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 L2-regularized mutual information via an approximate alternating direction method (ADM) is equivalent to 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.

We present a method that can dramatically accelerate object detection with part based models. The method is based on the observation that the cost of detection is likely to be dominated by the cost of matching each part to the image, and not by the cost of computing the optimal configuration of the parts as commonly assumed. Therefore accelerating detection requires minimizing the number of part-to-image comparisons. To this end we propose a multiple-resolutions hierarchical part based model and a corresponding coarse-to-fine inference procedure that recursively eliminates from the search space unpromising part placements. The method yields a ten-fold speedup over the standard dynamic programming approach and is complementary to the cascade-of-parts approach of. Compared to the latter, our method does not have parameters to be determined empirically, which simplifies its use during the training of the model. Most importantly, the two techniques can be combined to obtain a very significant speedup, of two orders of magnitude in some cases. We evaluate our method extensively on the PASCAL VOC and INRIA datasets, demonstrating a very high increase in the detection speed with little degradation of the accuracy.