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Deep Unsupervised Image Hashing by Maximizing Bit Entropy

Yunqiang Li, Jan van Gemert

arXiv:2012.12334v1cs.CV

TL;DR

Unsupervised hashing seeks compact codes that preserve semantic similarity for indexing visual collections without costly annotations. The paper proposes a parameter-free Bi-half layer to align continuous features with a half-half bit distribution, reporting state-of-the-art results across image and video benchmarks. It also reports that 16-bit codes can reduce storage and speed while improving accuracy on most evaluated datasets.

  • Problem

    Unsupervised hashing must produce compact binary codes that preserve semantic similarity for indexing large visual collections without annotated labels.

    Source: §1 · p. 1

  • Method

    Bi-half Net uses a parameter-free layer to maximize bit entropy by aligning continuous features with an optimal half-half distribution through a Wasserstein-distance objective.

    Source: §1 · p. 1, §3.1 · p. 3, §3.2 · p. 3

  • Results

    The authors report state-of-the-art unsupervised hashing results on five image datasets and two video datasets.

    Source: §1 · p. 1

  • Takeaways & Limitations

    Except for Nus-wide(II), the method's 16-bit codes outperform other methods' 64-bit codes, yielding a reported threefold storage and speed reduction while improving accuracy.

    Source: §4.3 · p. 7

    The method does not consider independence between different bits, which the authors leave for future work.

    Source: §5 · p. 7

Abstract

from arXiv · show

Unsupervised hashing is important for indexing huge image or video collections without having expensive annotations available. Hashing aims to learn short binary codes for compact storage and efficient semantic retrieval. We propose an unsupervised deep hashing layer called Bi-half Net that maximizes entropy of the binary codes. Entropy is maximal when both possible values of the bit are uniformly (half-half) distributed. To maximize bit entropy, we do not add a term to the loss function as this is difficult to optimize and tune. Instead, we design a new parameter-free network layer to explicitly force continuous image features to approximate the optimal half-half bit distribution. This layer is shown to minimize a penalized term of the Wasserstein distance between the learned continuous image features and the optimal half-half bit distribution. Experimental results on the image datasets Flickr25k, Nus-wide, Cifar-10, Mscoco, Mnist and the video datasets Ucf-101 and Hmdb-51 show that our approach leads to compact codes and compares favorably to the current state-of-the-art.

1 Introduction

Unsupervised hashing replaces large continuous image features with compact binary codes while preserving semantic similarity, without requiring labels. This paper introduces a parameter-free Bi-half layer that targets half-half bit distributions to maximize bit capacity and reports state-of-the-art results across image and video datasets.

1 Introduction

  • Unsupervised hashing learns compact binary codes that preserve semantic similarity without annotated labels, addressing the storage and speed burden of large continuous features.The passage describes deep-network features as typically around 1,000 floating-point values and says they are too slow and large for moderately sized datasets of a few million samples.Source: §1 · p. 1
  • A hash bit has maximal entropy when half the images map to −1 and half to +1, so the method forces continuous features toward that distribution.The paper frames the continuous-to-binary transition as a lossy communication channel and seeks to minimize information loss in it.Source: §1 · p. 1
  • Bi-half is a parameter-free layer that maximizes bit capacity by minimizing a Wasserstein-distance measure, rather than adding a difficult-to-tune loss term.The contribution summary says the Wasserstein distance aligns continuous features with the optimal discrete distribution end-to-end.Source: §1 · p. 1
  • The authors report state-of-the-art unsupervised hashing results on five image datasets and two video datasets.The contribution summary also describes the method as parameter-free and designed to maximize hash-channel information capacity.Source: §1 · p. 1

2 Related Work

Related work distinguishes hashing by its use of data and labels, and describes challenges in quantizing learned features and optimizing binary codes. Prior approaches encourage bit entropy with loss terms or median thresholding, while this work targets an end-to-end half-half distribution.

2 Related Work

  • Hashing methods are data-independent or data-dependent; unsupervised methods avoid labels, while supervised methods can learn codes from labels but require human annotations.Recent unsupervised methods also use deep learning for representation learning, which is the setting followed here.Source: §2 · p. 2
  • Sign quantization can waste discriminative information when all continuous values for a feature have the same sign, while continuous relaxations and continuation methods face optimization challenges.The passage illustrates sign quantization with four positive feature values and notes that continuation methods become less smooth during training, slowing convergence.Source: §2 · p. 2
  • Prior entropy methods add a loss term requiring hyperparameter tuning, while median thresholding is suboptimal for deep learning because its threshold should adapt to minibatch statistics.The paper instead describes an end-to-end optimal-transport approach that quantizes continuous features toward a half-half binary distribution.Source: §2 · p. 2

3 Approach

The approach treats quantization from continuous features U to binary codes B as a lossy channel, seeking high channel capacity through balanced bits and low conditional entropy. It uses an optimal-transport bi-half layer to assign binary codes and a proxy derivative to align feature updates with those assignments.

3.1 Maximizing hash channel capacity

  • Channel capacity is mutual information I(U; B), which equals H(B) − H(B|U); maximizing it requires high code entropy and low conditional entropy.Binary-code entropy is maximized by a half-half distribution, while conditional entropy is minimized when each continuous value is transmitted deterministically.Source: §3.1 · p. 3

3.2 Bi-half layer for quantization

  • For each bit, the bi-half layer sorts minibatch features, assigns the top half to +1 and the rest to −1, minimizing the 1-Wasserstein distance to balanced binary codes.The assignment is the optimal transport coupling between the continuous-feature and binary-code distributions.Source: §3.2 · p. 3, Figure 2 · p. 4
  • Random minibatches introduce transmission stochasticity during training, which the authors say can improve generalization like denoising.The layer is described as simple and readily embedded in existing deep architectures.Source: §3.2 · p. 3
  • The layer uses a straight-through estimator because binary codes lack continuous derivatives, setting U and B to have matching update states during backpropagation.Its proxy gradient adds γ(U − B) to the gradient with respect to B.Source: §3.2 · p. 4

4 Experiments

Experiments evaluate Bi-half across image and video retrieval settings, including an AutoEncoder trained from scratch and comparisons with other coding methods. The reported results favor Bi-half on the tested benchmarks, including settings where 16-bit codes match or outperform 64-bit alternatives.

4 Experiments

  • The experiments use five image datasets—Flickr25k, Nus-wide, Cifar-10, Mscoco, and Mnist—and two video datasets, Ucf-101 and Hmdb-51.Source: §4 · p. 4

4.1 Training an AutoEncoder from scratch

  • In the Mnist AutoEncoder experiment, Bi-half learns evenly distributed features, while sign-layer features tangle and entropy regularization requires careful tuning.The retrieval comparison shows entropy regularization is suboptimal to Bi-half; informative latent codes also reduce reconstruction loss.Source: §4.1 · p. 5, Figure 3 · p. 5

4.2 Empirical analysis

  • Bi-half approximates uniform per-bit distributions, outperforms other coding strategies, and performs better than median-based translation, whose results depend on batch size.The median estimate becomes unstable with smaller batches, while memory limits make very large batches difficult to use.Source: §4.2 · p. 6, Figure 4 · p. 6

4.3 Comparison with state-of-the art

  • On Mscoco, the proposed bi-half layer performs best among all methods on TopN-precision at hash lengths 16 and 32, and consistently achieves the best precision-recall results.Source: §4.3 · p. 7, Figure 6 · p. 7
  • For mAP@All on Flickr25k, Nus-wide(II), and Cifar-10(II), our method using 16 bits clearly outperforms other methods using 64 bits on all except Nus-wide(II), where results are on par.Source: §4.3 · p. 7, Table 2 · p. 7
  • On Ucf-101 and Hmdb-51, Bi-half consistently outperforms the sign layer across code lengths and both tested ResNet models.The reported metric is mAP@100; the paper notes the advantage is especially pronounced for short codes.Source: §4.3 · p. 7, Table 3 · p. 7

5 Conclusion

Bi-half Net uses a parameter-free layer to optimize bit entropy, and experiments on seven datasets show state-of-the-art results. The method often matches other methods’ 64-bit results using 16 bits, but does not model independence between bits.

5 Conclusion

  • Bi-half Net achieves state-of-the-art results on seven datasets and often outperforms methods using 64 bits with only 16-bit codes.The layer can be embedded in architectures such as AutoEncoders and has no hyper-parameters.Source: §5 · p. 7
  • The parameter-free Bi-half layer optimizes bit entropy, and its proxy derivative encourages continuous features to align with an ideal half-half distribution.The authors report that it compares favorably with minimizing bit entropy through an additional loss term and hyper-parameter.Source: §5 · p. 7
  • The method does not consider independence between bits, which the authors identify as future work.Source: §5 · p. 7
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