Defining Zhang's metric

In general, when we want to perform a task many times, we'll write a function, rather than coding up each individual instance. In this exercise, we'll define a function for Zhang's metric that takes an antecedent and consequent and outputs the metric itself. When the problems we solve become increasingly complicated in the following chapter, having a convenient means of computing a metric will greatly simplify things.

Note that numpy has been imported as np and pandas has been imported as pd. Additionally, recall that the expression for Zhang's metric in terms of support calculations is the following:

$$Zhang(A \rightarrow B) = $$ $$\frac{Support(A \& B) - Support(A) Support(B)}{ max[Support(AB) (1-Support(A)), Support(A)(Support(B)-Support(AB))]}$$

This is a part of the course

“Market Basket Analysis in Python”

Exercise instructions

Define the support values of the antecedent and consequent individually.
Define the support of {antecedent, consequent}.
Complete the expressions for the numerator and denominator.
Complete the expression for Zhang's metric.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Define a function to compute Zhang's metric
def zhang(antecedent, consequent):
	# Compute the support of each book
	supportA = antecedent.____
	supportC = consequent.____

	# Compute the support of both books
	supportAC = np.____(antecedent, consequent).____

	# Complete the expressions for the numerator and denominator
	numerator = supportAC - supportA*supportC
	denominator = ___(supportAC*(1-supportA), supportA*(supportC-supportAC))

	# Return Zhang's metric
	return numerator / denominator

Edit and Run Code

This exercise is part of the course

Market Basket Analysis in Python

IntermediateSkill Level

4.8+

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In this chapter, you’ll learn the basics of Market Basket Analysis: association rules, metrics, and pruning. You’ll then apply these concepts to help a small grocery store improve its promotional and product placement efforts.

Exercise 1: What is market basket analysis?Exercise 2: The basics of market basket analysis Exercise 3: Cross-selling products Exercise 4: Identifying association rules Exercise 5: Multiple antecedents and consequents Exercise 6: Preparing data for market basket analysis Exercise 7: Generating association rules Exercise 8: The simplest metric Exercise 9: One-hot encoding transaction data Exercise 10: Computing the support metric

Association rules tell us that two or more items are related. Metrics allow us to quantify the usefulness of those relationships. In this chapter, you’ll apply six metrics to evaluate association rules: supply, confidence, lift, conviction, leverage, and Zhang's metric. You’ll then use association rules and metrics to assist a library and an e-book seller.

Exercise 1: Confidence and lift Exercise 2: Recommending books with support Exercise 3: Refining support with confidence Exercise 4: Further refinement with lift Exercise 5: Leverage and conviction Exercise 6: Lift versus leverage Exercise 7: Computing conviction Exercise 8: Computing conviction with a function Exercise 9: Promoting ebooks with conviction Exercise 10: Association and dissociation Exercise 11: Computing association and dissociation Exercise 12: Defining Zhang's metric

Exercise 13: Applying Zhang's metric Exercise 14: Advanced rules Exercise 15: Filtering with support and conviction Exercise 16: Using multi-metric filtering to cross-promote books

The fundamental problem of Market Basket Analysis is determining how to translate vast amounts of customer decisions into a small number of useful rules. This process typically starts with the application of the Apriori algorithm and involves the use of additional strategies, such as pruning and aggregation. In this chapter, you’ll learn how to use these methods and will ultimately apply them in exercises where you assist a retailer in selecting a physical store layout and performing product cross-promotions.

Exercise 1: Aggregation Exercise 2: Performing aggregation Exercise 3: Defining an aggregation function Exercise 4: The Apriori algorithm Exercise 5: Pruning and Apriori Exercise 6: Identifying frequent itemsets with Apriori Exercise 7: Selecting a support threshold Exercise 8: Basic Apriori results pruning Exercise 9: Generating association rules Exercise 10: Pruning with lift Exercise 11: Pruning with confidence Exercise 12: Advanced Apriori results pruning Exercise 13: Aggregation and filtering Exercise 14: Applying Zhang's rule Exercise 15: Advanced filtering with multiple metrics

In this final chapter, you’ll learn how visualizations are used to guide the pruning process and summarize final results, which will typically take the form of itemsets or rules. You’ll master the three most useful visualizations -- heatmaps, scatterplots, and parallel coordinates plots – and will apply them to assist a movie streaming service.

Exercise 1: Heatmaps Exercise 2: Visualizing itemset support Exercise 3: Heatmaps with lift Exercise 4: Interpreting heatmaps Exercise 5: Scatterplots Exercise 6: Pruning with scatterplots Exercise 7: Optimality of the support-confidence border Exercise 8: Parallel coordinates plot Exercise 9: Using parallel coordinates to visualize rules Exercise 10: Refining a parallel coordinates plot Exercise 11: Congratulations!