Automatic Reassembly Method of 3D Thin-wall Fragments Based on Derivative Dynamic Time Warping

In order to address the automatic virtual reassembling of 3D thin-wall fragments, this paper proposes a 3D fragment reassembly method based on derivative dynamic time warping. Firstly, a calculation method of discrete curvature and torsion is designed to solve the difficulty of calculating curvature and torsion of discrete data points and eliminate effectively the noise interferences in the calculation process. Then, it takes curvature and torsion as the feature descriptors of the curve, searches the candidate matching line segments by the derivative dynamic time warping (DDTW) method with the feature descriptors, and records the positions of the starting and ending points of each candidate matching segment. After that, it designs a voting mechanism with the geometric invariant as the constraint information to select further the optimal matching line segments. Finally, it adopts the least squares method to estimate the rotation and transformation matrices and uses the iterative closest point (ICP) method to complete the reassembly of fragments. The experimental results show that the reassembly error is less than 1mm and that the reassembly effect is good. The method can solve the 3D curve matching in case there are partial feature defects, and can achieve the virtual restoration of the broken thin-wall fragment model quickly and effectively

An Experimental Evaluation of Nearest Neighbour Time Series Classification

Data mining research into time series classification (TSC) has focussed on alternative distance measures for nearest neighbour classifiers. It is standard practice to use 1-NN with Euclidean or dynamic time warping (DTW) distance as a straw man for comparison. As part of a wider investigation into elastic distance measures for TSC~\cite{lines14elastic}, we perform a series of experiments to test whether this standard practice is valid. Specifically, we compare 1-NN classifiers with Euclidean and DTW distance to standard classifiers, examine whether the performance of 1-NN Euclidean approaches that of 1-NN DTW as the number of cases increases, assess whether there is any benefit of setting $k$ for $k$-NN through cross validation whether it is worth setting the warping path for DTW through cross validation and finally is it better to use a window or weighting for DTW. Based on experiments on 77 problems, we conclude that 1-NN with Euclidean distance is fairly easy to beat but 1-NN with DTW is not, if window size is set through cross validation

Time series classification with ensembles of elastic distance measures

Several alternative distance measures for comparing time series have recently been proposed and evaluated on time series classification (TSC) problems. These include variants of dynamic time warping (DTW), such as weighted and derivative DTW, and edit distance-based measures, including longest common subsequence, edit distance with real penalty, time warp with edit, and move–split–merge. These measures have the common characteristic that they operate in the time domain and compensate for potential localised misalignment through some elastic adjustment. Our aim is to experimentally test two hypotheses related to these distance measures. Firstly, we test whether there is any significant difference in accuracy for TSC problems between nearest neighbour classifiers using these distance measures. Secondly, we test whether combining these elastic distance measures through simple ensemble schemes gives significantly better accuracy. We test these hypotheses by carrying out one of the largest experimental studies ever conducted into time series classification. Our first key finding is that there is no significant difference between the elastic distance measures in terms of classification accuracy on our data sets. Our second finding, and the major contribution of this work, is to define an ensemble classifier that significantly outperforms the individual classifiers. We also demonstrate that the ensemble is more accurate than approaches not based in the time domain. Nearly all TSC papers in the data mining literature cite DTW (with warping window set through cross validation) as the benchmark for comparison. We believe that our ensemble is the first ever classifier to significantly outperform DTW and as such raises the bar for future work in this area