The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series (2506.19759v1)

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.

• The paper demonstrates that TDA outperforms SAX methods in capturing complex, nonlinear patterns in volatile consumer time series data.
• The study reveals that while SAX and its enhanced version offer fast, interpretable clustering, they may produce ambiguous groupings when data show high variability.
• The paper highlights the potential of combining symbolic and topological techniques to create robust predictive models and improve consumer analytics.

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

The paper "The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series" presented by Pola Bereta and Ioannis Diamantis provides a thorough examination of consumer behavior as represented by Google Trends data, through the lens of Symbolic Aggregate approXimation (SAX), its enhanced version (eSAX), and Topological Data Analysis (TDA). The focus lies on addressing the challenges posed by the high dimensionality and volatility of time series data in evaluating public attention.

Google Trends constitutes a rich dataset reflecting the dynamics of public interest across various consumer categories. Serving as a proxy for consumer behavior, this data allows for the investigation of temporal patterns preceding consumer actions. Due to the complexity and variability inherent in such time series, the authors explore three unsupervised clustering methodologies to capture the shape and evolution of consumer attention over time.

Methodological Approach

The paper articulates the deployment of SAX and eSAX as symbolic methods adept at fast and interpretable clustering, albeit with limitations in handling volatile and complex time series. SAX operates by normalizing and reducing dimensionality via symbolic transformations, which offer computational efficiency but risk producing ambiguous clusters when confronted with highly dynamic data. The enhanced SAX (eSAX) attempts to mitigate this by considering additional information from each data segment — specifically the extremal values — though it introduces added complexity without necessarily achieving a better clustering outcome.

Conversely, TDA provides a fundamentally different analysis by emphasizing the topological structure inherent within the data. Utilizing persistent homology, TDA allows for a broader perspective capturing global structural features that might persist across various scales. This capability has demonstrated more balanced and meaningful groupings for consumer behavior data, capturing nonlinear relationships and dynamic transitions characteristic of volatilities within consumer interest.

Results and Numerical Analysis

The clustering results highlight strengths and weaknesses across the methodologies. SAX displayed certain prowess in efficient processing yet faltered when handling complexity, evidenced by high silhouette scores and Davies–Bouldin indices reflecting moderate cluster quality. TDA, while computationally more intensive, showed superiority in revealing the structural features for robust clustering by avoiding the formation of ambiguous "catch-all" clusters present in SAX, using persistence landscapes for capturing salient shapes and patterns.

However, TDA's impact is more pronounced in visual and structural interpretation rather than numerical metrics, manifest in its ability to meaningfully cluster complex keywords such as 'AI' and 'inflation.'

Implications and Future Research

This comparative paper elucidates the merit of combining symbolic and topological perspectives for consumer analytics. SAX and eSAX provide rapid, interpretable outputs suitable for straightforward series data but face challenges with intricate time series phenomena. TDA opens a pathway for in-depth analysis without presumptive constraints on the data distribution, suggesting potential in predictive models, anomaly detection, or real-time market analytics.

Future research could explore hybrid methodologies blending the strength of symbolic preprocessing with deep topological insights. Additionally, optimizing hyperparameters in TDA, incorporating external validation, and scaling real-time applications offer promising directions. As consumer interest evolves dynamically, adaptive models leveraging the detailed structural insights from TDA could play significant roles in anticipatory marketing strategies or behavioral segmentation.

In summation, the paper expands the analytical toolkit for time series data within consumer behavior studies, demonstrating how SAX, eSAX, and TDA offer complementary pathways to understanding the elusive shape of consumer interest.