# 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.