How to get pairwise distance matrices from dynamic time warping dtw on a matrix of time series ?

I have a matrix (1018 x 3744) where each column is a timeseries. The timestamps, which are the same for each row, are in a separete vector. Some of the time series contain NaN values at a variety of time points (rows).

1) If there are no NaNs, How can I generate pairwise distance matrices for all of the time series using the dynamic time warping function? I know how to do it for a single pair of time series vectors but not for all of the pairwise combinations in this matrix.

2) How can I do this if there are NaNs?

A subsample of the matrix (the first 10 columns is attached).

Thanks!

Answer 1

[Greg Dionne]

Your signals look extremely well time-aligned (within a sample).

Since you have NaN, I suppose you could just perform a weighted comparison over the points you currently have. Maybe something like:

function D = mdist(X)

n = size(X,2);
D = zeros(n);

for i=1:n
    for j=i+1:n
        idx = isfinite(X(:,i))&isfinite(X(:,j));
        D(i,j) = rms(X(idx,i)-X(idx,j));
    end
end

D = D+D';

>> mdist(subset)

ans =

0 0.0002 0.0005 0.0009 0.0015 0.0022 0.0030 0.0039 0.0049 0.0059

0.0002 0 0.0003 0.0008 0.0013 0.0021 0.0029 0.0038 0.0047 0.0058

0.0005 0.0003 0 0.0005 0.0010 0.0018 0.0026 0.0035 0.0044 0.0055

0.0009 0.0008 0.0005 0 0.0006 0.0013 0.0021 0.0030 0.0040 0.0051

0.0015 0.0013 0.0010 0.0006 0 0.0007 0.0015 0.0024 0.0034 0.0045

0.0022 0.0021 0.0018 0.0013 0.0007 0 0.0008 0.0017 0.0027 0.0038

0.0030 0.0029 0.0026 0.0021 0.0015 0.0008 0 0.0009 0.0019 0.0030

0.0039 0.0038 0.0035 0.0030 0.0024 0.0017 0.0009 0 0.0010 0.0021

0.0049 0.0047 0.0044 0.0040 0.0034 0.0027 0.0019 0.0010 0 0.0011

0.0059 0.0058 0.0055 0.0051 0.0045 0.0038 0.0030 0.0021 0.0011 0

[Joel Singley]

Thanks, I'll give this a try. There are quite a few time periods were the time series (especially those not in the sample) diverge from each other, so they are not always so well aligned.