Data On Customer Shopping Amounts Using An Account

Data On The Amount Of The Customers Shopping By Using An Account C

Data on the amount of the customers' shopping by using an account card and whether they decided to upgrade their account from silver status to platinum status after receiving the upgrade offer is shown in Table 2. a. Construct the k nearest neighbor scheme for predicting upgrades based on the data given in Table 2, and interpret the confusion matrix. 2. The data are given in part 1 estimate the probability of upgrade for each division of the purchase amount using Bayes' theorem.

Paper For Above instruction

The analysis of customer data, particularly regarding shopping behaviors and upgrade decisions, provides vital insights into consumer patterns and the effectiveness of marketing strategies. In this paper, we explore two statistical approaches—K-Nearest Neighbors (K-NN) and Bayesian probability estimation—to predict and understand customer upgrade behavior based on their shopping amounts and upgrade decisions. These methods facilitate targeted marketing, improve customer segmentation, and enhance resource allocation within retail operations.

Introduction

Customer upgrade behavior, especially in loyalty programs such as account status upgrades from silver to platinum, is crucial for businesses aiming to maximize revenue and customer retention. Understanding the predictors of such upgrades enables companies to tailor their marketing efforts effectively. The cutoff point for classification can often be refined through machine learning algorithms such as K-NN, which considers the similarity between data points, and Bayesian methods, which incorporate prior probabilities. This paper discusses constructing a K-NN classifier using customer transaction data and interpreting the resulting confusion matrix, followed by estimating upgrade probabilities for different purchase divisions using Bayes' theorem.

Constructing a K-Nearest Neighbor Scheme

The K-NN algorithm is a simple, intuitive machine learning method used for classification tasks. It predicts the class of a data point based on the majority class among its 'k' closest neighbors, where closeness is often determined by Euclidean distance. To implement K-NN using the dataset from Table 2, we first select an appropriate value for ‘k’ through cross-validation. The features used in this classifier include the customer's shopping amount, which is a key predictor of upgrade decisions.

Suppose we select k=3 for simplicity. For a customer with a particular shopping amount, we identify the three nearest neighbors in the dataset based on their shopping amounts. If two or more of these neighbors have upgraded to platinum, the customer is predicted to upgrade; otherwise, they are predicted to remain in the silver tier.

The confusion matrix resulting from the K-NN classifier summarizes the model's performance, showing true positives, false positives, true negatives, and false negatives. Interpreting this matrix helps us assess the classifier's accuracy, precision, recall, and F1-score—vital metrics in determining the effectiveness of the upgrade prediction model.

Interpreting the Confusion Matrix

The confusion matrix comprises four components: true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN). In our context:

  • TP: Customers correctly predicted to upgrade to platinum (they upgraded and the model predicted an upgrade).
  • FP: Customers incorrectly predicted to upgrade (they did not upgrade, but the model predicted an upgrade).
  • TN: Customers correctly predicted not to upgrade.
  • FN: Customers who upgrade but were not predicted to do so.

By analyzing these values, we evaluate model performance. A high number of TP and TN indicates good predictive power, whereas high FP or FN values suggest the need for model tuning, possibly by adjusting k-value or incorporating additional features.

Estimating Upgrade Probabilities Using Bayes' Theorem

Bayes' theorem allows us to compute the posterior probability of an event based on prior knowledge. Using the dataset, we estimate the probability that a customer will upgrade given their purchase amount division. For each division of purchase amounts, Bayes' theorem states:

\[ P(\text{Upgrade} | \text{Division}) = \frac{P(\text{Division} | \text{Upgrade}) \times P(\text{Upgrade})}{P(\text{Division})} \]

Where:

  • \( P(\text{Division} | \text{Upgrade}) \) is the likelihood of the division among upgraded customers.
  • \( P(\text{Upgrade}) \) is the overall probability of a customer upgrading.
  • \( P(\text{Division}) \) is the overall probability of a customer belonging to that division.

By calculating these probabilities from the data, we determine the likelihood of upgrade for each division of purchase amount, aiding targeted marketing efforts.

Conclusion

The combined use of K-NN for classification and Bayesian probability estimates offers a comprehensive approach to understanding and predicting customer upgrade behavior. The K-NN scheme provides a straightforward predictive model based on shopping amounts, while Bayesian analysis quantifies the probability of upgrades in different purchase divisions. These methods support more strategic segmentation and personalized marketing campaigns, ultimately leading to improved customer retention and increased revenue.

References

  • Altman, N. S. (1992). An Introduction to Kernel and Nearest-Neighbor Methods. The American Statistician, 46(3), 175-185.
  • Berry, M. J. A., & Linoff, G. (2004). Data Mining Techniques: For Marketing, Sales, and Customer Relationship Management. Wiley.
  • Friedman, J., Hastie, T., & Tibshirani, R. (2001). The Elements of Statistical Learning. Springer.
  • Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer.
  • Kim, K., & Kim, S. (2017). Customer Analytics Using Machine Learning Approaches. Journal of Business Analytics, 2(2), 120–134.
  • Mitchell, T. M. (1997). Machine Learning. McGraw-Hill.
  • Rish, I. (2001). An Empirical Study of the Naive Bayes Classifier. IJCAI 2001 Workshop on Empirical Methods in Artificial Intelligence, 3–9.
  • Schneiderman, B., & Klemmer, S. (2018). Customer Behavior and Data Analytics in Retail. Journal of Retail Analytics, 20(4), 45-59.
  • Witten, I. H., Frank, E., & Hall, M. A. (2011). Data Mining: Practical Machine Learning Tools and Techniques. Morgan Kaufmann.
  • Zhang, H., & Wang, Y. (2020). Probabilistic Models in Customer Purchase Prediction. Journal of Data Science, 18(3), 345-362.

Related Assignments