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

2025-06-24

AI Summary

Clustering high-dimensional, noisy Google Trends time series poses significant challenges due to their irregular fluctuations and low signal-to-noise ratio. Method: This paper proposes a hybrid approach integrating symbolic representation with topological data analysis (TDA). Building upon Symbolic Aggregate approXimation (SAX) and its enhanced variant eSAX, the method incorporates persistent homology to extract robust global shape features from time series, thereby overcoming the limited capacity of conventional symbolic methods to model complex temporal dynamics. Contribution/Results: Experiments demonstrate that the proposed method yields more balanced and interpretable clustering results, significantly outperforming purely symbolic approaches in analyzing highly volatile search behavior. The study empirically validates the efficacy of TDA for uncovering consumer online attention patterns and establishes a novel paradigm for real-time marketing decision-making and trend forecasting—one that jointly ensures robustness against noise and interpretability of outcomes.

Technology Category

• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Clustering

Application Category

• Web Mining and Content Analysis: Topic discovery and tracking
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

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.

Problem

• Analyze temporal patterns in online search behavior
• Evaluate clustering methods for noisy time-series data
• Compare symbolic and topological approaches for consumer analytics

Innovation

• Uses SAX for fast time-series clustering
• Applies eSAX to improve interpretability
• Leverages TDA for structural feature analysis