I'm confused about how to measure the similarity between two time series with the same length. For example, both time series are 2 hours in length and every 5 minutes a point. I really want to know which Distance Algorithm should I use. I have tried the Euclidean Distance but it didn't work well on this type of data. Should I find some point-to-point distance algorithms?
A classical approach for time series similarity computation is Dynamic Time Warping (DTW).
From your description, it may suit your use case:
In general, DTW is a method that calculates an optimal match between two given sequences (e.g. time series) with certain restriction and rules:
- Every index from the first sequence must be matched with one or more indices from the other sequence, and vice versa
- The first index from the first sequence must be matched with the first index from the other sequence (but it does not have to be its only match)
- The last index from the first sequence must be matched with the last index from the other sequence (but it does not have to be its only match)
- The mapping of the indices from the first sequence to indices from the other sequence must be monotonically increasing, and vice versa, i.e. if $j>i$ are indices from the first sequence, then there must not be two indices $l>k$ in the other sequence, such that index $i$ is matched with index $l$ and index $j$ is matched with index $k$, and vice versa
Some alternatives to DTW can be found in this literature review on time series dissimilarity measures.