# Matrix Profile¶

The Matrix Profile, $$MP$$, is a new time series that can be calculated based on an input time series $$T$$ and a subsequence length $$m$$. $$MP_i$$ corresponds to the minimal distance from the query subsequence $$T_{i\rightarrow i+m}$$ to any subsequence in $$T$$ 1. As the distance from the query subsequence to itself will be equal to zero, $$T_{i-\frac{m}{4}\rightarrow i+\frac{m}{4}}$$ is considered as an exclusion zone. In order to construct the Matrix Profile, a distance profile which is similar to the distance calculation used to transform time series into their shapelet-transform space, is calculated for each subsequence, as illustrated below:

## Implementation¶

The Matrix Profile implementation provided in tslearn uses numpy or wraps around STUMPY 2. Three different versions are available:

• numpy: a slow implementation

• stump: a fast CPU version, which requires STUMPY to be installed

• gpu_stump: the fastest version, which requires STUMPY to be installed and a GPU

## Possible Applications¶

The Matrix Profile allows for many possible applications, which are well documented on the page created by the original authors 3. Some of these applications include: motif and shapelet extraction, discord detection, earthquake detection, and many more.

## Examples Involving Matrix Profile¶

Matrix Profile

Matrix Profile

Distance and Matrix Profiles

Distance and Matrix Profiles

## References¶

1

C. M. Yeh, Y. Zhu, L. Ulanova, N.Begum et al. Matrix Profile I: All Pairs Similarity Joins for Time Series: A Unifying View that Includes Motifs, Discords and Shapelets. ICDM 2016.

2