Abstract
Due to the correlation among hashing bits, the retrieval performance improvement becomes slower when the hashing code length becomes longer. Existing methods try to regularize the projection matrix as an orthogonal matrix to decorrelate hashing codes. However, the binarization of projected data may completely break the orthogonality. In this paper, we propose a minimum correlation regularization (MCR) for multimodal hashing. Rather than being imposed on projection matrix, MCR is imposed on a differentiable function which approximates the binarization. On the other hand, binary labels could not precisely reflect the distances among data. Hence, we propose a label relaxation scheme to achieve better performance.
Highlights
Multimodal hashing which embeds data to binary codes is an efficient tool for retrieving heterogeneous but correlated multimedia data, such as image-text pairs in Facebook and videotag pairs in Youtube
Unlike aforementioned orthogonality constraints or regularizations [7] that are usually applied on the linear transformation matrices, the proposed minimum correlation regularization (MCR) is applied on the sigmoid function
DECORRELATED MULTIMODAL HASHING In our implementation, we found that subtracting identity matrix is somewhat redundant, so MCR can be simplified as: f
Summary
Multimodal hashing which embeds data to binary codes is an efficient tool for retrieving heterogeneous but correlated multimedia data, such as image-text pairs in Facebook and videotag pairs in Youtube. There are two widely used ways to approximate orthogonal code matrix: (1) adopting orthogonal vectors and thresholding them to generate binary codes [5], [6]; (2) imposing an orthogonality regularization on the objective function [7], [8] These methods on approximating orthogonality have a theoretical defect that the orthogonality is corrupted by quantization. Unlike aforementioned orthogonality constraints or regularizations [7] that are usually applied on the linear transformation matrices, the proposed MCR is applied on the sigmoid function. Because the output of sigmoid function approximates a binary code and the hashing code matrix directly depends on the quantization of it, the propose MCR works better on decorrelating hashing codes (Fig. 1).
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