Fast Binary Embedding via Circulant Downsampled Matrix -- A Data-Independent Approach

TL;DR

This paper introduces a fast, data-independent binary embedding method that uses circulant matrices and downsampling to efficiently produce low-dimensional binary codes while maintaining discriminative power.

Contribution

The authors propose a novel binary embedding scheme combining downsampling and circulant matrices, reducing computation and storage costs with theoretical guarantees for sparse data.

Findings

Achieves O(N + M log M) computation and O(N) storage costs.

Performs comparably to existing methods in image applications.

Effective for sparse data with similarity preservation.

Abstract

Binary embedding of high-dimensional data aims to produce low-dimensional binary codes while preserving discriminative power. State-of-the-art methods often suffer from high computation and storage costs. We present a simple and fast embedding scheme by first downsampling N-dimensional data into M-dimensional data and then multiplying the data with an MxM circulant matrix. Our method requires O(N +M log M) computation and O(N) storage costs. We prove if data have sparsity, our scheme can achieve similarity-preserving well. Experiments further demonstrate that though our method is cost-effective and fast, it still achieves comparable performance in image applications.