Binary Shapelet Transform for Multiclass Time Series Classification

Shapelets have recently been proposed as a new primitive for time series classification. Shapelets are subseries of series that best split the data into its classes. In the original research, shapelets were found recursively within a decision tree through enumeration of the search space. Subsequent research indicated that using shapelets as the basis for transforming datasets leads to more accurate classifiers. Both these approaches evaluate how well a shapelet splits all the classes. However, often a shapelet is most useful in distinguishing between members of the class of the series it was drawn from against all others. To assess this conjecture, we evaluate a one vs all encoding scheme. This technique simplifies the quality assessment calculations, speeds up the execution through facilitating more frequent early abandon and increases accuracy for multi-class problems. We also propose an alternative shapelet evaluation scheme which we demonstrate significantly speeds up the full search

Classification of time series by shapelet transformation

Time-series classification (TSC) problems present a specific challenge for classification algorithms: how to measure similarity between series. A \emph{shapelet} is a time-series subsequence that allows for TSC based on local, phase-independent similarity in shape. Shapelet-based classification uses the similarity between a shapelet and a series as a discriminatory feature. One benefit of the shapelet approach is that shapelets are comprehensible, and can offer insight into the problem domain. The original shapelet-based classifier embeds the shapelet-discovery algorithm in a decision tree, and uses information gain to assess the quality of candidates, finding a new shapelet at each node of the tree through an enumerative search. Subsequent research has focused mainly on techniques to speed up the search. We examine how best to use the shapelet primitive to construct classifiers. We propose a single-scan shapelet algorithm that finds the best $k$ shapelets, which are used to produce a transformed dataset, where each of the $k$ features represent the distance between a time series and a shapelet. The primary advantages over the embedded approach are that the transformed data can be used in conjunction with any classifier, and that there is no recursive search for shapelets. We demonstrate that the transformed data, in conjunction with more complex classifiers, gives greater accuracy than the embedded shapelet tree. We also evaluate three similarity measures that produce equivalent results to information gain in less time. Finally, we show that by conducting post-transform clustering of shapelets, we can enhance the interpretability of the transformed data. We conduct our experiments on 29 datasets: 17 from the UCR repository, and 12 we provide ourselve

Deconvolution with Shapelets

We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and compare it to other published approaches. We show that convolution in shapelet space leads to a shapelet model of order $n_{max}^h = n_{max}^g + n_{max}^f$ with $n_{max}^f$ and $n_{max}^g$ being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation which maps a certain number of convolved coefficients onto a generally smaller number of deconvolved coefficients. By inferring the latter number from data, we construct the maximum-likelihood solution for this transformation and obtain unbiased shear estimates with a remarkable amount of noise reduction compared to established approaches. This finding is particularly valid for complicated PSF models and low $S/N$ images, which renders our approach suitable for typical weak-lensing conditions.Comment: 9 pages, 9 figures, submitted to A&

Ensembles of Randomized Time Series Shapelets Provide Improved Accuracy while Reducing Computational Costs

Shapelets are discriminative time series subsequences that allow generation of interpretable classification models, which provide faster and generally better classification than the nearest neighbor approach. However, the shapelet discovery process requires the evaluation of all possible subsequences of all time series in the training set, making it extremely computation intensive. Consequently, shapelet discovery for large time series datasets quickly becomes intractable. A number of improvements have been proposed to reduce the training time. These techniques use approximation or discretization and often lead to reduced classification accuracy compared to the exact method. We are proposing the use of ensembles of shapelet-based classifiers obtained using random sampling of the shapelet candidates. Using random sampling reduces the number of evaluated candidates and consequently the required computational cost, while the classification accuracy of the resulting models is also not significantly different than that of the exact algorithm. The combination of randomized classifiers rectifies the inaccuracies of individual models because of the diversity of the solutions. Based on the experiments performed, it is shown that the proposed approach of using an ensemble of inexpensive classifiers provides better classification accuracy compared to the exact method at a significantly lesser computational cost