| Description: | Grabocka $et\:al.$ describe a shapelet discovery algorithm that adopts a heuristic gradient descent shapelet search procedure rather than enumeration. LS finds $k$ shapelets that, unlike FS and ST, are not restricted to being subseries in the training data. The $k$ shapelets are initialised through a $k$-means clustering of candidates from the training data. The objective function for the optimisation process is a logistic loss function (with regularization term) $L$ based on a logistic regression model for each class. The algorithm jointly learns the weights for the regression ${\bf W}$, and the shapelets ${\bf S}$ in a two stage iterative process to produce a final logistic regression model.
Algorithm 11 gives a high level view of the algorithm. LS restricts the search to shapelets of length
$\{L^{min},2L^{min},\ldots,RL^{min}\}.$ A check is performed at certain intervals as to whether divergence has occurred (line 7). This is defined as a train set error of 1 or infinite loss. The check is performed when half the number of allowed iterations is complete. This criteria meant that for some problems, LS never terminated during model selection. Hence we limited the the algorithm to a maximum of five restarts. |
