Learning to Hash with Binary Deep Neural Network
This work proposes deep network models and learning algorithms for unsupervised and supervised binary hashing. Our novel network design constrains one hidden layer to directly output the binary codes. This addresses a challenging issue in some previous wo
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Abstract. This work proposes deep network models and learning algorithms for unsupervised and supervised binary hashing. Our novel network design constrains one hidden layer to directly output the binary codes. This addresses a challenging issue in some previous works: optimizing non-smooth objective functions due to binarization. Moreover, we incorporate independence and balance properties in the direct and strict forms in the learning. Furthermore, we include similarity preserving property in our objective function. Our resulting optimization with these binary, independence, and balance constraints is difficult to solve. We propose to attack it with alternating optimization and careful relaxation. Experimental results on three benchmark datasets show that our proposed methods compare favorably with the state of the art.
Keywords: Learning optimizatization
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Introduction
We are interested in learning binary hash codes for large scale visual search. Two main difficulties with large scale visual search are efficient storage and fast searching. An attractive approach for handling these difficulties is binary hashing, where each original high dimensional vector x ∈ RD is mapped to a very compact binary vector b ∈ {−1, 1}L , where L D. Hashing methods can be divided into two categories: data-independent and data-dependent. Methods in data-independent category [1–4] rely on random projections for constructing hash functions. Methods in data-dependent category use the available training data to learn the hash functions in unsupervised [5–9] or supervised manner [10–15]. The review of data-independent/data-dependent hashing methods can be found in recent surveys [16–18]. One difficult problem in hashing is to deal with the binary constraint on the codes. Specifically, the outputs of the hash functions have to be binary. In general, this binary constraint leads to a NP-hard mixed-integer optimization problem. To handle this difficulty, most aforementioned methods relax the constraint during the learning of hash functions. With this relaxation, the continuous codes are learned first. Then, the codes are binarized (e.g., with thresholding). c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part V, LNCS 9909, pp. 219–234, 2016. DOI: 10.1007/978-3-319-46454-1 14
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This relaxation greatly simplifies the original binary constrained problem. However, the solution can be suboptimal, i.e., the binary codes resulting from thresholded continuous codes could be inferior to those that are obtained by including the binary constraint in the learning. Furthermore, a good hashing method should produce binary codes with the properties [5]: (i) similarity preserving, i.e., (dis)similar inputs should likely have (dis)similar binary codes; (ii) independence, i.e., different bits in the binary codes are independent to each other; (iii) balance, i.e., each bit has a 50 % chance of being 1 or −1. The direct incorporation of the independent and balance properties
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