Exact Mean Computation in Dynamic Time Warping Spaces

Dynamic time warping constitutes a major tool for analyzing time series. In particular, computing a mean series of a given sample of series in dynamic time warping spaces (by minimizing the Fr\'echet function) is a challenging computational problem, so far solved by several heuristic and inexact strategies. We spot some inaccuracies in the literature on exact mean computation in dynamic time warping spaces. Our contributions comprise an exact dynamic program computing a mean (useful for benchmarking and evaluating known heuristics). Based on this dynamic program, we empirically study properties like uniqueness and length of a mean. Moreover, experimental evaluations reveal substantial deficits of state-of-the-art heuristics in terms of their output quality. We also give an exact polynomial-time algorithm for the special case of binary time series

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

Representative Scanpath Identification for Group Viewing Pattern Analysis

Scanpaths are composed of fixations and saccades. Viewing trends reflected by scanpaths play an important role in scientific studies like saccadic model evaluation and real-life applications like artistic design. Several scanpath synthesis methods have been proposed to obtain a scanpath that is representative of the group viewing trend. But most of them either target a specific category of viewing materials like webpages or leave out some useful information like gaze duration. Our previous work defined the representative scanpath as the barycenter of a group of scanpaths, which actually shows the averaged shape of multiple scanpaths. In this paper, we extend our previous framework to take gaze duration into account, obtaining representative scanpaths that describe not only attention distribution and shift but also attention span. The extended framework consists of three steps: Eye-gaze data preprocessing, scanpath aggregation and gaze duration analysis. Experiments demonstrate that the framework can well serve the purpose of mining viewing patterns and “barycenter” based representative scanpaths can better characterize the pattern

SymED: Adaptive and Online Symbolic Representation of Data on the Edge

The edge computing paradigm helps handle the Internet of Things (IoT) generated data in proximity to its source. Challenges occur in transferring, storing, and processing this rapidly growing amount of data on resource-constrained edge devices. Symbolic Representation (SR) algorithms are promising solutions to reduce the data size by converting actual raw data into symbols. Also, they allow data analytics (e.g., anomaly detection and trend prediction) directly on symbols, benefiting large classes of edge applications. However, existing SR algorithms are centralized in design and work offline with batch data, which is infeasible for real-time cases. We propose SymED - Symbolic Edge Data representation method, i.e., an online, adaptive, and distributed approach for symbolic representation of data on edge. SymED is based on the Adaptive Brownian Bridge-based Aggregation (ABBA), where we assume low-powered IoT devices do initial data compression (senders) and the more robust edge devices do the symbolic conversion (receivers). We evaluate SymED by measuring compression performance, reconstruction accuracy through Dynamic Time Warping (DTW) distance, and computational latency. The results show that SymED is able to (i) reduce the raw data with an average compression rate of 9.5%; (ii) keep a low reconstruction error of 13.25 in the DTW space; (iii) simultaneously provide real-time adaptability for online streaming IoT data at typical latencies of 42ms per symbol, reducing the overall network traffic.Comment: 14 pages, 5 figure