  Most existing Time series classification (TSC) models lack interpretability
and are difficult to inspect. Interpretable machine learning models can aid in
discovering patterns in data as well as give easy-to-understand insights to
domain specialists. In this study, we present Neuro-Symbolic Time Series
Classification (NSTSC), a neuro-symbolic model that leverages signal temporal
logic (STL) and neural network (NN) to accomplish TSC tasks using multi-view
data representation and expresses the model as a human-readable, interpretable
formula. In NSTSC, each neuron is linked to a symbolic expression, i.e., an STL
(sub)formula. The output of NSTSC is thus interpretable as an STL formula akin
to natural language, describing temporal and logical relations hidden in the
data. We propose an NSTSC-based classifier that adopts a decision-tree approach
to learn formula structures and accomplish a multiclass TSC task. The proposed
smooth activation functions for wSTL allow the model to be learned in an
end-to-end fashion. We test NSTSC on a real-world wound healing dataset from
mice and benchmark datasets from the UCR time-series repository, demonstrating
that NSTSC achieves comparable performance with the state-of-the-art models.
Furthermore, NSTSC can generate interpretable formulas that match with domain
knowledge.
