Image representation and approximate query is always a research challenge and is affected greatly by the dimension and size of images. Since hash-based methods and binary encodings in combination with other techniques, such as kernel tricks, a longer binary code and mapping vectors rotation, can maintain a linear query time and query accuracy, they have been used in this area broadly. This paper develops principal component analysis hashing (PCAH) and unequal length of binary coding to divide images into more categories, denoted as PCA-MD, to improve accuracy of the representation and lookup of images. This paper firstly proves that the eigenvector mapping is locality sensitive, which is the basis for more classes division. For the anisotropy of the eigenvectors, PCA-MD utilizes an unequal length of binary coding and fewer eigenvectors, rather than an equal code, to divide the images mapped on every eigenvector to more categories. Moreover, L1-norm distance is applied to measure the distances of images to avoid the enormous computation of Euclidean distance. Theoretical analysis and extensive experimental results demonstrate that the PCA-MD has a higher query performance and a slight longer run time than the state-of-the-art approaches based on the Hamming distance. This in turn verifies that PCAH is a locality sensitive hash and that partitioning into more categories rather than only two categories is reasonable.

中文翻译：

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一种基于主成分分析的图像呈现与检索哈希方案

图像表示和近似查询一直是一个研究挑战，并且受图像维度和大小的影响很大。由于基于哈希的方法和二进制编码与其他技术（例如内核技巧、更长的二进制代码和映射向量旋转）相结合，可以保持线性查询时间和查询精度，因此它们已广泛应用于该领域。本文开发了主成分分析散列（PCAH）和不等长的二进制编码来将图像分成更多的类别，表示为 PCA-MD，以提高图像的表示和查找的准确性。本文首先证明了特征向量映射是局部敏感的，这是更多类划分的基础。对于特征向量的各向异性，PCA-MD 使用不等长的二进制编码和更少的特征向量，而不是一个相等的代码，将映射到每个特征向量上的图像划分为更多类别。此外，L1范数距离用于测量图像的距离以避免欧氏距离的大量计算。理论分析和大量实验结果表明，与基于汉明距离的最新方法相比，PCA-MD 具有更高的查询性能和稍长的运行时间。这反过来又验证了 PCAH 是一个局部敏感的哈希，并且划分为更多类别而不是仅仅两个类别是合理的。理论分析和广泛的实验结果表明，与基于汉明距离的最新方法相比，PCA-MD 具有更高的查询性能和稍长的运行时间。这反过来又验证了 PCAH 是一个局部敏感的哈希，并且划分为更多类别而不是仅仅两个类别是合理的。理论分析和大量实验结果表明，与基于汉明距离的最新方法相比，PCA-MD 具有更高的查询性能和稍长的运行时间。这反过来又验证了 PCAH 是一个局部敏感的哈希，并且划分为更多类别而不是仅仅两个类别是合理的。