MREC: a fast and versatile framework for aligning and matching point clouds with applications to single cell molecular data

TL;DR

MREC is a recursive framework designed for efficient alignment and matching of large datasets, demonstrated on single cell molecular data, offering flexibility and scalability for complex data matching tasks.

Contribution

The paper introduces MREC, a novel recursive decomposition algorithm that improves matching efficiency and flexibility for large datasets, including applications in single cell molecular data analysis.

Findings

MREC effectively aligns large datasets with high accuracy.

The framework is adaptable to various matching algorithms and partitioning strategies.

Demonstrated successful application to single cell molecular data alignment.

Abstract

Comparing and aligning large datasets is a pervasive problem occurring across many different knowledge domains. We introduce and study MREC, a recursive decomposition algorithm for computing matchings between data sets. The basic idea is to partition the data, match the partitions, and then recursively match the points within each pair of identified partitions. The matching itself is done using black box matching procedures that are too expensive to run on the entire data set. Using an absolute measure of the quality of a matching, the framework supports optimization over parameters including partitioning procedures and matching algorithms. By design, MREC can be applied to extremely large data sets. We analyze the procedure to describe when we can expect it to work well and demonstrate its flexibility and power by applying it to a number of alignment problems arising in the analysis of single cell molecular data.