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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 an 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 first developed a novel algorithm to estimate the number of clusters in a given dataset. We then 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 multimodality bridge between image and text, we develop a simple yet effective self-labeling algorithm that produces meaningful captions for the clusters. Through extensive experiments, we show that our pipeline works well on standard datasets such as CIFAR-10, CIFAR-100, and ImageNet-1k. It also extends to datasets that are not curated for clustering, such as LAION-Aesthetics and WikiArts. We released the code in https://github.com/LeslieTrue/CPP 

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data. 

The problem of clustering points on a union of subspaces finds numerous applications in machine learning and computer vision, and it has been extensively studied in the past two decades. When the subspaces are low-dimensional, the problem can be formulated as a convex sparse optimization problem, for which numerous accurate, efficient and robust methods exist. When the subspaces are of high relative dimension (e.g., hyperplanes), the problem is intrinsically non-convex, and existing methods either lack theory, are computationally costly, lack robustness to outliers, or learn hyperplanes one at a time. In this paper, we propose Hyperplane ARangentment Descent (HARD), a method that robustly learns all the hyperplanes simultaneously by solving a novel non-convex non-smooth ℓ1 minimization problem. We provide geometric conditions under which the ground-truth hyperplane arrangement is a coordinate-wise minimizer of our objective. Furthermore, we devise efficient algorithms, and give conditions under which they converge to coordinate-wise minimizes. We provide empirical evidence that HARD surpasses state-of-the-art methods and further show an interesting experiment in clustering deep features on CIFAR-10.