  Matrix profile has been recently proposed as a promising technique to the
problem of all-pairs-similarity search on time series. Efficient algorithms
have been proposed for computing it, e.g., STAMP, STOMP and SCRIMP++. All these
algorithms use the z-normalized Euclidean distance to measure the distance
between subsequences. However, as we observed, for some datasets other
Euclidean measurements are more useful for knowledge discovery from time
series. In this paper, we propose efficient algorithms for computing matrix
profile for a general class of Euclidean distances. We first propose a simple
but efficient algorithm called AAMP for computing matrix profile with the
"pure" (non-normalized) Euclidean distance. Then, we extend our algorithm for
the p-norm distance. We also propose an algorithm, called ACAMP, that uses the
same principle as AAMP, but for the case of z-normalized Euclidean distance. We
implemented our algorithms, and evaluated their performance through
experimentation. The experiments show excellent performance results. For
example, they show that AAMP is very efficient for computing matrix profile for
non-normalized Euclidean distances. The results also show that the ACAMP
algorithm is significantly faster than SCRIMP++ (the state of the art matrix
profile algorithm) for the case of z-normalized Euclidean distance.
