Private Clustering with List-Decodable Covers and Lower-Dimensional Search
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Solution Overview
Problem
Existing clustering algorithms in the differential privacy model suffer from unfeasible runtimes and/or fail to achieve the desired level of privacy, particularly in real-world applications involving sensitive data.
Innovation Solution
A method involving dimensionality reduction, sparse selection techniques, and clustering algorithms in a lower dimensional space to identify clusters, followed by determining cluster centers, while ensuring differential privacy through probabilistic sampling and lattice-based covers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional clustering algorithms are applied in the differential privacy model, then privacy protection is achieved, but runtime becomes unfeasible
Solution Approach 1:
The algorithm segments the clustering process into two distinct phases: (1) a private preprocessing phase that computes quantized centroids and distance thresholds with differential privacy guarantees, and (2) a non-private efficient phase that performs actual clustering using the precomputed structures. This segmentation allows the privacy-intensive operations to be performed once offline, while the online clustering operates efficiently without repeated privacy computations.
Solution Approach 2:
The algorithm performs preliminary computation of quantized centroids, distance thresholds, and cover sets before the actual clustering task. These precomputed private structures (quantized centroids, thresholds, and covers) are stored and reused during the clustering process, eliminating the need to repeatedly perform expensive private computations for each clustering operation.
2Reliability
If traditional clustering algorithms are applied in the differential privacy model, then privacy protection is achieved, but computational complexity increases
Solution Approach 1:
The algorithm changes the parameter representation by introducing quantized centroids and distance thresholds as discrete parameters. Instead of working with continuous high-dimensional space, the algorithm discretizes the space using quantization levels and thresholds, which reduces the effective search space and simplifies the clustering computations while maintaining privacy guarantees.
Solution Approach 2:
The algorithm introduces intermediate data structures (quantized centroids, distance thresholds, and cover sets) that act as mediators between the private input data and the clustering output. These intermediaries encapsulate the privacy-sensitive computations and provide a simplified interface for the subsequent non-private clustering operations, reducing overall computational complexity.
3Productivity
If dimensionality reduction is performed, then computational efficiency is improved, but clustering precision may be affected
Solution Approach 1:
The algorithm changes the dimensional representation by projecting high-dimensional data onto lower-dimensional subspaces defined by the quantized centroids. This parameter transformation reduces computational complexity while the use of multiple quantization levels and thresholds preserves clustering precision by maintaining sufficient detail in the reduced representation.
Solution Approach 2:
The algorithm creates compressed representations (copies) of the original data in the form of quantized centroids and distance thresholds. These copies capture the essential clustering structure of the high-dimensional data in a lower-dimensional format, enabling efficient computations while preserving clustering accuracy through the fidelity of the compressed representation.
Data Source
AI summary
Example techniques are provided for the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, the present disclosure provides efficient differentially private algorithms that achieve essentially the same approximation ratios as those that can be obtained by any non-private algorithm, while incurring only small additive errors. This improves upon existing efficient algorithms that only achieve some large constant approximation factors.