Analyzing numerous or long time series is difficult in practice due to the high storage costs and computational requirements. Therefore, techniques have been proposed to generate compact similarity-preserving representations of time series, enabling real-time similarity search on large in-memory data collections. However, the existing techniques are not ideally suited for assessing similarity when sequences are locally out of phase. In this paper, we propose the use of product quantization for efficient similarity-based comparison of time series under time warping. The idea is to first compress the data by partitioning the time series into equal length sub-sequences which are represented by a short code. The distance between two time series can then be efficiently approximated by pre-computed elastic distances between their codes. The partitioning into sub-sequences forces unwanted alignments, which we address with a pre-alignment step using the maximal overlap discrete wavelet transform (MODWT). To demonstrate the efficiency and accuracy of our method, we perform an extensive experimental evaluation on benchmark datasets in nearest neighbors classification and clustering applications. Overall, the proposed solution emerges as a highly efficient (both in terms of memory usage and computation time) replacement for elastic measures in time series applications.
Université de Bretagne Sud（南布列塔尼大学）；IRISA（法国国家信息与自动化研究所/雷恩信息与自动化研究所（IRISA为法国国家科学研究中心与雷恩第一大学等共建的信息与自动化研究所，通用译名为IRISA研究所））
This paper proposes a framework dedicated to the construction of what we call discrete elastic inner product allowing one to embed sets of non-uniformly sampled multivariate time series or sequences of varying lengths into inner product space structures. This framework is based on a recursive definition that covers the case of multiple embedded time elastic dimensions. We prove that such inner products exist in our general framework and show how a simple instance of this inner product class operates on some prospective applications, while generalizing the Euclidean inner product. Classificatio…
The majority of machine learning algorithms assumes that objects are represented as vectors. But often the objects we want to learn on are more naturally represented by other data structures such as sequences and time series. For these representations many standard learning algorithms are unavailable. We generalize gradient-based learning algorithms to time series under dynamic time warping. To this end, we introduce elastic functions, which extend functions on time series to matrix spaces. Necessary conditions are presented under which generalized gradient learning on time series is consisten…
This paper contributes multivariate versions of seven commonly used elastic similarity and distance measures for time series data analytics. Elastic similarity and distance measures are a class of similarity measures that can compensate for misalignments in the time axis of time series data. We adapt two existing strategies used in a multivariate version of the well-known Dynamic Time Warping (DTW), namely, Independent and Dependent DTW, to these seven measures. While these measures can be applied to various time series analysis tasks, we demonstrate their utility on multivariate time series c…
UMR CNRS IRISA（法国国家科学研究中心UMR IRISA实验室）；Université de Bretagne Sud（南布列塔尼大学）
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 alignm…
FP=xINT:Representing Neural Networks via Low-Bit Series Basis Functions
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Pengcheng Laboratory（鹏城实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Harbin Institute of Technology（哈尔滨工业大学）；South China University of Technology（华南理工大学）
UMR CNRS IRISA（法国国家科学研究中心UMR IRISA实验室）；Université Bretagne Sud（南布列塔尼大学）
In the light of regularized dynamic time warping kernels, this paper re-considers the concept of time elastic centroid for a setof time series. We derive a new algorithm based on a probabilistic interpretation of kernel alignment matrices. This algorithm expressesthe averaging process in terms of a stochastic alignment automata. It uses an iterative agglomerative heuristic method for averagingthe aligned samples, while also averaging the times of occurrence of the aligned samples. By comparing classification accuracies for45 heterogeneous time series datasets obtained by first nearest centroid…
Nearest neighbor search under elastic distances is a key tool for time series analysis, supporting many applications. However, straightforward implementations of distances require $O(n^2)$ space and time complexities, preventing these applications from scaling to long series. Much work has been devoted to speeding up the NN search process, mostly with the development of lower bounds, allowing to avoid costly distance computations when a given threshold is exceeded. This threshold, provided by the similarity search process, also allows to early abandon the computation of a distance itself. Anot…
Data-driven Force Observer for Human-Robot Interaction with Series Elastic Actuators using Gaussian Processes
Technical University of Munich（慕尼黑工业大学）；TUM School of Computation, Information and Technology（慕尼黑工业大学计算、信息与技术学院）；BioRobotics Institute, Scuola Superiore Sant’Anna（圣安娜高等学校生物机器人研究所）；ETH Zurich（苏黎世联邦理工学院）
The nearest neighbor method together with the dynamic time warping (DTW) distance is one of the most popular approaches in time series classification. This method suffers from high storage and computation requirements for large training sets. As a solution to both drawbacks, this article extends learning vector quantization (LVQ) from Euclidean spaces to DTW spaces. The proposed LVQ scheme uses asymmetric weighted averaging as update rule. Empirical results exhibited superior performance of asymmetric generalized LVQ (GLVQ) over other state-of-the-art prototype generation methods for nearest n…
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 a…
Effectiveness of High-Dimensional Distance Metrics on Solar Flare Time Series
Department of Computer Science, University of Missouri-St. Louis, USA（计算机科学系，密苏里大学圣路易斯分校）；Bay Area Environmental Research Institute, NASA Research Park, Moffett Field, CA 94035, USA（湾区环境研究机构，NASA研究园，莫菲特场，CA 94035，USA）；Lockheed Martin Solar and Astrophysics Laboratory, 3251 Hanover Street, Building 203, Palo Alto, CA 94306, USA（洛克希德马丁太阳与天体物理学实验室，3251汉诺威街，203号楼，帕洛阿尔托，CA 94306，USA）
