|
18 | 18 | * *DTW Barycenter Averaging (DBA)* is an iteratively refined barycenter, |
19 | 19 | starting out with a (potentially) bad candidate and improving it |
20 | 20 | until convergence criteria are met. The optimization can be accomplished |
21 | | - with (a) expectation-maximization [1] and (b) stochastic subgradient |
22 | | - descent [2]. Empirically, the latter "is [often] more stable and finds better |
23 | | - solutions in shorter time" [2]. |
| 21 | + with (a) expectation-maximization [1]_ and (b) stochastic subgradient |
| 22 | + descent [2]_. Empirically, the latter "is [often] more stable and finds better |
| 23 | + solutions in shorter time" [2]_. |
24 | 24 | * *Soft-DTW barycenter* uses a differentiable loss function to iteratively |
25 | | - find a barycenter [3]. The method itself and the parameter |
| 25 | + find a barycenter [3]_. The method itself and the parameter |
26 | 26 | :math:`\\gamma=1.0` is described in more detail in the section on |
27 | 27 | :ref:`DTW<dtw>`. There is also a dedicated |
28 | 28 | :ref:`example<sphx_glr_auto_examples_clustering_plot_barycenter_interpolate.py>` |
29 | 29 | available. |
30 | 30 |
|
31 | | -[1] F. Petitjean, A. Ketterlin & P. Gancarski. A global averaging method for |
32 | | -dynamic time warping, with applications to clustering. Pattern Recognition, |
33 | | -Elsevier, 2011, Vol. 44, Num. 3, pp. 678-693. |
| 31 | +.. [1] F. Petitjean, A. Ketterlin & P. Gancarski. A global averaging method for |
| 32 | + dynamic time warping, with applications to clustering. Pattern Recognition, |
| 33 | + Elsevier, 2011, Vol. 44, Num. 3, pp. 678-693. |
34 | 34 |
|
35 | | -[2] D. Schultz & B. Jain. Nonsmooth Analysis and Subgradient Methods for |
36 | | -Averaging in Dynamic Time Warping Spaces. Pattern Recognition, 74, 340-358. |
| 35 | +.. [2] D. Schultz & B. Jain. Nonsmooth Analysis and Subgradient Methods for |
| 36 | + Averaging in Dynamic Time Warping Spaces. Pattern Recognition, 74, 340-358. |
37 | 37 |
|
38 | | -[3] M. Cuturi & M. Blondel. Soft-DTW: a Differentiable Loss Function for |
39 | | -Time-Series. ICML 2017. |
| 38 | +.. [3] M. Cuturi & M. Blondel. Soft-DTW: a Differentiable Loss Function for |
| 39 | + Time-Series. ICML 2017. |
40 | 40 | """ |
41 | 41 |
|
42 | 42 | # Author: Romain Tavenard, Felix Divo |
|
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