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A Pan Matrix Profile of a time series T is a matrix whose rows are the matrix profiles P of T.
The Pan Matrix Profile can be easily illustrated using a text string analog. Consider the text string:
d3icdmy19qicdmnu19a
We can compute its Matrix Profile at every subsequence length from 1 to 5. In the discrete case, the colors are discrete since subsequences either match or do not. Corresponding to locations at the apex of each dark triangle, we have maximal motifs of length four beginning at location 3 (icdm) and length two beginning at location 8 (19) which correspond to locations 11 and 17, respectively.
Figure: A binary-valued visualization of the Pan Matrix Profile where subsequences either match (black) or do not match (white) for subsequence lengths one through five.
In a real-valued time series case, the colors of the Pan Matrix Profile can take on subtle graduations of color or gray scale to indicate the degree of similarity.
Figure: A real-valued visualization of the Pan Matrix Profile of a time series with an embedded "noisy" motif. Darker regions indicate a strong similarity.
In a real-valued time series case, the colors of the Pan Matrix Profile can take on subtle graduations of color or gray scale to indicate the degree of similarity. Though the sine wave motif is more easily detectable for larger subsequence lengths, the presence of noise makes the motif difficult to detect for smaller subsequence lengths.
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