  Symbolic representations of time series have proven to be effective for time
series classification, with many recent approaches including SAX-VSM, BOSS,
WEASEL, and MrSEQL. The key idea is to transform numerical time series to
symbolic representations in the time or frequency domain, i.e., sequences of
symbols, and then extract features from these sequences. While achieving high
accuracy, existing symbolic classifiers are computationally expensive. In this
paper we present MrSQM, a new time series classifier which uses multiple
symbolic representations and efficient sequence mining, to extract important
time series features. We study four feature selection approaches on symbolic
sequences, ranging from fully supervised, to unsupervised and hybrids. We
propose a new approach for optimal supervised symbolic feature selection in
all-subsequence space, by adapting a Chi-squared bound developed for
discriminative pattern mining, to time series. Our extensive experiments on 112
datasets of the UEA/UCR benchmark demonstrate that MrSQM can quickly extract
useful features and learn accurate classifiers with the classic logistic
regression algorithm. Interestingly, we find that a very simple and fast
feature selection strategy can be highly effective as compared with more
sophisticated and expensive methods. MrSQM advances the state-of-the-art for
symbolic time series classifiers and it is an effective method to achieve high
accuracy, with fast runtime.
