tslearn.barycenters.dtw_barycenter_averaging_subgradient(X, barycenter_size=None, init_barycenter=None, max_iter=30, initial_step_size=0.05, final_step_size=0.005, tol=1e-05, random_state=None, weights=None, metric_params=None, verbose=False)[source]

DTW Barycenter Averaging (DBA) method estimated through subgradient descent algorithm.

DBA was originally presented in [1]. This implementation is based on a idea from [2] (Stochastic Subgradient Mean Algorithm).

Parameters: X : array-like, shape=(n_ts, sz, d) Time series dataset. barycenter_size : int or None (default: None) Size of the barycenter to generate. If None, the size of the barycenter is that of the data provided at fit time or that of the initial barycenter if specified. init_barycenter : array or None (default: None) Initial barycenter to start from for the optimization process. max_iter : int (default: 30) Number of iterations of the Expectation-Maximization optimization procedure. initial_step_size : float (default: 0.05) Initial step size for the subgradient descent algorithm. Default value is the one suggested in [2]. final_step_size : float (default: 0.005) Final step size for the subgradient descent algorithm. Default value is the one suggested in [2]. tol : float (default: 1e-5) Tolerance to use for early stopping: if the decrease in cost is lower than this value, the Expectation-Maximization procedure stops. random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. weights: None or array Weights of each X[i]. Must be the same size as len(X). If None, uniform weights are used. metric_params: dict or None (default: None) DTW constraint parameters to be used. See tslearn.metrics.dtw_path for a list of accepted parameters If None, no constraint is used for DTW computations. verbose : boolean (default: False) Whether to print information about the cost at each iteration or not. numpy.array of shape (barycenter_size, d) or (sz, d) if barycenter_size is None DBA barycenter of the provided time series dataset.

References

 [1] F. Petitjean, A. Ketterlin & P. Gancarski. A global averaging method for dynamic time warping, with applications to clustering. Pattern Recognition, Elsevier, 2011, Vol. 44, Num. 3, pp. 678-693
 [2] (1, 2, 3) D. Schultz and B. Jain. Nonsmooth Analysis and Subgradient Methods for Averaging in Dynamic Time Warping Spaces. Pattern Recognition, 74, 340-358.

Examples

>>> time_series = [[1, 2, 3, 4], [1, 2, 4, 5]]