Recent technological advances have enabled the easy collection of consumer behavior data in real time. Typically, these data contain the time at which a consumer engages in a particular activity such as entering a store, buying a product, or making a call. The occurrence time of certain events must be analyzed as circular random variables, with 24:00 corresponding to 0:00. To effectively implement a marketing strategy (pricing, promotion, or product design), consumers should be segmented into homogeneous groups. This paper proposes a methodology based on circular statistical models from which we construct a clustering algorithm based on the use patterns of consumers. In particular, we model temporal patterns as circular distributions based on nonnegative trigonometric sums (NNTSs). Consumers are clustered into homogeneous groups based on their vectors of parameter estimates by using a spherical k -means clustering algorithm. For this purpose, we define the parameter space of NNTS models as a hypersphere. The methodology is applied to three real datasets comprising the times at which individuals send short-service messages and start voice calls and the check-in times of the users of a mobile application Foursquare.

中文翻译：

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基于使用模式的消费者细分

最近的技术进步使实时收集消费者行为数据成为可能。通常，这些数据包含消费者参与特定活动的时间，例如进入商店、购买产品或拨打电话。某些事件的发生时间必须作为循环随机变量进行分析，24:00对应0:00。为了有效地实施营销策略（定价、促销或产品设计），消费者应该被划分为同质的群体。本文提出了一种基于循环统计模型的方法，我们从中构建了基于消费者使用模式的聚类算法。特别是，我们将时间模式建模为基于非负三角和 (NNTS) 的圆形分布。通过使用球形 k 均值聚类算法，根据消费者的参数估计向量将消费者聚类为同质组。为此，我们将 NNTS 模型的参数空间定义为超球面。该方法应用于三个真实数据集，包括个人发送短消息和开始语音呼叫的时间以及移动应用程序 Foursquare 用户的签到时间。