  We propose an approximation algorithm for efficient correlation search in
time series data. In our method, we use Fourier transform and neural network to
embed time series into a low-dimensional Euclidean space. The given space is
learned such that time series correlation can be effectively approximated from
Euclidean distance between corresponding embedded vectors. Therefore, search
for correlated time series can be done using an index in the embedding space
for efficient nearest neighbor search. Our theoretical analysis illustrates
that our method's accuracy can be guaranteed under certain regularity
conditions. We further conduct experiments on real-world datasets and the
results show that our method indeed outperforms the baseline solution. In
particular, for approximation of correlation, our method reduces the
approximation loss by a half in most test cases compared to the baseline
solution. For top-$k$ highest correlation search, our method improves the
precision from 5\% to 20\% while the query time is similar to the baseline
approach query time.
