Unsupervised Representation Learning for Time Series with Temporal Neighborhood Coding (2106.00750v1)

Abstract: Time series are often complex and rich in information but sparsely labeled and therefore challenging to model. In this paper, we propose a self-supervised framework for learning generalizable representations for non-stationary time series. Our approach, called Temporal Neighborhood Coding (TNC), takes advantage of the local smoothness of a signal's generative process to define neighborhoods in time with stationary properties. Using a debiased contrastive objective, our framework learns time series representations by ensuring that in the encoding space, the distribution of signals from within a neighborhood is distinguishable from the distribution of non-neighboring signals. Our motivation stems from the medical field, where the ability to model the dynamic nature of time series data is especially valuable for identifying, tracking, and predicting the underlying patients' latent states in settings where labeling data is practically impossible. We compare our method to recently developed unsupervised representation learning approaches and demonstrate superior performance on clustering and classification tasks for multiple datasets.

Unsupervised Representation Learning for Time Series with Temporal Neighborhood Coding: An In-Depth Analysis

The paper focuses on a novel approach for the unsupervised representation learning of non-stationary time series data, termed Temporal Neighborhood Coding (TNC). TNC operates under the framework of self-supervised learning, which has been prominently used in tasks where labeling is sparse or unavailable. The proposed methodology is particularly motivated by medical applications, where temporal dynamics in patient monitoring data play a crucial role but are often devoid of reliable labels.

Technical Overview

The primary concept driving TNC is the exploitation of local smoothness properties inherent in time series data to establish temporal neighborhoods. These neighborhoods are used to form clusters characterized by stationary properties. The core idea is to ensure that representations of signals from within a defined temporal neighborhood are distinguishable from those of non-neighboring signals in the encoding space. This is achieved by employing a debiased contrastive learning objective that mitigates sampling bias, a common issue in contrastive learning frameworks where negative samples might unintentionally contain instances similar to positive samples.

TNC's effectiveness is contingent on a few critical elements outlined in the paper:

1. Temporal Neighborhood Construction: A Gaussian-based model is used to define temporal neighborhoods. The parameter $\eta$, crucial in determining neighborhood boundaries, is dynamically set based on statistical tests for stationarity using the Augmented Dickey-Fuller (ADF) test.
2. Self-Supervised Framework: The TNC framework comprises an encoder that compresses time series windows into lower-dimensional representations and a discriminator that assesses the likelihood of two representations arising from the same temporal neighborhood.
3. Debiased Contrastive Loss: To counteract the bias of negative sampling, the TNC methodology incorporates techniques from Positive-Unlabeled learning by reweighting the contributions of unlabeled samples—presumed non-neighboring samples—in the loss calculation.

Strong Numerical Results

The paper reports compelling performance of TNC on various datasets, including simulation data, real-world ECG waveform data, and Human Activity Recognition (HAR) data. TNC significantly outperformed other unsupervised frameworks like Contrastive Predictive Coding (CPC) and Triplet Loss on clustering and classification tasks. For example, on the simulation dataset, TNC achieved an Silhouette score of 0.71 compared to CPC’s 0.51, which indicates more distinct clustering of underlying states in the representation space.

Implications and Future Directions

The TNC framework has notable implications for fields where time series are prevalent, notably in healthcare. It provides a means of autonomously extracting meaningful representations from complex, high-dimensional, non-stationary data without the burden of acquiring exhaustive labels. The ability to accurately model patient state transitions could enhance patient monitoring systems, offering clinicians insights into disease progression and stability.

From a theoretical standpoint, TNC's demonstration of leveraging neighborhood smoothness properties in non-stationary data opens avenues for further exploration in unsupervised learning. The adaptive neighborhood boundary estimation suggests potential for integration with domain knowledge, enhancing the contextual richness of the representations learned through TNC.

In conclusion, the paper exhibits TNC as a robust framework for unsupervised representation learning on non-stationary time series, presenting substantial improvements over existing approaches in identification and classification tasks. The methods outlined offer potential applicability beyond the discussed datasets, with various fields able to benefit from the framework's ability to discern complex underlying dynamics autonomously. Future advancements could focus on optimizing computational efficiency and expanding the framework's applicability to a broader spectrum of temporal datasets.