# tslearn.barycenters¶

The `tslearn.barycenters`

module gathers algorithms for time series
barycenter computation.

A barycenter (or *Fréchet mean*) is a time series \(b\) which minimizes
the sum of squared distances to the time series of a given data set \(x\):

\[\min \sum_i d( b, x_i )^2\]

Only the methods `dtw_barycenter_averaging()`

and
`softdtw_barycenter()`

can operate on variable-length time-series
(see here).

See the barycenter examples for an overview.

Functions

`euclidean_barycenter` (X[, weights]) |
Standard Euclidean barycenter computed from a set of time series. |

`dtw_barycenter_averaging` (X[, …]) |
DTW Barycenter Averaging (DBA) method estimated through Expectation-Maximization algorithm. |

`dtw_barycenter_averaging_subgradient` (X[, …]) |
DTW Barycenter Averaging (DBA) method estimated through subgradient descent algorithm. |

`softdtw_barycenter` (X[, gamma, weights, …]) |
Compute barycenter (time series averaging) under the soft-DTW [1] geometry. |