Modeling Cardinality in Image Hashing

Cardinality constraint, namely, constraining the number of nonzero outputs of models, has been widely used in structural learning. It can be used for modeling the dependencies between multidimensional labels. In hashing, the final outputs are also binary codes, which are similar to multidimensional labels. It has been validated that estimating how many 1's in a multidimensional label vector is easier than directly predicting which elements are 1 and estimating cardinality as a prior step will improve the classification performance. Hence, in this article, we incorporate cardinality constraint into the unsupervised image hashing problem. The proposed model is divided into two steps: 1) estimating the cardinalities of hashing codes and 2) then estimating which bits are 1. Unlike multidimensional labels that are known and fixed in the training phase, the hashing codes are generally learned through an iterative method and, therefore, their cardinalities are unknown and not fixed during the learning procedure. We use a neural network as a cardinality predictor and its parameters are jointly learned with the hashing code generator, which is an autoencoder in our model. The experiments demonstrate the efficiency of our proposed method.