局部敏感二元码的双线性随机投影
Bilinear Random Projections for Locality-Sensitive Binary Codes
摘要：
局部敏感散列（LSH）是一种流行的数据无关索引方法，用于近似相似性搜索，其中随机投影，然后量化散列数据库中的点，以确保相互接近的对象的碰撞概率远远高于相距较远的对象。大多数图像的高维视觉描述符都具有自然的矩阵结构。当视觉描述符由高维特征向量表示并且分配长二进制码时，随机投影矩阵在空间和时间上都需要昂贵的复杂性。在本文中，我们分析了双线性随机投影方法，其中特征矩阵转化为二进制码由两个较小的随机投影矩阵。我们的理论分析的基础上扩展Raginsky和Lazebnik的结果，随机傅立叶特征组成的随机二进制量化器，形成局部敏感的二进制码。为此，我们回答以下两个问题：（1）双线性随机投影是否也产生相似性保持二进制码;（2）与大线性投影相比，双线性随机投影是否产生性能增益或损失。关于第一个问题，我们提出了上界和下界的预期汉明距离产生的双线性随机投影的二进制码。关于第二个问题，我们分析了二进制码的两个比特之间的协方差的上界和下界，表明两个比特之间的相关性很小。在MNIST和Flickr 45 K数据集上的数值实验验证了该方法的有效性。
英文摘要：
Locality-sensitive hashing (LSH) is a popular data-independent indexing method for approximate similarity search, where random projections followed by quantization hash the points from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. Most of high-dimensional visual descriptors for images exhibit a natural matrix structure. When visual descriptors are represented by high-dimensional feature vectors and long binary codes are assigned, a random projection matrix requires expensive complexities in both space and time. In this paper we analyze a bilinear random projection method where feature matrices are transformed to binary codes by two smaller random projection matrices. We base our theoretical analysis on extending Raginsky and Lazebnik's result where random Fourier features are composed with random binary quantizers to form locality sensitive binary codes. To this end, we answer the following two questions: (1) whether a bilinear random projection also yields similarity-preserving binary codes; (2) whether a bilinear random projection yields performance gain or loss, compared to a large linear projection. Regarding the first question, we present upper and lower bounds on the expected Hamming distance between binary codes produced by bilinear random projections. In regards to the second question, we analyze the upper and lower bounds on covariance between two bits of binary codes, showing that the correlation between two bits is small. Numerical experiments on MNIST and Flickr45K datasets confirm the validity of our method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
