Net Tree Encoding for Private Non-Interactive K-Means Communication
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Solution Overview
Problem
Existing k-means clustering algorithms are NP-hard and require multiple rounds of communication, making them inefficient and incompatible with certain differential privacy models, especially in distributed settings where an aggregator device may not be trustworthy.
Innovation Solution
A net tree-based approach is used to construct a private coreset of input points, which is then encoded for non-interactive differentially private communication, allowing a single-round transmission to an aggregator device while maintaining privacy guarantees and reducing approximation ratios.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If existing k-means clustering algorithms are used, then clustering functionality is achieved, but multiple rounds of communication are required which is incompatible with noninteractive local models
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing a net tree data structure that captures the geometric relationships among data points. This net tree is constructed beforehand and can be reused for multiple clustering queries without requiring additional communication rounds, thus enabling noninteractive operation while maintaining clustering functionality.
Solution Approach 2:
The patent introduces a net tree as an intermediary data structure that mediates between the raw data and the clustering algorithm. The net tree serves as a preprocessed representation that enables efficient querying and clustering operations without requiring direct interaction between clients and the central server, thereby achieving noninteractive local differential privacy.
2Reliability
If differential privacy is implemented in distributed settings, then privacy guarantees are provided, but compatibility with k-means clustering is lost
Solution Approach 1:
The patent segments the clustering process into distinct phases: (1) construction of the net tree from raw data, (2) encoding of query parameters using local differential privacy, and (3) decoding and execution of clustering operations. This segmentation allows differential privacy to be applied selectively to the encoding phase while preserving the integrity of the k-means clustering algorithm in the execution phase.
Solution Approach 2:
The patent changes the parameter representation by encoding cluster center queries and data point representations through a net tree structure. This parameter transformation enables the application of local differential privacy mechanisms while maintaining the mathematical properties required for k-means clustering to function correctly.
3Measurement precision
If NP-hard k-means algorithms are used, then accurate clustering is achieved, but computational intractability arises
Solution Approach 1:
The patent applies preliminary action by pre-computing the net tree structure that organizes data points in a hierarchical manner. This preprocessing step enables subsequent clustering queries to be answered efficiently by traversing the precomputed structure, avoiding the need to solve the NP-hard k-means problem from scratch for each query.
Solution Approach 2:
The patent introduces dynamics by using the net tree to adaptively select and refine cluster centers based on query parameters. The hierarchical structure of the net tree allows the algorithm to dynamically adjust the level of detail and precision based on the specific clustering requirements, balancing accuracy and computational efficiency.
Data Source
AI summary
A computer-implemented method for encoding data for communications with improved privacy includes obtaining, by a computing system comprising one or more computing devices, input data including one or more input data points. The method can include constructing, by the computing system, a net tree including potential representatives of the one or more input data points, the potential representatives arranged in a plurality of levels, the net tree including a hierarchical data structure including a plurality of hierarchically organized nodes. The method can include determining, by the computing system, a representative of each of the one or more input data points from the potential representatives of the net tree, the representative including one of the plurality of hierarchically organized nodes. The method can include encoding, by the computing system, the representative of each of the one or more input data points for communication.