tasks because they provide high memory efficiency and fast Hamming distance calculation. There are a lot of methods proposed. Major approaches are categorized as Vector Quantization (VQ) based methods [@Wang2010a; @Norouzi2013; @He2013; @Ge2013], hyperplane based linear methods [@Gong2013b; @Liu2012a; @Gong2013], and nonlinear hashing function methods [@Weiss2008; @Joly2011; @Weiss2012; @Liu2012b; @Fan2013].

A typical nonlinear method is Spectral Hashing [@Weiss2008], whose hashing functions are nonlinear eigenfunctions derived from a distribution of data. Some family of Locality Sensitive Hashing uses nonlinear hashing functions[@Pauleve2010]. Kernelized approaches have also been proposed [@Kulis2009a; @Kulis2009b; @Raginsky2009]. Spectral Hashing, ordinary uses a uniform distribution to deriving analytical solution, and its precision is empirically lower compared to ITQ[@Gong2013b] and other state-of-the-art methods for non-uniformly distributed data. To overcome this difficulty, a kernel based approaches are proposed[@Chaudhry2010]. But it is difficult to apply to high-dimensions. Recently proposed method called Spherical Hashing [@Heo2012] is a example of non-kernelized nonlinear method. Since its hashing function is hyper-sphere based, it also needs euclidean distance calculation for hashing. The computational cost is getting large for high-dimensional data.

Recently, a bilinear hashing method, which is called BPBC, that is feasible in high-dimensions was proposed [@Gong2013]. To our knowledge, this is the first binary hashing method 