of higher order terms enables analytical treatments, which can provide a simple and computationally efficient binarization procedure. Despite the fact that the higher order terms are disregarded, the proposed method still achieves considerably high accuracy as explained below.

Experiments {#sec:experiments}
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In the experiments, 128-dimensional gaussian toy data, 128-dimensional SIFT data, and high-dimensional VLAD data with various dimensions are used. The gaussian data is used for evaluating the theoretical behavior of the proposed algorithm. The SIFT data is used for comparing existing methods that is not feasible in high dimensions. The VLAD data is used for evaluating the algorithm in comparison with the state-of-the-art high-dimensional method.

Experimental Protocols {#sec:experimental_protocols}
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### Settings

We use Top-10 recall as performance measure of binary hashing. Euclidean nearest neighbors in original feature space is used as ground truth. For the gaussian data, 10K data points for training, 2K for query and 100K for database is used. For SIFT data, we use SIFT1M dataset[@Jegou2011] and obey the original protocol (100K training set, 10K query set, and 1M database set). For creating VLAD data, we use ILSVRC2010 dataset [@Deng2009]. 25600-dimensional and 64000-dimensional VLAD is calculated from original SIFT data. 20K points for training and 5K points 