Recently, a word-valued source has been proposed as a new class of information source models. A word-valued source is regarded as a source with a probability distribution over a word set. Although a word-valued source is a nonstationary source in general, it has been proved that an entropy rate of the source exists and the Asymptotic Equipartition Property (AEP) holds when the word set of the source is prefix-free. However, when the word set is not prefix-free (non-prefix-free), only an upper bound on the entropy density rate for an i.i.d. word-valued source has been derived so far. In this paper, we newly derive a lower bound on the entropy density rate for an i.i.d. word-valued source with a finite non-prefix-free word set. Then some numerical examples are given in order to investigate the behavior of the bounds.
Understanding customer behaviour is crucial for business success. For achieving this goal, the Recency-Frequency-Monetary (RFM) model has been commonly recognised as an effective approach to analyse customer behaviour. However, the traditional RFM approach is a coarse method for quantifying customer loyalty and contribution that can only provide a single lump-sum value of the recency (R), frequency (F), and monetary value (M); hence, it discards information regarding customers' product preferences. Typically, different customers make different purchases. Subsequently, purchases are likely to be different across customers. This creates data sparsity, which affects the performance of conventional clustering methods. In this study, we integrated the group RFM analysis and probabilistic latent semantic analysis models to perform customer segmentation and customer analysis. The results indicated that the developed approach takes into account the product preference and provides insight into and captures a wide ABOUT THE AUTHORS Arthit Apichottanakul is currently working as lecturer in the Faculty of Technology, Khon Kaen University, Thailand. He completed his PhD in Industrial Engineering from Khon Kaen University, Thailand. His current research interests include intelligent applications, optimization and data science in logistics and supply chain management.
The electronic commerce site (EC site) has become an important marketing channel where consumers can purchase many kinds of products; their access logs, including purchase records and browsing histories, are saved in the EC sites' databases. These log data can be utilized for the purpose of web marketing. The customers who purchase many product items are good customers, whereas the other customers, who do not purchase many items, must not be good customers even if they browse many items. If the attributes of good customers and those of other customers are clarified, such information is valuable as input for making a new marketing strategy. Regarding the product items, the characteristics of good items that are bought by many users are valuable information. It is necessary to construct a method to efficiently analyze such characteristics. This paper proposes a new latent class model to analyze both purchasing and browsing histories to make latent item and user clusters. By applying the proposal, an example of data analysis on an EC site is demonstrated. Through the clusters obtained by the proposed latent class model and the classification rule by the decision tree model, new findings are extracted from the data of purchasing and browsing histories.
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