Times series averaging from a probabilistic interpretation of time-elastic kernel

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. Unfortunately 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

Automatic Analysis of Facial Expressions Based on Deep Covariance Trajectories

In this paper, we propose a new approach for facial expression recognition using deep covariance descriptors. The solution is based on the idea of encoding local and global Deep Convolutional Neural Network (DCNN) features extracted from still images, in compact local and global covariance descriptors. The space geometry of the covariance matrices is that of Symmetric Positive Definite (SPD) matrices. By conducting the classification of static facial expressions using Support Vector Machine (SVM) with a valid Gaussian kernel on the SPD manifold, we show that deep covariance descriptors are more effective than the standard classification with fully connected layers and softmax. Besides, we propose a completely new and original solution to model the temporal dynamic of facial expressions as deep trajectories on the SPD manifold. As an extension of the classification pipeline of covariance descriptors, we apply SVM with valid positive definite kernels derived from global alignment for deep covariance trajectories classification. By performing extensive experiments on the Oulu-CASIA, CK+, and SFEW datasets, we show that both the proposed static and dynamic approaches achieve state-of-the-art performance for facial expression recognition outperforming many recent approaches.Comment: A preliminary version of this work appeared in "Otberdout N, Kacem A, Daoudi M, Ballihi L, Berretti S. Deep Covariance Descriptors for Facial Expression Recognition, in British Machine Vision Conference 2018, BMVC 2018, Northumbria University, Newcastle, UK, September 3-6, 2018. ; 2018 :159." arXiv admin note: substantial text overlap with arXiv:1805.0386

Transformation Based Ensembles for Time Series Classification

Until recently, the vast majority of data mining time series classification (TSC) research has focused on alternative distance measures for 1-Nearest Neighbour (1-NN) classifiers based on either the raw data, or on compressions or smoothing of the raw data. Despite the extensive evidence in favour of 1-NN classifiers with Euclidean or Dynamic Time Warping distance, there has also been a flurry of recent research publications proposing classification algorithms for TSC. Generally, these classifiers describe different ways of incorporating summary measures in the time domain into more complex classifiers. Our hypothesis is that the easiest way to gain improvement on TSC problems is simply to transform into an alternative data space where the discriminatory features are more easily detected. To test our hypothesis, we perform a range of benchmarking experiments in the time domain, before evaluating nearest neighbour classifiers on data transformed into the power spectrum, the autocorrelation function, and the principal component space. We demonstrate that on some problems there is dramatic improvement in the accuracy of classifiers built on the transformed data over classifiers built in the time domain, but that there is also a wide variance in accuracy for a particular classifier built on different data transforms. To overcome this variability, we propose a simple transformation based ensemble, then demonstrate that it improves performance and reduces the variability of classifiers built in the time domain only. Our advice to a practitioner with a real world TSC problem is to try transforms before developing a complex classifier; it is the easiest way to get a potentially large increase in accuracy, and may provide further insights into the underlying relationships that characterise the problem