How to use Matrix Profile for dimension reduction and clustering

Question

Matrix Profile (MP) has been used for clustering time-series segments. In the slideshow tutorial featured on the MP website, they use a figure to demonstrate projecting segment similarity onto an M-dimensional space:

How is this projection from 1-dimensional MP onto M-dimensional space accomplished?

Answer 1

The procedure is described in the paper "Matrix Profile III: The Matrix Profile Allows Visualization of Salient Subsequences in Massive Time Series" by Yeh et al.

At a high level, the steps are:

1. Acquire time-series subsequence relevance metric from Matrix Profile
2. Use metric to select a subset of subsequences
3. Project subset of subsequences into reduced space using some form of dimension reduction. The paper uses MDS, which is roughly equivalent to PCA.

As described in the paper, the selection of subsequences to reduce is the most important part of this process. If one reduces all subsequences, the result becomes nonsensical, as first presented in the paper "Clustering of streaming time series is meaningless" by Lin et al.