct a Dimensionality reduction algorithm first, then clustering the reduced labeled features and from each cluster picking one time history.

It would be great if i could use an unsupervised method, rather than a step by step method

thanks

The first step is to define correlation between two time series, i and j. Let's say we have time series s_i and s_j. Here you can use the cross-correlation function: https://nwfsc-timeseries.github.io/atsa-labs/sec-tslab-correlation-within-and-among-time-series.html

So you need the sample absolute cross-correlation function (CCF), let's define it as abs(CCF(i, j)).

The second step is to define n. As I understand, you select it yourself arbitrarily.

Then I do not think you need clustering here, but the step-by-step approach may help.

You can use the following algorithm.

Suppose you have a set of time series, D having m series, you need to find a set S having n series as different as possible.

STEP 1

Find a pair having min(abs(CCF(i, j))), add series s_i and s_j to your set of selected series, S. So S will have 2 time series.

STEP 2

For each time series s_k in D that do not belong to S calculate the following. Try adding s_k to S and find max(abs(CCF(i, j)))) for S.

Add the series giving min(max(abs(CCF(i, j)))))

STEP 3

Repeat step 2 until S has n series.