845 research outputs found
On Recursive Edit Distance Kernels with Application to Time Series Classification
This paper proposes some extensions to the work on kernels dedicated to
string or time series global alignment based on the aggregation of scores
obtained by local alignments. The extensions we propose allow to construct,
from classical recursive definition of elastic distances, recursive edit
distance (or time-warp) kernels that are positive definite if some sufficient
conditions are satisfied. The sufficient conditions we end-up with are original
and weaker than those proposed in earlier works, although a recursive
regularizing term is required to get the proof of the positive definiteness as
a direct consequence of the Haussler's convolution theorem. The classification
experiment we conducted on three classical time warp distances (two of which
being metrics), using Support Vector Machine classifier, leads to conclude
that, when the pairwise distance matrix obtained from the training data is
\textit{far} from definiteness, the positive definite recursive elastic kernels
outperform in general the distance substituting kernels for the classical
elastic distances we have tested.Comment: 14 page
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
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