Correlating Time Series with Interpretable Convolutional Kernels

• URL: http://arxiv.org/abs/2409.01362v1
• Date: Mon, 2 Sep 2024 16:29:21 GMT
• Title: Correlating Time Series with Interpretable Convolutional Kernels
• Authors: Xinyu Chen, HanQin Cai, Fuqiang Liu, Jinhua Zhao,
• Abstract summary: This study addresses the problem of convolutional kernel learning in time series data. We use tensor computations to reformulate the convolutional kernel learning problem in the form of tensors. This study lays an insightful foundation for automatically learning convolutional kernels from time series data.
• Score: 18.77493756204539
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This study addresses the problem of convolutional kernel learning in univariate, multivariate, and multidimensional time series data, which is crucial for interpreting temporal patterns in time series and supporting downstream machine learning tasks. First, we propose formulating convolutional kernel learning for univariate time series as a sparse regression problem with a non-negative constraint, leveraging the properties of circular convolution and circulant matrices. Second, to generalize this approach to multivariate and multidimensional time series data, we use tensor computations, reformulating the convolutional kernel learning problem in the form of tensors. This is further converted into a standard sparse regression problem through vectorization and tensor unfolding operations. In the proposed methodology, the optimization problem is addressed using the existing non-negative subspace pursuit method, enabling the convolutional kernel to capture temporal correlations and patterns. To evaluate the proposed model, we apply it to several real-world time series datasets. On the multidimensional rideshare and taxi trip data from New York City and Chicago, the convolutional kernels reveal interpretable local correlations and cyclical patterns, such as weekly seasonality. In the context of multidimensional fluid flow data, both local and nonlocal correlations captured by the convolutional kernels can reinforce tensor factorization, leading to performance improvements in fluid flow reconstruction tasks. Thus, this study lays an insightful foundation for automatically learning convolutional kernels from time series data, with an emphasis on interpretability through sparsity and non-negativity constraints.

Related papers

• Dynamic Multi-Network Mining of Tensor Time Series [8.59982222642104]
  Subsequence clustering of time series is an essential task in data mining. We present a new method, Dynamic Multinetwork time series clustering (DMM) Our method outperforms the state-of-the-art methods in terms of clustering accuracy.
  arXiv  Detail & Related papers  (2024-02-19T02:06:04Z)
• Diffeomorphic Transformations for Time Series Analysis: An Efficient Approach to Nonlinear Warping [0.0]
  The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods. Traditional distance measures such as the Euclidean are not well-suited due to the time-dependent nature of the data. This thesis proposes novel elastic alignment methods that use parametric & diffeomorphic warping transformations.
  arXiv  Detail & Related papers  (2023-09-25T10:51:47Z)
• Correlation-aware Spatial-Temporal Graph Learning for Multivariate Time-series Anomaly Detection [67.60791405198063]
  We propose a correlation-aware spatial-temporal graph learning (termed CST-GL) for time series anomaly detection. CST-GL explicitly captures the pairwise correlations via a multivariate time series correlation learning module. A novel anomaly scoring component is further integrated into CST-GL to estimate the degree of an anomaly in a purely unsupervised manner.
  arXiv  Detail & Related papers  (2023-07-17T11:04:27Z)
• Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models [61.10851158749843]
  Key insights can be obtained by discovering lead-lag relationships inherent in the data. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models.
  arXiv  Detail & Related papers  (2023-05-11T10:30:35Z)
• Nonparametric Factor Trajectory Learning for Dynamic Tensor Decomposition [20.55025648415664]
  We propose NON FActor Trajectory learning for dynamic tensor decomposition (NONFAT) We use a second-level GP to sample the entry values and to capture the temporal relationship between the entities. We have shown the advantage of our method in several real-world applications.
  arXiv  Detail & Related papers  (2022-07-06T05:33:00Z)
• Multi-scale Attention Flow for Probabilistic Time Series Forecasting [68.20798558048678]
  We propose a novel non-autoregressive deep learning model, called Multi-scale Attention Normalizing Flow(MANF) Our model avoids the influence of cumulative error and does not increase the time complexity. Our model achieves state-of-the-art performance on many popular multivariate datasets.
  arXiv  Detail & Related papers  (2022-05-16T07:53:42Z)
• Convolutional generative adversarial imputation networks for spatio-temporal missing data in storm surge simulations [86.5302150777089]
  Generative Adversarial Imputation Nets (GANs) and GAN-based techniques have attracted attention as unsupervised machine learning methods. We name our proposed method as Con Conval Generative Adversarial Imputation Nets (Conv-GAIN)
  arXiv  Detail & Related papers  (2021-11-03T03:50:48Z)
• Hankel-structured Tensor Robust PCA for Multivariate Traffic Time Series Anomaly Detection [9.067182100565695]
  This study proposes a Hankel-structured tensor version of RPCA for anomaly detection in spatial data. We decompose the corrupted matrix into a low-rank Hankel tensor and a sparse matrix. We evaluate the method by synthetic data and passenger flow time series.
  arXiv  Detail & Related papers  (2021-10-08T19:35:39Z)
• Neural Ordinary Differential Equation Model for Evolutionary Subspace Clustering and Its Applications [36.700813256689656]
  We propose a neural ODE model for evolutionary subspace clustering to overcome this limitation. We demonstrate that this method can not only interpolate data at any time step for the evolutionary subspace clustering task, but also achieve higher accuracy than other state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-07-22T07:02:03Z)
• Contrastive learning of strong-mixing continuous-time stochastic processes [53.82893653745542]
  Contrastive learning is a family of self-supervised methods where a model is trained to solve a classification task constructed from unlabeled data. We show that a properly constructed contrastive learning task can be used to estimate the transition kernel for small-to-mid-range intervals in the diffusion case.
  arXiv  Detail & Related papers  (2021-03-03T23:06:47Z)
• Convolutional Tensor-Train LSTM for Spatio-temporal Learning [116.24172387469994]
  We propose a higher-order LSTM model that can efficiently learn long-term correlations in the video sequence. This is accomplished through a novel tensor train module that performs prediction by combining convolutional features across time. Our results achieve state-of-the-art performance-art in a wide range of applications and datasets.
  arXiv  Detail & Related papers  (2020-02-21T05:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.