How can I do K-means clustering of time series data? I understand how this works when the input data is a set of points, but I don't know how to cluster a time series with 1XM, where M is the data length. In particular, I'm not sure how to update the mean of the cluster for time series data.
I have a set of labelled time series, and I want to use the K-means algorithm to check whether I will get back a similar label or not. My X matrix will be N X M, where N is number of time series and M is data length as mentioned above.
Does anyone know how to do this? For example, how could I modify this k-means MATLAB code so that it would work for time series data? Also, I would like to be able to use different distance metrics besides Euclidean distance.
To better illustrate my doubts, here is the code I modified for time series data:
% Check if second input is centroids
if ~isscalar(k)
c=k;
k=size(c,1);
else
c=X(ceil(rand(k,1)*n),:); % assign centroid randomly at start
end
% allocating variables
g0=ones(n,1);
gIdx=zeros(n,1);
D=zeros(n,k);
% Main loop converge if previous partition is the same as current
while any(g0~=gIdx)
% disp(sum(g0~=gIdx))
g0=gIdx;
% Loop for each centroid
for t=1:k
% d=zeros(n,1);
% Loop for each dimension
for s=1:n
D(s,t) = sqrt(sum((X(s,:)-c(t,:)).^2));
end
end
% Partition data to closest centroids
[z,gIdx]=min(D,[],2);
% Update centroids using means of partitions
for t=1:k
% Is this how we calculate new mean of the time series?
c(t,:)=mean(X(gIdx==t,:));
end
end
Time series are usually high-dimensional. And you need specialized distance function to compare them for similarity. Plus, there might be outliers.
k-means is designed for low-dimensional spaces with a (meaningful) euclidean distance. It is not very robust towards outliers, as it puts squared weight on them.
Doesn't sound like a good idea to me to use k-means on time series data. Try looking into more modern, robust clustering algorithms. Many will allow you to use arbitrary distance functions, including time series distances such as DTW.