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 Variable-Length Motif Discovery (VLMD) @cite_16 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.
@cite_16
2152671946 2019654077 1999306137 1602142193
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. This paper proposes a generalized motif-based method for detecting defects in 16 out of 17 wallpaper groups in 2D patterned texture. It assumes that most patterned texture can be decomposed into lattices and their constituents-motifs. It then utilizes the symmetry property of motifs to calculate the energy of moving subtraction and its variance among different motifs. By learning the distribution of these values over a number of defect-free patterns, boundary conditions for discerning defective and defect-free patterns can be determined. This paper presents the theoretical foundation of the method, and defines the relations between motifs and lattice, from which a new concept called energy of moving subtraction is derived using norm metric measurement between a collection of circular shift matrices of motif and itself. It has been shown in this paper that the energy of moving subtraction amplifies the defect information of the defective motif. Together with its variance, an energy-variance space is further defined where decision boundaries are drawn for classifying defective and defect-free motifs. As the 16 wallpaper groups of patterned fabric can be transformed into three major groups, the proposed method is evaluated over these three major groups, from which 160 defect-free lattices samples are used for defining the decision boundaries, with 140 defect-free and 113 defective samples used for testing. An overall detection success rate of 93.32 is achieved for the proposed method. No other generalized approach can achieve this success rate has been reported before, and hence this result outperforms all other previously published approaches. As one of the most essential data mining tasks, finding frequently occurring patterns, i.e., motif discovery, has drawn a lot of attention in the past decade. Despite successes in speedup of motif discovery algorithms, most of the existing algorithms still require predefined parameters. The critical and most cumbersome one is time series motif length since it is difficult to manually determine the proper length of the motifs-even for the domain experts. In addition, with variability in the motif lengths, ranking among these motifs becomes another major problem. In this work, we propose a novel algorithm using compression ratio as a heuristic to discover meaningful motifs in proper lengths. The ranking of these various length motifs relies on an ability to compress time series by its own motif as a hypothesis. Furthermore, other than being an anytime algorithm, our experimental evaluation also demonstrates that our proposed method outperforms existing works in various domains both in terms of speed and accuracy. Discovering motifs in sequence databases has been receiving abundant attentions from both database and data mining communities, where the motif is the most correlated pair of subsequences in a sequence object. Motif discovery is expensive for emerging applications which may have very long sequences (e.g., million observations per sequence) or the queries arrive rapidly (e.g., per 10 seconds). Prior works cannot offer fast correlation computations and prune subsequence pairs at the same time, as these two techniques require different orderings on examining subsequence pairs. In this work, we propose a novel framework named Quick-Motif which adopts a two-level approach to enable batch pruning at the outer level and enable fast correlation calculation at the inner level. We further propose two optimization techniques for the outer and the inner level. In our experimental study, our method is up to 3 orders of magnitude faster than the state-of-the-art methods.