At the light of regularized dynamic time warping kernels, this paper reconsider the concept of time elastic centroid (TEC) for a set of time series. From this perspective, we show first how TEC can easily be addressed as a preimage problem. Unfortuna
tely this preimage problem is ill-posed, may suffer from over-fitting especially for long time series and getting a sub-optimal solution involves heavy computational costs. We then derive two new algorithms based on a probabilistic interpretation of kernel alignment matrices that expresses in terms of probabilistic distributions over sets of alignment paths. The first algorithm is an iterative agglomerative heuristics inspired from the state of the art DTW barycenter averaging (DBA) algorithm proposed specifically for the Dynamic Time Warping measure. The second proposed algorithm achieves a classical averaging of the aligned samples but also implements an averaging of the time of occurrences of the aligned samples. It exploits a straightforward progressive agglomerative heuristics. An experimentation that compares for 45 time series datasets classification error rates obtained by first near neighbors classifiers exploiting a single medoid or centroid estimate to represent each categories show that: i) centroids based approaches significantly outperform medoids based approaches, ii) on the considered experience, the two proposed algorithms outperform the state of the art DBA algorithm, and iii) the second proposed algorithm that implements an averaging jointly in the sample space and along the time axes emerges as the most significantly robust time elastic averaging heuristic with an interesting noise reduction capability. Index Terms-Time series averaging Time elastic kernel Dynamic Time Warping Time series clustering and classification.
We address in this paper the co-clustering and co-classification of bilingual data laying in two linguistic similarity spaces when a comparability measure defining a mapping between these two spaces is available. A new approach that we can characteri
zed as a three-mode analysis scheme, is proposed to mix the comparability measure with the two similarity measures. Our aim is to improve jointly the accuracy of classification and clustering tasks performed in each of the two linguistic spaces, as well as the quality of the final alignment of comparable clusters that can be obtained. We used first some purely synthetic random data sets to assess our formal similarity-comparability mixing model. We then propose two variants of the comparability measure that has been defined by (Li and Gaussier 2010) in the context of bilingual lexicon extraction to adapt it to clustering or categorizing tasks. These two variant measures are subsequently used to evaluate our similarity-comparability mixing model in the context of the co-classification and co-clustering of comparable textual data sets collected from Wikipedia categories for the English and French languages. Our experiments show clear improvements in clustering and classification accuracies when mixing comparability with similarity measures, with, as expected, a higher robustness obtained when the two comparability variant measures that we propose are used. We believe that this approach is particularly well suited for the construction of thematic comparable corpora of controllable quality.
