Image Clustering via the Principle of Rate Reduction in the Age of Pretrained Models

The advent of large pre-trained models has brought about a paradigm shift in both visual representation learning and natural language processing. However, clustering unlabeled images, as a fundamental and classic machine learning problem, still lacks effective solution, particularly for large-scale datasets. In this paper, we propose a novel image clustering pipeline that leverages the powerful feature representation of large pre-trained models such as CLIP and cluster images effectively and efficiently at scale. We show that the pre-trained features are significantly more structured by further optimizing the rate reduction objective. The resulting features may significantly improve the clustering accuracy, e.g., from 57\% to 66\% on ImageNet-1k. Furthermore, by leveraging CLIP's image-text binding, we show how the new clustering method leads to a simple yet effective self-labeling algorithm that successfully works on unlabeled large datasets such as MS-COCO and LAION-Aesthetics. We will release the code in https://github.com/LeslieTrue/CPP.

Unsupervised Manifold Linearizing and Clustering

Clustering data lying close to a union of low-dimensional manifolds, with each manifold as a cluster, is a fundamental problem in machine learning. When the manifolds are assumed to be linear subspaces, many methods succeed using low-rank and sparse priors, which have been studied extensively over the past two decades. Unfortunately, most real-world datasets can not be well approximated by linear subspaces. On the other hand, several works have proposed to identify the manifolds by learning a feature map such that the data transformed by the map lie in a union of linear subspaces, even though the original data are from non-linear manifolds. However, most works either assume knowledge of the membership of samples to clusters, or are shown to learn trivial representations. In this paper, we propose to simultaneously perform clustering and learn a union-of-subspace representation via Maximal Coding Rate Reduction. Experiments on synthetic and realistic datasets show that the proposed method achieves clustering accuracy comparable with state-of-the-art alternatives, while being more scalable and learning geometrically meaningful representations.

Efficient Maximal Coding Rate Reduction by Variational Forms

The principle of Maximal Coding Rate Reduction (MCR$^2$) has recently been proposed as a training objective for learning discriminative low-dimensional structures intrinsic to high-dimensional data to allow for more robust training than standard approaches, such as cross-entropy minimization. However, despite the advantages that have been shown for MCR$^2$ training, MCR$^2$ suffers from a significant computational cost due to the need to evaluate and differentiate a significant number of log-determinant terms that grows linearly with the number of classes. By taking advantage of variational forms of spectral functions of a matrix, we reformulate the MCR$^2$ objective to a form that can scale significantly without compromising training accuracy. Experiments in image classification demonstrate that our proposed formulation results in a significant speed up over optimizing the original MCR$^2$ objective directly and often results in higher quality learned representations. Further, our approach may be of independent interest in other models that require computation of log-determinant forms, such as in system identification or normalizing flow models.

Boosting RANSAC via Dual Principal Component Pursuit

In this paper, we revisit the problem of local optimization in RANSAC. Once a so-far-the-best model has been found, we refine it via Dual Principal Component Pursuit (DPCP), a robust subspace learning method with strong theoretical support and efficient algorithms. The proposed DPCP-RANSAC has far fewer parameters than existing methods and is scalable. Experiments on estimating two-view homographies, fundamental and essential matrices, and three-view homographic tensors using large-scale datasets show that our approach consistently has higher accuracy than state-of-the-art alternatives.

Learning to Parse Wireframes in Images of Man-Made Environments

In this paper, we propose a learning-based approach to the task of automatically extracting a "wireframe" representation for images of cluttered man-made environments. The wireframe (see Fig. 1) contains all salient straight lines and their junctions of the scene that encode efficiently and accurately large-scale geometry and object shapes. To this end, we have built a very large new dataset of over 5,000 images with wireframes thoroughly labelled by humans. We have proposed two convolutional neural networks that are suitable for extracting junctions and lines with large spatial support, respectively. The networks trained on our dataset have achieved significantly better performance than state-of-the-art methods for junction detection and line segment detection, respectively. We have conducted extensive experiments to evaluate quantitatively and qualitatively the wireframes obtained by our method, and have convincingly shown that effectively and efficiently parsing wireframes for images of man-made environments is a feasible goal within reach. Such wireframes could benefit many important visual tasks such as feature correspondence, 3D reconstruction, vision-based mapping, localization, and navigation. The data and source code are available at https://github.com/huangkuns/wireframe.