SOM-CPC: UNSUPERVISED CONTRASTIVE LEARNING WITH SELF-ORGANIZING MAPS FOR STRUCTURED REPRESENTATIONS OF HIGH-RATE TIME SERIES

Abstract

Continuous monitoring with an ever-increasing number of sensors has become ubiquitous across many application domains. Acquired data are typically highdimensional and difficult to interpret, but they are also hypothesized to lie on a lowdimensional manifold. Dimensionality reduction techniques have, therefore, been sought for. Recently, expressive non-linear deep learning (DL) models have gained popularity over more conventional methods like Principle Component Analysis (PCA) and Self-Organizing Maps (SOMs). However, the resulting latent space of a DL model often remains difficult to interpret. In this work we propose SOM-CPC, a model that jointly optimizes Contrastive Predictive Coding and a SOM to find an organized 2D manifold, while preserving higher-dimensional information. We address a largely unexplored and challenging set of scenarios comprising highrate time series, and show on both synthetic and real-life data (medical sleep data and audio recordings) that SOM-CPC outperforms both DL-based feature extraction, followed by PCA, K-means or a SOM, and strong deep-SOM baselines that jointly optimize a DL model and a SOM. SOM-CPC has great potential to expose latent patterns in high-rate data streams and may therefore contribute to a better understanding of many different processes and systems.

1. INTRODUCTION

The improvement and abundance of sensor technology has led to large amounts of high-dimensional, information-rich continuous data streams. However, gaining actionable insights from these data is challenging due to their low interpretability. The main objective of this study is, therefore, to develop an algorithm for acquiring a structured and interpretable representation of (high-rate) time series. We define such an interpretable representation as one that has the ability to be informative and to facilitate exploration of the underlying structure (Lipton, 2018) . According to the manifold hypothesis, high-dimensional real-world data lies on a low-dimensional manifold, comprising disentangled latent factors of variation. The area of unsupervised representation learning is concerned with models that learn this manifold from a set of training data, without the bias of human annotations. Dimensionality reduction techniques like Principle Component Analysis (PCA), possibly in combination with clustering methods like K-means clustering, have conventionally been used for this purpose. Acquiring an interpretable representation with PCA requires omitting many principle components in order to achieve an interpretable number of components. This, however, may discard important information that can not linearly be projected on these few dimensions. A Self-Organizing Map (Kohonen, 1990) , on the other hand, is an extension of K-means clustering that creates a low-dimensional interpretable visualization, while still representing the data in multiple dimensions. However, SOMs typically act on features, which need to be selected heuristically and may, therefore, strongly depend on the use case and/or data modality. Deep learning (DL) models have become popular alternatives for non-linear dimensionality reduction that can be applied directly on raw data. Such models have been combined with joint clustering objectives in the latent space (Xie et al., 2016; Yang et al., 2017; Madiraju, 2018; Lee & Schaar, 2020) . These methods, however, do typically not create a (visually) interpretable representation, and sometimes make use of label information during training (Lee & Schaar, 2020). To enhance

