In this paper we develop a new model for deep image clustering, using convolutional neural networks and tensor kernels. The proposed Deep Tensor Kernel Clustering (DTKC) consists of a convolutional neural network (CNN), which is trained to reflect a common cluster structure at the output of its intermediate layers. Encouraging a consistent cluster structure throughout the network has the potential to guide it towards meaningful clusters, even though these clusters might appear to be nonlinear in the input space. The cluster structure is enforced through the idea of unsupervised companion objectives, where separate loss functions are attached to layers in the network. These unsupervised companion objectives are constructed based on a proposed generalization of the Cauchy-Schwarz (CS) divergence, from vectors to tensors of arbitrary rank. Generalizing the CS divergence to tensor-valued data is a crucial step, due to the tensorial nature of the intermediate representations in the CNN. Several experiments are conducted to thoroughly assess the performance of the proposed DTKC model. The results indicate that the model outperforms, or performs comparable to, a wide range of baseline algorithms. We also empirically demonstrate that our model does not suffer from objective function mismatch, which can be a problematic artifact in autoencoder-based clustering models.

中文翻译：

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使用张量核和无监督伴随目标进行深度图像聚类

在本文中，我们使用卷积神经网络和张量内核开发了一种用于深度图像聚类的新模型。所提出的深度张量核聚类 (DTKC) 由卷积神经网络 (CNN) 组成，该网络经过训练以在其中间层的输出端反映常见的聚类结构。在整个网络中鼓励一致的集群结构有可能将其引导到有意义的集群，即使这些集群在输入空间中可能看起来是非线性的。集群结构是通过无监督伴随目标的想法来实施的，其中单独的损失函数附加到网络中的层。这些无监督的伴随目标是基于 Cauchy-Schwarz (CS) 散度的拟议泛化构建的，从向量到任意等级的张量。由于 CNN 中中间表示的张量性质，将 CS 散度推广到张量值数据是关键的一步。进行了多次实验以彻底评估所提出的 DTKC 模型的性能。结果表明，该模型优于或与各种基线算法相媲美。我们还凭经验证明我们的模型不会受到目标函数不匹配的影响，这在基于自动编码器的聚类模型中可能是一个有问题的工件。广泛的基线算法。我们还凭经验证明我们的模型不会受到目标函数不匹配的影响，这在基于自动编码器的聚类模型中可能是一个有问题的工件。广泛的基线算法。我们还凭经验证明我们的模型不会受到目标函数不匹配的影响，这在基于自动编码器的聚类模型中可能是一个有问题的工件。