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.
@cite_20: Subspace clustering is the task of identifying clusters in subspaces of the input dimensions of a given dataset. Noisy data in certain attributes cause difficulties for traditional clustering algorithms, because the high discrepancies within them can make objects appear too different to be grouped in the same cluster. This requires methods specially designed for subspace clustering. This paper presents our second approach to subspace and projected clustering based on self-organizing maps (SOMs), which is a local adaptive receptive field dimension selective SOM. By introducing a time-variant topology, our method is an improvement in terms of clustering quality, computational cost, and parameterization. This enables the method to identify the correct number of clusters and their respective relevant dimensions, and thus it presents nearly perfect results in synthetic datasets and surpasses our previous method in most of the real-world datasets considered.
The operation of the map takes place in three phases: the organization phase, the convergence phase, and the clustering phase @cite_20 . In the organization phase, nodes are dynamically inserted, removed and adjusted in the map in order to cover the regions of the input space in which the input patterns are found as well as possible. When an input pattern is presented for the network, a level of activation is computed for each node in the map, and the node with the highest activation is considered the winner of the competition. This activation level is an inverse function of the distance between the center of the node and the input pattern. An activation threshold, @math , is used for determining when if the winner node is close enough to be adjusted or if it is necessary to insert a new node in the map. The nodes that do not cluster a significant percentage of the input patterns are periodically removed.