  Few-shot Time Series Classification (few-shot TSC) is a challenging problem
in time series analysis. It is more difficult to classify when time series of
the same class are not completely consistent in spectral domain or time series
of different classes are partly consistent in spectral domain. To address this
problem, we propose a novel method named Spectral Propagation Graph Network
(SPGN) to explicitly model and propagate the spectrum-wise relations between
different time series with graph network. To the best of our knowledge, SPGN is
the first to utilize spectral comparisons in different intervals and involve
spectral propagation across all time series with graph networks for few-shot
TSC. SPGN first uses bandpass filter to expand time series in spectral domain
for calculating spectrum-wise relations between time series. Equipped with
graph networks, SPGN then integrates spectral relations with label information
to make spectral propagation. The further study conveys the bi-directional
effect between spectral relations acquisition and spectral propagation. We
conduct extensive experiments on few-shot TSC benchmarks. SPGN outperforms
state-of-the-art results by a large margin in $4\% \sim 13\%$. Moreover, SPGN
surpasses them by around $12\%$ and $9\%$ under cross-domain and cross-way
settings respectively.
