期刊
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
卷 43, 期 6, 页码 1887-1896出版社
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2019.2962683
关键词
Deep clustering; convolutional neural networks; alternating direction methods; k-means; mutual information; Kullback-Leibler (KL) divergence; regularization; multilogit regression
资金
- NSERC (Natural Sciences and Engineering Research Council of Canada)
- FRQNT (Fonds de recherche du Quebec Nature et technologies)
In recent deep clustering studies, discriminative models have shown competitive performance and are found to be equivalent to K-means under certain conditions. A new soft and regularized deep K-means algorithm is proposed, connecting state-of-the-art discriminative models directly to K-means and achieving competitive performance on image clustering benchmarks.
In the context of recent deep clustering studies, discriminative models dominate the literature and report the most competitive performances. These models learn a deep discriminative neural network classifier in which the labels are latent. Typically, they use multinomial logistic regression posteriors and parameter regularization, as is very common in supervised learning. It is generally acknowledged that discriminative objective functions (e.g., those based on the mutual information or the KL divergence) are more flexible than generative approaches (e.g., K-means) in the sense that they make fewer assumptions about the data distributions and, typically, yield much better unsupervised deep learning results. On the surface, several recent discriminative models may seem unrelated to K-means. This study shows that these models are, in fact, equivalent to K-means under mild conditions and common posterior models and parameter regularization. We prove that, for the commonly used logistic regression posteriors, maximizing the L-2 regularized mutual information via an approximate alternating direction method (ADM) is equivalent to minimizing a soft and regularized K-means loss. Our theoretical analysis not only connects directly several recent state-of-the-art discriminative models to K-means, but also leads to a new soft and regularized deep K-means algorithm, which yields competitive performance on several image clustering benchmarks.
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