Practice - Mathematical Formulation - 8.3.2
Practice Questions
Test your understanding with targeted questions
What metaphor does the CRP use to explain clustering?
💡 Hint: Think about how customers relate to data points and tables to clusters.
What does the concentration parameter \( \alpha \) represent?
💡 Hint: Consider how it impacts the probability of starting new tables.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the concentration parameter (α) influence in the CRP?
💡 Hint: Think about how new decisions are made.
True or False: The CRP allows for a set number of clusters.
💡 Hint: Consider the concept of 'infinity' in the restaurant metaphor.
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Challenge Problems
Push your limits with advanced challenges
Consider a scenario where you have a CRP in a data set with a concentration parameter α = 5 and a total of n = 10 existing customers. Calculate the probability of a new customer joining an existing table with the following distribution of customers at combinations: Table 1 (4), Table 2 (3), Table 3 (2), and Table 4 (1). Draw conclusions!
💡 Hint: Focus on calculating probabilities using the defined formulas.
Create a thoughtful case study analyzing how varying the concentration parameter α impacts the clustering behavior in a dataset of customer purchases.
💡 Hint: Consider examples of datasets and apply the impact of α.
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Reference links
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