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The Powers of the Covariance Matrix: A Novel Approach for Customer Churn Prediction in the Telecom Sector
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Resumo(s)
Customer churn prediction remains a key challenge for telecom providers in saturated
markets. This paper introduces a novel feature engineering technique for churn prediction
based on fractional powers of covariance matrices, which reveal structural relationships
among customer features. Namely, we transform tabular customer data into covariance
matrices, apply fractional power transformations (α ∈ [-4,4]), and use the resulting matrices
as input features to a Convolutional Neural Network (CNN). The optimal power is selected
based on class-wise recall performance (from the training samples only).
To address the limitations of having only a single instance per customer and to test
generalization of our approach under class imbalance without synthetic oversampling, we
propose a novel training pipeline that employs homogenous class-based subsets and encodes
individual test instances through outer product representations.
On the IBM Telco dataset (7,043 customers, 27% churn rate), our method achieved 90% recall
for churners (minority class), exhibiting state of the art performance. The model also achieved
81% recall for non-churners, indicating balanced performance.
The empirical success of our approach may be explained by the observed consistent
separation between our churners and non-churners engineered features in their natural
ambient space: the space of symmetric positive-definite (SPD) matrices, endowed with the
Affine-Invariant Riemannian Metric (AIRM). This structural separability suggests that our
matrix power features offer high identifiability, which is essential for the consistency and
generalization of supervised learning models. Our work highlights the benefits of combining
deep learning with structure-informed representations of tabular data.
Descrição
Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced Analytics, specialization in Business Analytics
Palavras-chave
Customer Churn Prediction Convolutional Neural Networks Fractional Matrix Powers Incremental Learning Structural Consistency Telecom Sector SDG 8 - Decent work and economic growth SDG 9 - Industry, innovation and infrastructure SDG 12 - Responsible production and consumption