Professional Assignment 1 - CLO 1, 2, 3, 6

Professional Assignment 1 - CLO 1, CLO 2, CLO 3, CLO 6, CLO 7 Data on T

Professional Assignment 1 requires constructing a k-nearest neighbors (k-NN) scheme for predicting customer account upgrades based on shopping data and interpreting the confusion matrix. Additionally, it involves estimating the probability of account upgrades for each division of purchase amount using Bayes' theorem, based on provided data.

Paper For Above instruction

The task at hand involves two primary analytical components: the development of a k-nearest neighbors (k-NN) classifier and the application of Bayesian probability to estimate upgrade probabilities. These methods are fundamental in data science for classification and probabilistic inference, respectively. This paper elaborates on both these techniques in the context of customer upgrade prediction based on shopping data.

Data Context and Objective

The dataset, as referenced, encapsulates customer transactional data, specifically focusing on the amount spent in shopping that is recorded via account cards. Customers are categorized based on their upgrade status—whether they have upgraded from a silver to a platinum account—and the data specifies if they received an upgrade offer and their subsequent decision. The primary goal is to develop a predictive model that accurately classifies whether a customer will upgrade based on their shopping behavior, and to understand the likelihood of upgrade within different spending brackets.

Construction of k-Nearest Neighbors Classifier

The k-NN algorithm is a non-parametric method used for classification that predicts the class of a data point based on the classes of its 'k' closest neighbors in the feature space. Its effectiveness depends on choosing an appropriate 'k' value and a meaningful distance metric.

Step 1: Data Preparation and Feature Selection

The dataset's key feature is the shopping amount per customer, which must be preprocessed—handling missing values, normalizing or standardizing data to ensure uniformity in distance calculations, especially when dealing with monetary values.

Step 2: Distance Metric and Neighbor Selection

For numerical features like purchase amounts, Euclidean distance is commonly used. Given a new data point (a customer's purchase amount), the algorithm computes the distance to all existing data points and selects the 'k' closest neighbors.

Step 3: Choosing the Parameter 'k'

Selecting the optimal 'k' involves techniques such as cross-validation, where different 'k' values are tested to minimize misclassification errors. Small 'k' values tend to be sensitive to noise, while larger 'k' values smooth out decision boundaries.

Step 4: Classification and Prediction

The class with the majority vote among the neighbors determines the customer's predicted upgrade status. For example, if 7 neighbors are considered and 5 of them have upgraded, the model predicts the customer will upgrade.

Interpretation of Confusion Matrix

The confusion matrix summarizes the classifier's performance, typically consisting of four components:

- True Positives (TP): correctly predicted upgrades

- True Negatives (TN): correctly predicted non-upgrades

- False Positives (FP): non-upgrades incorrectly predicted as upgrades

- False Negatives (FN): upgrades incorrectly predicted as non-upgrades

From these, key metrics such as accuracy, precision, recall, and F1-score can be derived. A high recall indicates the model's effectiveness in capturing actual upgrades, whereas high precision ensures few false alarms. Balancing these metrics is crucial for practical deployment.

Probabilistic Estimation Using Bayes' Theorem

Bayes' theorem offers a framework to compute the posterior probability that a customer will upgrade, given their purchase amount division. It is expressed as:

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

Dividing Purchase Amounts into Classes

Purchase amounts can be divided into categories (e.g., low, medium, high). Prior probabilities \( P(\text{Upgrade}) \) are estimated based on the overall upgrade rate in the population.

Likelihood Estimation

Conditional probabilities \( P(\text{Purchase Amount} | \text{Upgrade}) \) are estimated using historical data—how purchase amounts distribute among upgraded versus non-upgraded customers.

Applying Bayes' Theorem

For each division, these estimates enable calculation of the probability that a customer in that category will upgrade. For instance, suppose high spenders historically upgrade more often; Bayes' theorem quantifies this likelihood given observed purchase behavior.

Conclusion

Constructing a k-NN classifier facilitates creating an intuitive, data-driven model for predicting customer upgrade status based on shopping amounts. Its simple implementation makes it suitable for initial exploratory analysis, although tuning parameters like 'k' is vital for optimal performance. The interpretation of the confusion matrix reveals the strengths and weaknesses of the model, guiding further refinement.

Applying Bayesian inference enables a nuanced understanding of upgrade probabilities across different purchase brackets, supporting targeted marketing strategies. Both methods together form a comprehensive approach to customer behavior analysis, aiding organizations in designing personalized upgrade offers that maximize conversion rates.

References

1. Cover, T., & Hart, P. (1967). Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 13(1), 21-27.

2. Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.

3. Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer.

4. Han, J., Kamber, M., & Pei, J. (2011). Data Mining: Concepts and Techniques. Morgan Kaufmann.

5. Russell, S., & Norvig, P. (2020). Artificial Intelligence: A Modern Approach. Pearson.

6. Murphy, K. P. (2012). Machine Learning: A Probabilistic Perspective. MIT Press.

7. Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer.

8. Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.

9. Friedman, J., Hastie, T., & Tibshirani, R. (2001). The Elements of Statistical Learning. Data Mining, Inference, and Prediction. Springer.

10. Sue, V. M. (2013). Understanding Measurement and Research. Oxford University Press.