One application for time-series alignment that we consider is the task of answering similarity queries as illustrated in Figure 1.
This algorithm relaxes the assumption, common to previous work in expression time-series alignment, that all genes should be warped in the same way.
The two main contributions of this work are algorithms that are designed to address both of these issues when computing time-series alignments.
Figure 2 shows the alignment of two time series in alignment space, using a multi-segment alignment method.
The KNN algorithm is less robust because it computes point-wise similarities between time series without any temporal alignment; as the variance of the temporal shifts increases, we observe a significant drop in accuracy.
Their method, however, computes a single alignment of multiple time series, whereas our method computes a clustered alignment of a pair of time series.
That is, we want to allow alignments of the two time series are not necessarily aligned at Zt0.
For a comparison purpose, the same data preprocessing techniques, including using z-score to standardize the data and randomly shuffling the original data matrix, were applied to attenuate noise and improve spatial alignment of time series data [53].
Alignment of time series gene expression between group of genes or species could also be important in other biological experiments.
Listgarten et al. (2005) have developed a method for multiple alignment of time series data that has some similarities to our approach.
For alignment of time series from repeated experiments, the signals were multiplied with a scalar to minimize the sum of mean-squared distances of measurements at the same time points.
