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.
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.
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Large scale clusters running MapReduce, Spark etc. routinely process data that are on the orders of petabytes or more. The philosophy in these methods is to split the overall job into smaller tasks that are executed on different servers; this is called the map phase. This is followed by a data shuffling phase where appropriate data is exchanged between the servers. The final reduce phase, completes the computation. Prior work has explored a mechanism for reducing the overall execution time by operating on a computation vs. communication tradeoff. Specifically, the idea is to run redundant copies of map tasks that are placed on judiciously chosen servers. The shuffle phase exploits the location of the nodes and utilizes coded transmission. The main drawback of this approach is that it requires the original job to be split into a number of map tasks that grows exponentially in the system parameters. This is problematic, as we demonstrate that splitting jobs too finely can in fact adversely affect the overall execution time. In this work we show that one can simultaneously obtain low communication loads while ensuring that jobs do not need to be split too finely. Our approach uncovers a deep relationship between this problem and a class of combinatorial structures called resolvable designs. We present experimental results obtained on Amazon EC2 clusters for a widely known distributed algorithm, namely TeraSort. We obtain over 4.69x improvement in speedup over the baseline approach and more than 2.6x over current state of the art.