High-dimensional approximate nearest neighbor: k-d Generalized Randomized Forests (1603.09596v1)

Abstract: We propose a new data-structure, the generalized randomized kd forest, or kgeraf, for approximate nearest neighbor searching in high dimensions. In particular, we introduce new randomization techniques to specify a set of independently constructed trees where search is performed simultaneously, hence increasing accuracy. We omit backtracking, and we optimize distance computations, thus accelerating queries. We release public domain software geraf and we compare it to existing implementations of state-of-the-art methods including BBD-trees, Locality Sensitive Hashing, randomized kd forests, and product quantization. Experimental results indicate that our method would be the method of choice in dimensions around 1,000, and probably up to 10,000, and pointsets of cardinality up to a few hundred thousands or even one million; this range of inputs is encountered in many critical applications today. For instance, we handle a real dataset of $10^6$ images represented in 960 dimensions with a query time of less than $1$sec on average and 90\% responses being true nearest neighbors.

• The paper presents kd-GeRaF, a generalized k-tree using randomization techniques to enhance approximate nearest neighbor search in high-dimensional spaces.
• It employs multiple independently built trees and backtracking optimizations to achieve sub-second query times on datasets with up to one million points.
• Empirical results show kd-GeRaF outperforming methods like BBD-trees, LSH, and product quantization, making it valuable for computer vision and machine learning applications.

Overview of "High-dimensional approximate nearest neighbor: k Generalized Randomized Forests"

This paper introduces a novel data structure known as the k Generalized Randomized Forest (kd-GeRaF) for the task of approximate nearest neighbor (ANN) searching in high-dimensional spaces. The authors propose this framework to effectively and efficiently address the challenges associated with high-dimensional datasets where traditional exact nearest neighbor search methods fall short due to computational infeasibility.

Core Contributions

1. Generalization of k-trees: The kd-GeRaF is an extension and generalization of k-trees, optimized for high-dimensional spaces with extensive data points, ranging from a few hundred thousand to up to a million.
2. Randomization Techniques: A critical innovation of this approach involves the integration of randomization techniques to construct several independently built trees. The search is conducted across these trees simultaneously, which enhances the accuracy of the ANN search by mitigating potential pitfalls of deterministic approaches.
3. Optimization Approach: The innovation extends to optimization techniques that minimize backtracking within the search procedure and streamline distance computations. These optimizations significantly accelerate query response times.
4. Empirical Evaluation: The algorithm's effectiveness is demonstrated through experimental comparisons with existing state-of-the-art techniques such as BBD-trees, Locality Sensitive Hashing (LSH), and product quantization. The new method shows superior performance in scenarios with dimensionalities around 1,000 up to 10,000.

Experimental Results

The empirical results are robust, showcasing that kd-GeRaF consistently outperforms competitive methods within specified parameter ranges. One significant finding is the method's capability to handle datasets with up to 10$^6$ images, each represented in 960-dimensional space, with an average query time of under one second and achieving a 90% rate of true nearest neighbor responses.

Implications and Future Directions

The implications of this research are substantial for applications in computer vision, machine learning, and data mining, where high-dimensional data representations are prevalent. The efficient ANN searching provided by kd-GeRaF can improve computational efficiency and enhance the performance of algorithms dependent on fast and reliable neighbor searches, such as clustering and classification.

Looking forward, potential avenues for further exploration include the adaptation of kd-GeRaF to support dynamic datasets, allowing for efficient insertions and deletions. Another area of interest may be extending this framework for distributed search architectures, which could provide additional scalability benefits. Further work on adaptive parameter configurations based on heuristic or learning approaches could also stabilize search accuracy and performance under varying data characteristics.

Conclusion

In conclusion, this paper presents a viable alternative for ANN searching in high-dimensional contexts, characterized by improved speed and accuracy. The kd-GeRaF framework advances the field of geometric search algorithms, providing valuable insights into mitigating complexity issues inherent in high-dimensional data processing. The algorithm's openness in software form also indicates a commitment to allowing further development and benchmarking by the research community.