Efficient Temporal Kernels Between Feature Sets for Time Series Classification

In the time-series classification context, the majority of the most accurate core methods are based on the Bag-of-Words framework, in which sets of local features are first extracted from time series. A dictionary of words is then learned and each time series is finally represented by a histogram of word occurrences. This representation induces a loss of information due to the quantization of features into words as all the time series are represented using the same fixed dictionary. In order to overcome this issue, we introduce in this paper a kernel operating directly on sets of features. Then, we extend it to a time-compliant kernel that allows one to take into account the temporal information. We apply this kernel in the time series classification context. Proposed kernel has a quadratic complexity with the size of input feature sets, which is problematic when dealing with long time series. However, we show that kernel approximation techniques can be used to define a good trade-off between accuracy and complexity. We experimentally demonstrate that the proposed kernel can significantly improve the performance of time series classification algorithms based on Bag-of-Words.