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

TL;DR

This paper compares symbolic and topological clustering methods for analyzing noisy, high-dimensional Google Trends data to better understand consumer behavior patterns.

Contribution

It evaluates and contrasts SAX, eSAX, and TDA methods for clustering consumer interest time series, highlighting TDA's advantages in capturing complex structures.

Findings

TDA provides more meaningful clusters for volatile data.

SAX and eSAX are faster but less effective with noisy series.

Hybrid approaches show promise for future consumer analytics.

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.