Hashing hyperplane queries to near points with applications to large-scale active learning

Area of Science:

• Computer Science
• Machine Learning
• Data Mining

Background:

• Efficiently retrieving nearest neighbors to a hyperplane is crucial for large datasets.
• Exhaustive scanning is computationally prohibitive for millions of data points.
• Sublinear time algorithms are needed for practical nearest neighbor search.

Purpose of the Study:

• To propose novel hashing-based solutions for nearest hyperplane query retrieval.
• To enable efficient nearest neighbor search without full database scans.
• To apply these methods to pool-based active learning for practical large-scale selection.

Main Methods:

• Developed two locality-sensitive hashing approaches for hyperplane queries.
• Method 1: Maps data to 2-bit binary keys sensitive to hyperplane normal angles.
• Method 2: Embeds data into a vector space where Euclidean norm approximates distance.

Main Results:

• Both hashing methods achieve sublinear time retrieval of nearest points.
• Method 1 offers more efficient preprocessing.
• Method 2 provides stronger accuracy guarantees.
• Demonstrated practical application to pool-based active learning with millions of points.

Conclusions:

• Hashing-based methods provide efficient solutions for nearest hyperplane queries.
• These algorithms significantly improve the scalability of active learning.
• The trade-offs between preprocessing efficiency and accuracy are empirically demonstrated.