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Numerous dimensionality-reducing representations of time series have been proposed in data mining and have proved to be useful, especially in handling a high volume of time series data. Among them, widely used symbolic representations such as symbolic aggregate approximation and piecewise aggregate approximation focus on information of local averages of time series. To compensate for such methods, several attempts were made to include trend information. However, the included trend information is quite simple, leading to great information loss. Such information is hardly extendable, so adjusting the level of simplicity to a higher complexity is difficult. In this paper, we propose a new symbolic representation method called transitional symbolic aggregate approximation that incorporates transitional information into symbolic aggregate approximations. We show that the proposed method, satisfying a lower bound of the Euclidean distance, is able to preserve meaningful information, including dynamic trend transitions in segmented time series, while still reducing dimensionality. We also show that this method is advantageous from theoretical aspects of interpretability, and practical and superior in terms of time-series classification tasks when compared with existing symbolic representation methods.

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By identifying useful relationships between massive datasets, association rule mining can provide new insights to decision-makers. Item assignment models based on association between items are used to place items in a retail or e-commerce environment to increase sales. However, existing models fail to combine these associations with item-specific information, such as profit and purchasing frequency. To find effective assignments with item-specific information, we propose a new hybrid genetic algorithm that incorporates a robust tabu search with a novel rectangular partially matched crossover, focusing on rectangular layouts. Interestingly, we show that our item assignment model is equivalent to popular quadratic assignment NP-hard problems. We show the effectiveness of the proposed algorithm, using benchmark instances from QAPLIB and synthetic databases that represent real-life retail situations, and compare our algorithm with other existing algorithms. We also show that the proposed crossover operator outperforms a few existing ones in both fitness values and search times. The experimental results show that not only does the proposed item assignment model generates a more profitable assignment plan than the other tested models based on association alone but it also obtains better solutions than the other tested algorithms.