Dynamic Boundary Time Warping for Sub-sequence Matching with Few Examples

TL;DR

The paper presents a novel method of finding a fragment in a long temporal sequence similar to the set of shorter sequences and is the first to propose an algorithm for such a search that does not rely on computing the average sequence from query examples.

Abstract

The paper presents a novel method of finding a fragment in a long temporal sequence similar to the set of shorter sequences. We are the first to propose an algorithm for such a search that does not rely on computing the average sequence from query examples. Instead, we use query examples as is, utilizing all of them simultaneously. The introduced method based on the Dynamic Time Warping (DTW) technique is suited explicitly for few-shot query-by-example retrieval tasks. We evaluate it on two different few-shot problems from the field of Natural Language Processing. The results show it either outperforms baselines and previous approaches or achieves comparable results when a low number of examples is available.

Figures (6)

• Figure 1: The problem considered is to align multiple sequences (here $\mathcal{X}_1$, $\mathcal{X}_2$, $\mathcal{X}_3$) optimally within the target sequence $\mathcal{Y}$, assuming all have to be matched to the same sub-sequence of $\mathcal{Y}$. Optimal alignment is one that minimizes the cost over all possible alignments. An example from Natural Language Processing is to locate a named entity within the sentence, given a few examples of other named entities.
• Figure 2: DTW between two time series and the optimal alignment path. The dashed line connects elements aligned between up and down time series. The plot on the right depicts which time step was aligned to which, with each off-diagonal move indicating warping.
• Figure 3: The DBTW matching using the semantic distance between word embeddings applied to the Named Entity Recognition problem. Here, the three examples of time expressions were matched to the Friday morning sub-sequence.
• Figure 4: The problem of determining the optimal match between sequences considered on $n \times m$ unit grid.
• Figure 5: The problem of determining the optimal match between sequences $\mathcal{X}_1, \mathcal{X}_2, \mathcal{Y}$ considered on the rectangular cuboid. Computing the optimal match would have $\mathcal{O}(n_1 n_2 m)$ time complexity.