You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Time Series Motif Discovery (TSMD) is defined as searching for patterns that are previously unknown and appear with a given frequency in time series. Another problem strongly related with TSMD is Word Segmentation. This problem has received much attention from the community that studies early language acquisition in babies and toddlers. The development of biologically plausible models for word segmentation could greatly advance this field. Therefore, in this article, we propose the Variable Input Length Map (VILMAP) for Motif Discovery and Word Segmentation. The model is based on the Self-Organizing Maps and can identify Motifs with different lengths in time series. In our experiments, we show that VILMAP presents good results in finding Motifs in a standard Motif discovery dataset and can avoid catastrophic forgetting when trained with datasets with increasing values of input size. We also show that VILMAP achieves results similar or superior to other methods in the literature developed for the task of word segmentation.

Cited Abstract(s):
[1]: One significant task in time series mining research area is motif discovery which is the first step needed to be done in finding interesting patterns in time series sequence. Recently, many motif discovery algorithms have been proposed in place of the untenable brute-force algorithm, to improve its time complexity. However, those motif discovery algorithms still need a predefined sliding window length that must be known a priori. In this paper, we present a novel motif discovery algorithm that requires no window length parameter. This sliding window length is sensitive in that a small difference in the value can lead to huge difference of motif results. The proposed algorithm automatically returns suitable motif lengths from all possible sliding window lengths; in other words, our algorithm efficiently reduces a large set of possibilities of the sliding window lengths down to a few truly-interesting variable-length motifs.
The Variable-Length Motif Discovery (VLMD) [1] is a method that has been proposed to automatically find a suitable set of variable length Motifs. VLMD iteratively separates Motifs of different sizes into groups based on similarity. Within a group, a representative Motif with a normalized minimum distance between pairs of subsequences is selected. Finally, the VLMD returns a set of useful representative Motifs, which is extremely small compared to all possibilities of sliding window lengths. The operation of VLMD consists of two steps. Firstly, it finds a set of groups of Motifs looking for all possible lengths of a sliding window to obtain Motifs of different lengths. If the current Motif and the previous Motif overlap, the current Motif is added to the same set of the previous Motif; Otherwise, a new Motif group is created. Then, for each group of Motifs, a representative Motif is selected with a minimum normalized distance for the others in the group.