Fast Binary Embedding via Circulant Downsampled Matrix -- A   Data-Independent Approach
  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. 
Sung-Hsien Hsieh, Chun-Shien Lu, Soo-Chang Pei
cs.IT cs.CV cs.LG math.IT