t-closeness explained

Summary

This video explores T-closeness, a crucial concept in database anonymization that builds on K-anonymity. It measures the distribution distance of sensitive values between equivalence classes and the original database, using Earth Mover's Distance (EMD) for numeric data like salary. For categorical data like diseases, a hierarchy is used to calculate distances. The video demonstrates how to calculate EMD and apply it to anonymize data, ensuring privacy like Bob's, and concludes with a teaser for the next topic: differential privacy.

Takeaways

• 📊 T-closeness is an extension of K-anonymity that measures the distance between sensitive values' distributions in equivalence classes and the original database.
• 🔢 Numerical data like salary is easier to work with for T-closeness because distances between distributions can be directly calculated.
• 📉 Earth Mover's Distance (EMD) is used to calculate the effort required to transform one distribution into another by 'moving' data points.
• 📐 The EMD is calculated by subtracting and dividing values between distributions, minimizing distance for optimal mass flow.
• 🏥 For categorical data (e.g., diseases), a hierarchy tree is used to calculate distances between different values based on shared ancestors in the tree.
• 🌳 The height of the tree and the number of steps needed to find a common ancestor determine the distance between categories.
• ⚖️ The process of measuring T-closeness helps ensure that equivalence classes are not too different from the original distribution, preserving privacy.
• 🔍 In practice, T-closeness helps prevent sensitive information (like Bob's salary or health condition) from being inferred by measuring the 'closeness' of generalized data.
• 🔒 This anonymization process results in data being 3-anonymous, 3-diverse, and within acceptable T-closeness levels for salary and disease.
• 📈 Future videos will cover more topics like differential privacy as the series on database anonymization continues.

Q & A

What is the main topic of the video?

The video discusses the concept of T-closeness, an extension of K-anonymity used in database anonymization, and how it measures the distance between the distribution of sensitive values in equivalence classes and the original database.

How does T-closeness extend K-anonymity?

T-closeness extends K-anonymity by measuring the closeness of the distribution of sensitive values between equivalence classes and the original database, ensuring that the privacy risk is minimized by considering both the quasi-identifiers and the sensitive attributes.

What are the sensitive attributes in the example used in the video?

The sensitive attributes in the example are salary (numeric data) and disease (categorical data).

What metric is used to calculate the distance between distributions for numeric data?

The metric used is called Earth Mover's Distance, which calculates the effort needed to transform one distribution into another by minimizing the distance between the elements of the distributions.

How is the Earth Mover's Distance calculated in the example?

In the example, the difference between elements from the equivalence class distribution and the original distribution is calculated, then divided by the total number of elements minus one. The resulting value is divided again by the probability mass (1/9 in this case) to get the final distance.

How is the distance for categorical data calculated?

For categorical data, the distance is calculated using a hierarchy of elements. The distance between two elements is determined by finding their common ancestor in the hierarchy and dividing by the height of the tree.

What is the maximum possible distance for categorical data using this metric?

The maximum possible distance is 1, which occurs when two elements share only the root node as their common ancestor in the hierarchy.

What strategy is used to protect Bob’s privacy in the example?

Bob's privacy is protected by further generalizing some of his quasi-identifiers, such as using broader age brackets, while maintaining some utility in the data by keeping other identifiers, like ZIP code, less generalized.

What does it mean for a database to be 'T-close'?

A database is T-close if the distance between the distribution of sensitive values in equivalence classes and the overall distribution in the original data does not exceed a threshold (T), which ensures that individual sensitive information is not easily inferred.

What is the next topic in the database anonymization series mentioned in the video?

The next topic in the series will cover differential privacy, a more advanced concept in database anonymization.