I would like to find similar motifs in a time-series using Matrix Profile, but by selecting the sub-sequence manually, instead of doing dimension reduction.
Matrix Profile
From what I understand, Matrix Profile is a means of extracting a meta-time-series from a time-series to identify repeated motifs. For example, in the figure below [1], the Matrix Profile ($P_{AB}$) reveals two repeating motifs in the time series ($T_{A}$), one for the sin wave and one for the saw wave. Additionally, the point of transition between the two motifs is a global maximum in the Matrix Profile.
In the Matrix Profile tutorial, this intuition, of repeated motifs having lower values and unique motifs having high values, is reinforced:
Matrix Profile Index and Joins
Later in the tutorial, the concept of Matrix Profile Index is presented in the context of comparing two time series. The time series are compared by appending one to the other and computing Matrix Profile on each of them:
Question
Can Matrix Profile be used to identify the location of similar motifs in a single time-series, without having to do dimension reduction, by using the Matrix Profile Index by using Joins? Using the first example, if I were to select one of the sin wave minimas, could I find another similar wave-like sub-sequence using the Matrix Profile? Would the way to find this "nearest neighbour" or "most similar sub-sequence" be to find the closest Matrix Profile value? Is this the function of the Matrix Profile Index and Joins? This seems possible to me, since in the first example, the minimums for the sine wave seemed to have different values than the saw wave.
[1] Taken from "An Ultra-Fast Time Series Distance Measure to allow Data Mining in more Complex Real-World Deployments" by Gharghabi et al.
