Reconstructable and Interpretable Representations for Time Series with Time-Skip Sparse Dictionary Learning

It is challenging to summarize time series signals into essential patterns that preserve the original characteristics of the signals. Good summarization allows one to reconstruct the original signal back while the reduced data size saves storage space and in turn accelerates processing that follows. This paper proposes a dictionary learning method for time series signals with a mechanism of skipping sparse codes along the time axis, utilizing redundancy in time. The proposed method gives compact and accurate representations of time series. Experimental results demonstrate that low errors in both signal reconstruction and classification are achieved by the proposed method while the size of representations is reduced. The degradation of the signal reconstruction errors caused by the proposed skipping mechanism was about 5% of the error magnitude, with about a 18 times fewer representation size. The accuracy of classification based on the proposed methods is always better than the state-of-the-art dictionary learning method for time series. The proposed idea can be an effective option when using dictionary learning, which is one of the fundamental techniques in signal processing and has various applications.