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Learning Without Augmenting: Unsupervised Time Series Representation Learning via Frame Projections

Berken Utku Demirel, Christian Holz

TL;DR

This work tackles self-supervised learning for temporal sequences without handcrafted augmentations by projecting data into an orthonormal Fourier basis and an overcomplete Gabor frame to create multiple, information-rich views. It trains with cross-domain instance discrimination across time, frequency, and time–frequency domains, leveraging a pair of lightweight latent-space mappers to translate across latent manifolds. The approach yields consistent improvements across nine datasets and five tasks, with up to 15–20% gains and strong cross-domain generalization, while maintaining competitive inference costs. The findings suggest that exploiting intrinsic geometric biases via principled transformations can outperform augmentation-heavy SSL, offering a path toward augmentation-free generalization in time-series representation learning.

Abstract

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data. Most SSL approaches rely on strong, well-established, handcrafted data augmentations to generate diverse views for representation learning. However, designing such augmentations requires domain-specific knowledge and implicitly imposes representational invariances on the model, which can limit generalization. In this work, we propose an unsupervised representation learning method that replaces augmentations by generating views using orthonormal bases and overcomplete frames. We show that embeddings learned from orthonormal and overcomplete spaces reside on distinct manifolds, shaped by the geometric biases introduced by representing samples in different spaces. By jointly leveraging the complementary geometry of these distinct manifolds, our approach achieves superior performance without artificially increasing data diversity through strong augmentations. We demonstrate the effectiveness of our method on nine datasets across five temporal sequence tasks, where signal-specific characteristics make data augmentations particularly challenging. Without relying on augmentation-induced diversity, our method achieves performance gains of up to 15--20\% over existing self-supervised approaches. Source code: https://github.com/eth-siplab/Learning-with-FrameProjections

Learning Without Augmenting: Unsupervised Time Series Representation Learning via Frame Projections

TL;DR

This work tackles self-supervised learning for temporal sequences without handcrafted augmentations by projecting data into an orthonormal Fourier basis and an overcomplete Gabor frame to create multiple, information-rich views. It trains with cross-domain instance discrimination across time, frequency, and time–frequency domains, leveraging a pair of lightweight latent-space mappers to translate across latent manifolds. The approach yields consistent improvements across nine datasets and five tasks, with up to 15–20% gains and strong cross-domain generalization, while maintaining competitive inference costs. The findings suggest that exploiting intrinsic geometric biases via principled transformations can outperform augmentation-heavy SSL, offering a path toward augmentation-free generalization in time-series representation learning.

Abstract

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data. Most SSL approaches rely on strong, well-established, handcrafted data augmentations to generate diverse views for representation learning. However, designing such augmentations requires domain-specific knowledge and implicitly imposes representational invariances on the model, which can limit generalization. In this work, we propose an unsupervised representation learning method that replaces augmentations by generating views using orthonormal bases and overcomplete frames. We show that embeddings learned from orthonormal and overcomplete spaces reside on distinct manifolds, shaped by the geometric biases introduced by representing samples in different spaces. By jointly leveraging the complementary geometry of these distinct manifolds, our approach achieves superior performance without artificially increasing data diversity through strong augmentations. We demonstrate the effectiveness of our method on nine datasets across five temporal sequence tasks, where signal-specific characteristics make data augmentations particularly challenging. Without relying on augmentation-induced diversity, our method achieves performance gains of up to 15--20\% over existing self-supervised approaches. Source code: https://github.com/eth-siplab/Learning-with-FrameProjections
Paper Structure (90 sections, 4 theorems, 36 equations, 8 figures, 18 tables, 2 algorithms)

This paper contains 90 sections, 4 theorems, 36 equations, 8 figures, 18 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Method
  3. Notations
  4. Setup
  5. Orthonormal Bases and Overcomplete Frames
  6. Instance Discrimination
  7. Invariances
  8. Collections of Manifolds
  9. Experiments
  10. Datasets
  11. Heart rate
  12. Activity recognition
  13. Cardiovascular disease (CVD) classification
  14. Step counting
  15. Sleep stage classification
  16. ...and 75 more sections

Key Result

Proposition 2.1

Let $f_d^{\ast}$ denote an optimal encoder under NT-Xent for domain $d \in \{t,\mathcal{F},\mathcal{W}\}$. If for some unintended transformation $W$, the encoder is invariant, i.e., $f_d^{\ast}(W\mathrm{x}) = f_d^{\ast}(\mathrm{x}),$ then for any anchor sample $x$ the NT-Xent loss across domains is where $K \geq 1$ is the number of negatives that become near-positives due to the invariance.

Figures (8)

  • Figure 1: Overview of our method. (a) Original data and its transformed versions. The Fourier transformation is given in polar coordinates where we feed to the model magnitude and angle of each harmonic separately. (b) Representations $\boldsymbol{h}$ from each encoder lie on distinct manifolds $\mathcal{M}$, with latent mappers $\Phi^{t \rightarrow d}_{\boldsymbol{h}}$ translating across domain-specific spaces. (c) Embeddings $\boldsymbol{z}$ from each projection, with non-linear mappers used during pre-training to improve predictability across spaces.
  • Figure 2: Radial histograms illustrating angle distributions. (a) Top: Angle density of $\arccos( \langle \boldsymbol{h}^{(t)}, \boldsymbol{h}^{(\mathcal{F})} \rangle )$; Bottom: Angle density of $\Delta_{ij}$. (b) Same illustration from the Gabor wavelet $\boldsymbol{h}^{(\mathcal{W})}$. In both cases, representations of the same samples across domains approach orthogonality, while pairwise angle differences remain widely distributed.
  • Figure 3: Performance of our method on DaLiA (a) using correlation ($\rho$) and on Chapman (b) using F1 score, compared to other self-supervised learning techniques. Barlow Twins is abbreviated as (BWTW), and backbone sizes are shown in millions of parameters. The red circle in each plot denotes our method, which achieves higher performance with fewer parameters.
  • Figure 4: Performance comparison across datasets, (a) DaLiA ($\rho$), (b) HHAR (F1), and (c) Chapman (F1), when adding a third view for instance discrimination similar to our method. While prior methods benefit from the additional view, their performance still lags behind our approach by a large margin.
  • Figure 5: Pairwise $\ell_2$ distance comparisons across domains and datasets for heart rate estimation.
  • ...and 3 more figures

Theorems & Definitions (8)

  • Proposition 2.1
  • proof
  • Proposition 2.2: Angle Concentration vs. Pairwise Spread
  • proof
  • Proposition A.1: Angle Concentration vs. Pairwise Spread
  • proof
  • Proposition A.2
  • proof