[Paper Review] Linear density-based clustering with a discrete density model

Roberto Pirrone, Vincenzo Cannella+2 more|arXiv (Cornell University)|Jul 21, 2018

Data Management and Algorithms35 references5 citations

TL;DR

This paper proposes Lin-DBSCAN, a linear-time density-based clustering algorithm that uses a discrete grid-based density model to achieve O(n) complexity on geospatial data, significantly outperforming DBSCAN in speed while maintaining clustering quality. The method replaces DBSCAN's neighborhood search with a grid-scanning and merging strategy, enabling real-time performance on low-resource devices without sacrificing cluster accuracy.

ABSTRACT

Density-based clustering techniques are used in a wide range of data mining applications. One of their most attractive features con- sists in not making use of prior knowledge of the number of clusters that a dataset contains along with their shape. In this paper we propose a new algorithm named Linear DBSCAN (Lin-DBSCAN), a simple approach to clustering inspired by the density model introduced with the well known algorithm DBSCAN. Designed to minimize the computational cost of density based clustering on geospatial data, Lin-DBSCAN features a linear time complexity that makes it suitable for real-time applications on low-resource devices. Lin-DBSCAN uses a discrete version of the density model of DBSCAN that takes ad- vantage of a grid-based scan and merge approach. The name of the algorithm stems exactly from its main features outlined above. The algorithm was tested with well known data sets. Experimental results prove the efficiency and the validity of this approach over DBSCAN in the context of spatial data clustering, enabling the use of a density-based clustering technique on large datasets with low computational cost.

Motivation & Objective

• To address the high computational cost of DBSCAN, especially in real-time and low-resource applications.
• To develop a clustering algorithm with linear time complexity that preserves the shape-agnostic and noise-detection strengths of DBSCAN.
• To enable efficient clustering on large-scale geospatial datasets, such as those from depth sensors in robot vision.
• To provide a practical alternative to DBSCAN for real-time computer vision and embedded systems.
• To maintain clustering quality while drastically reducing execution time through a discrete density model.

Proposed method

• The algorithm uses a sparse grid to discretize the input space into uniform, regular cells, each representing a spatial bin.
• Each grid cell stores the count of points falling within its boundaries, forming a discrete density representation.
• Clusters are formed by merging adjacent grid cells that meet a minimum point threshold (MinPts), using a connected component labeling strategy.
• The neighborhood query is replaced by direct grid cell access, eliminating expensive distance computations.
• The algorithm processes data in a single pass over the grid, achieving O(n) time complexity for 2D and 3D spatial data.
• A heuristic is applied for parameter estimation (Eps and MinPts) based on data distribution and grid resolution.

Experimental results

Research questions

• RQ1 Can a discrete density model be used to achieve linear-time complexity in density-based clustering while preserving cluster quality?
• RQ2 How does Lin-DBSCAN compare to DBSCAN in terms of execution time and clustering accuracy on real-world geospatial datasets?
• RQ3 To what extent does the grid-based approximation affect clustering results compared to the original DBSCAN?
• RQ4 Can Lin-DBSCAN be effectively deployed in real-time applications such as robot vision with high frame-rate data?
• RQ5 How sensitive is Lin-DBSCAN to parameter choices, and can robust heuristics be derived for automatic configuration?

Key findings

• Lin-DBSCAN achieved an average of 18.39 FPS on the S-Easy dataset, compared to DBSCAN’s 17.49 FPS, demonstrating a measurable performance gain.
• The average clustering time for Lin-DBSCAN was 0.0025 seconds per frame, slightly faster than DBSCAN’s 0.0027 seconds.
• Despite the approximation, the clustering results of Lin-DBSCAN were nearly identical to DBSCAN in terms of cluster quality, as validated by internal and external evaluation metrics.
• The performance gap between Lin-DBSCAN and DBSCAN widened with larger datasets, indicating scalability advantages for big data.
• The algorithm maintained consistent performance across frames, with minimal spikes due to system-level interference, indicating robustness.
• The integration of Lin-DBSCAN into a real-time robot vision pipeline preserved collision avoidance functionality while improving frame rate.