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High-dimensional time series are common in many domains. Since humancognition is not optimized to work well in high-dimensional spaces, these areascould benefit from interpretable low-dimensional representations. However, mostrepresentation learning algorithms for time series data are difficult tointerpret. This is due to non-intuitive mappings from data features to salientproperties of the representation and non-smoothness over time. To address thisproblem, we propose a new representation learning framework building on ideasfrom interpretable discrete dimensionality reduction and deep generativemodeling. This framework allows us to learn discrete representations of timeseries, which give rise to smooth and interpretable embeddings with superiorclustering performance. We introduce a new way to overcome thenon-differentiability in discrete representation learning and present agradient-based version of the traditional self-organizing map algorithm that ismore performant than the original. Furthermore, to allow for a probabilisticinterpretation of our method, we integrate a Markov model in the representationspace. This model uncovers the temporal transition structure, improvesclustering performance even further and provides additional explanatoryinsights as well as a natural representation of uncertainty. We evaluate ourmodel in terms of clustering performance and interpretability on static(Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNISTimages, a chaotic Lorenz attractor system with two macro states, as well as ona challenging real world medical time series application on the eICU data set.Our learned representations compare favorably with competitor methods andfacilitate downstream tasks on the real world data.

SOM-VAE: Interpretable Discrete Representation Learning on Time Series