dCMF: Learning interpretable evolving patterns from temporal multiway data

• URL: http://arxiv.org/abs/2502.19367v1
• Date: Wed, 26 Feb 2025 18:04:01 GMT
• Title: dCMF: Learning interpretable evolving patterns from temporal multiway data
• Authors: Christos Chatzis, Carla Schenker, Jérémy E. Cohen, Evrim Acar,
• Abstract summary: We bridge the gap between tensor factorizations and dynamical modeling by exploring the relationship between LDS, Coupled Matrix Factorizations (CMF) and the PARAFAC2 model.<n>We propose a time-aware coupled factorization model called d(ynamical)CMF that constrains the temporal evolution of the latent factors to adhere to a specific LDS structure.
• Score: 0.7285444492473742
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multiway datasets are commonly analyzed using unsupervised matrix and tensor factorization methods to reveal underlying patterns. Frequently, such datasets include timestamps and could correspond to, for example, health-related measurements of subjects collected over time. The temporal dimension is inherently different from the other dimensions, requiring methods that account for its intrinsic properties. Linear Dynamical Systems (LDS) are specifically designed to capture sequential dependencies in the observed data. In this work, we bridge the gap between tensor factorizations and dynamical modeling by exploring the relationship between LDS, Coupled Matrix Factorizations (CMF) and the PARAFAC2 model. We propose a time-aware coupled factorization model called d(ynamical)CMF that constrains the temporal evolution of the latent factors to adhere to a specific LDS structure. Using synthetic datasets, we compare the performance of dCMF with PARAFAC2 and t(emporal)PARAFAC2 which incorporates temporal smoothness. Our results show that dCMF and PARAFAC2-based approaches perform similarly when capturing smoothly evolving patterns that adhere to the PARAFAC2 structure. However, dCMF outperforms alternatives when the patterns evolve smoothly but deviate from the PARAFAC2 structure. Furthermore, we demonstrate that the proposed dCMF method enables to capture more complex dynamics when additional prior information about the temporal evolution is incorporated.

Related papers

• Grassmannian Geometry Meets Dynamic Mode Decomposition in DMD-GEN: A New Metric for Mode Collapse in Time Series Generative Models [0.0]
  Generative models like Generative Adversarial Networks (GANs) and Variational Autoencoders (Es) often fail to capture the full diversity of their training data, leading to mode collapse. We introduce a new definition of mode collapse specific to time series and propose a novel metric, DMD-GEN, to quantify its severity.
  arXiv  Detail & Related papers  (2024-12-15T19:53:17Z)
• tPARAFAC2: Tracking evolving patterns in (incomplete) temporal data [0.7285444492473742]
  We introduce t(emporal)PARAFAC2 which utilizes temporal smoothness regularization on the evolving factors. Our numerical experiments on both simulated and real datasets demonstrate the effectiveness of the temporal smoothness regularization.
  arXiv  Detail & Related papers  (2024-07-01T15:10:55Z)
• Binarized Diffusion Model for Image Super-Resolution [61.963833405167875]
  Binarization, an ultra-compression algorithm, offers the potential for effectively accelerating advanced diffusion models (DMs) Existing binarization methods result in significant performance degradation. We introduce a novel binarized diffusion model, BI-DiffSR, for image SR.
  arXiv  Detail & Related papers  (2024-06-09T10:30:25Z)
• UniTST: Effectively Modeling Inter-Series and Intra-Series Dependencies for Multivariate Time Series Forecasting [98.12558945781693]
  We propose a transformer-based model UniTST containing a unified attention mechanism on the flattened patch tokens. Although our proposed model employs a simple architecture, it offers compelling performance as shown in our experiments on several datasets for time series forecasting.
  arXiv  Detail & Related papers  (2024-06-07T14:39:28Z)
• Adaptive Multi-Scale Decomposition Framework for Time Series Forecasting [26.141054975797868]
  We propose a novel Adaptive Multi-Scale Decomposition (AMD) framework for time series forecasting (TSF) Our framework decomposes time series into distinct temporal patterns at multiple scales, leveraging the Multi-Scale Decomposable Mixing (MDM) block. Our approach effectively models both temporal and channel dependencies and utilizes autocorrelation to refine multi-scale data integration.
  arXiv  Detail & Related papers  (2024-06-06T05:27:33Z)
• Structural Knowledge Informed Continual Multivariate Time Series Forecasting [23.18105409644709]
  We propose a novel Structural Knowledge Informed Continual Learning (SKI-CL) framework to perform MTS forecasting within a continual learning paradigm. Specifically, we develop a forecasting model based on graph structure learning, where a consistency regularization scheme is imposed between the learned variable dependencies and the structural knowledge. We develop a representation-matching memory replay scheme that maximizes the temporal coverage of MTS data to efficiently preserve the underlying temporal dynamics and dependency structures of each regime.
  arXiv  Detail & Related papers  (2024-02-20T05:11:20Z)
• Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspective [63.60312929416228]
  textbftextitAttraos incorporates chaos theory into long-term time series forecasting. We show that Attraos outperforms various LTSF methods on mainstream datasets and chaotic datasets with only one-twelfth of the parameters compared to PatchTST.
  arXiv  Detail & Related papers  (2024-02-18T05:35:01Z)
• Causal Temporal Regime Structure Learning [49.77103348208835]
  We present CASTOR, a novel method that concurrently learns the Directed Acyclic Graph (DAG) for each regime.<n>We establish the identifiability of the regimes and DAGs within our framework.<n>Experiments show that CASTOR consistently outperforms existing causal discovery models.
  arXiv  Detail & Related papers  (2023-11-02T17:26:49Z)
• A Time-aware tensor decomposition for tracking evolving patterns [0.7958824725263767]
  Time-evolving data sets can often be arranged as a higher-order tensor with one of the modes being the time mode. While tensor factorizations have been successfully used to capture the underlying patterns in such higher-order data sets, the temporal aspect is often ignored. We propose temporal PARAFAC2: a PARAFAC2-based tensor factorization method with temporal regularization to extract gradually evolving patterns from temporal data.
  arXiv  Detail & Related papers  (2023-08-14T13:13:50Z)
• Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations [58.720142291102135]
  Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract coherent schemes. This paper proposes a strategy to enable DMD to extract from observations with different mesh topologies and dimensions.
  arXiv  Detail & Related papers  (2021-04-28T22:14:25Z)
• TAM: Temporal Adaptive Module for Video Recognition [60.83208364110288]
  temporal adaptive module (bf TAM) generates video-specific temporal kernels based on its own feature map. Experiments on Kinetics-400 and Something-Something datasets demonstrate that our TAM outperforms other temporal modeling methods consistently.
  arXiv  Detail & Related papers  (2020-05-14T08:22:45Z)

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.