标题： 消费者行为的形状：时间序列的符号与拓扑分析 显示英文标题

标题： The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series

摘要： 理解在线搜索行为中的时间模式对于实时营销和趋势预测至关重要。 Google Trends 为公众兴趣提供了丰富的代理数据，但其时间序列数据的高维度和噪声给有效的聚类带来了挑战。 本研究评估了三种无监督聚类方法，符号聚合近似（SAX）、增强型 SAX（eSAX）和拓扑数据分析（TDA），应用于代表主要消费者类别的 20 个 Google Trends 关键词。 我们的结果表明，尽管 SAX 和 eSAX 对于稳定的时间序列提供了快速且可解释的聚类，但它们在波动性和复杂性方面存在困难，常常产生模糊的“万能”聚类。 相比之下，TDA 通过持久同调捕捉全局结构特征，并实现了更平衡且有意义的分组。 我们最后提供了在消费者分析中使用符号和拓扑方法的实用指导，并建议结合这两种视角的混合方法在未来应用中具有强大的潜力。 显示英文摘要

摘要： Understanding temporal patterns in online search behavior is crucial for real-time marketing and trend forecasting. Google Trends offers a rich proxy for public interest, yet the high dimensionality and noise of its time-series data present challenges for effective clustering. This study evaluates three unsupervised clustering approaches, Symbolic Aggregate approXimation (SAX), enhanced SAX (eSAX), and Topological Data Analysis (TDA), applied to 20 Google Trends keywords representing major consumer categories. Our results show that while SAX and eSAX offer fast and interpretable clustering for stable time series, they struggle with volatility and complexity, often producing ambiguous ``catch-all'' clusters. TDA, by contrast, captures global structural features through persistent homology and achieves more balanced and meaningful groupings. We conclude with practical guidance for using symbolic and topological methods in consumer analytics and suggest that hybrid approaches combining both perspectives hold strong potential for future applications.