Fitting a linear subspace to a dataset corrupted by outliers is a fundamental problem in machine learning and statistics, primarily known as(Robust) Principal Component Analysis (PCA)[10,2].

Theresults showthat(1)IRLS canhandle alargernumber ofoutliers thanother methods, (2) it is faster than competing methods at the same level of accuracy, (3) it restores a sparsely corrupted face image with satisfactory visual quality.

The performance of spectral clustering heavily relies on the quality of affinity matrix.

Our key idea is to introduce a novel self-expressive layer between the encoder and the decoder to mimic the "self-expressiveness" property that has proven effective in traditional subspace clustering.

We present a novel deep neural network architecture for unsupervised subspace clustering. This architecture is built upon deep auto-encoders, which non-linearly map the input data into a latent space. Our key idea is to introduce a novel self-expressive layer between the encoder and the decoder to mimic the "selfexpressiveness" property that has proven effective in traditional subspace clustering. Being differentiable, our new self-expressive layer provides a simple but effective way to learn pairwise affinities between all data points through a standard backpropagation procedure. Being nonlinear, our neural-network based method is able to cluster data points having complex (often nonlinear) structures. We further propose pre-training and fine-tuning strategies that let us effectively learn the parameters of our subspace clustering networks. Our experiments show that our method significantly outperforms the state-of-the-art unsupervised subspace clustering techniques.

Contrastive learning has been frequently investigated to learn effective representations for text clustering tasks. While existing contrastive learning-based text clustering methods only focus on modeling instance-wise semantic similarity relationships, they ignore contextual information and underlying relationships among all instances that needs to be clustered. In this paper, we propose a novel text clustering approach called Subspace Contrastive Learning (SCL) which models cluster-wise relationships among instances. Specifically, the proposed SCL consists of two main modules: (1) a self-expressive module that constructs virtual positive samples and (2) a contrastive learning module that further learns a discriminative subspace to capture task-specific cluster-wise relationships among texts. Experimental results show that the proposed SCL method not only has achieved superior results on multiple task clustering datasets but also has less complexity in positive sample construction.

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 text labels 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 without predefined labels, 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.

Interpretability benefits the theoretical understanding of representations. Existing word embeddings are generally dense representations. Hence, the meaning of latent dimensions is difficult to interpret. This makes word embeddings like a black-box and prevents them from being human-readable and further manipulation. Many methods employ sparse representation to learn interpretable word embeddings for better interpretability. However, they also suffer from the unstable issue of grouped selection in $\ell1$ and online dictionary learning. Therefore, they tend to yield different results each time. To alleviate this challenge, we propose a novel method to associate data self-representation with a shallow neural network to learn expressive, interpretable word embeddings. In experiments, we report that the resulting word embeddings achieve comparable and even slightly better interpretability than baseline embeddings. Besides, we also evaluate that our approach performs competitively well on all downstream tasks and outperforms benchmark embeddings on a majority of them.