Subspace clustering aims to recover low-dimensional subspaces from high-dimensional data and assign each data point to its corresponding subspace. State-of-the-art subspace clustering methods rely on self-expressive models to represent each data point as a linear combination of other data points. However, these methods typically suffer from scalability challenges when dealing with large-scale datasets. In particular, the limited capacity to capture similarities among data points within the same subspace leads to poor connectivity of the affinity matrix, often resulting in over-segmentation. In this paper, we propose a scalable self-expressive model based on consensus learning with selectively sampled subsets to address the connectivity issue. Our core insight is that an ideal alignment between global and local solutions across multiple small subsets plays a key role in promoting dense connections in the affinity matrix for large-scale datasets. To this end, our model is designed to flexibly fuse sparse local solutions obtained from small subsets in a consensus-aware manner to derive a global solution that captures richer pairwise relationships within each subspace. Moreover, we introduce a selective subsampling strategy to generate subsets that effectively approximate the spatial support of the original dataset. This contributes to the reliability of solved local solutions, which further enables robust clustering even in imbalanced datasets. Extensive experiments on synthetic and five real-world datasets show that our method achieves state-of-the-art performance, in terms of clustering accuracy and connectivity.

ABSTRACT Unsupervised anomaly localization aims to identify anomalous regions that deviate from normal sample patterns. Most recent methods perform feature matching or reconstruction for the target sample with pre‐trained deep neural networks. However, they still struggle to address challenging anomalies because the deep embeddings stored in the memory bank can be less powerful and informative. Specifically, prior methods often overly rely on the finite resources stored in the memory bank, which leads to low robustness to unseen targets. In this paper, we propose a novel subspace‐guided feature reconstruction framework to pursue adaptive feature approximation for anomaly localization. It first learns to construct low‐dimensional subspaces from the given nominal samples, and then learns to reconstruct the given deep target embedding by linearly combining the subspace basis vectors using the self‐expressive model. Our core is that, despite the limited resources in the memory bank, the out‐of‐bank features can be alternatively “mimicked” to adaptively model the target. Moreover, we propose a sampling method that leverages the sparsity of subspaces and allows the feature reconstruction to depend only on a small resource subset, contributing to less memory overhead. Extensive experiments on three benchmark datasets demonstrate that our approach generally achieves state‐of‐the‐art anomaly localization performance.

The task of incomplete multi-view clustering (IMvC) aims to partition multi-view data with a lack of completeness into different clusters. The incompleteness can be typically categorized into the case of instance-missing and view-unaligned MvC. However, prior methods either consider each of them or struggle to pursue consistent latent representations among views. In this paper, we propose two forms of contrastive learning paradigms to jointly handle both cases for IMvC. Specifically, we design an instance-oriented contrastive (IOC) learning strategy to achieve intra-class consistency. As negative samples within different datasets can exhibit diverse distributions, we formulate a parameterized boundary for IOC learning to flexibly deal with such differing data modes. To preserve inter-view consistency, we further devise category-oriented contrastive (COC) learning such that data from different views can be seamlessly integrated into a combined semantic space. We also recover the missing instances with the learned latent representations in a reconstructing manner for realigning the incomplete multi-view data to facilitate clustering. Our approach unifies the solution to both incomplete cases into one formulation. To demonstrate the effectiveness of our model, we conduct four types of MvC tasks on six benchmark multi-view datasets and compare our method against state-of the-art IMvC methods. Extensive experiments show that our method achieves state-of-the-art performance, quantitatively and qualitatively.

Speech-driven facial animation aims to synthesize lip-synchronized 3D talking faces following the given speech signal. Prior methods to this task mostly focus on pursuing realism with deterministic systems, yet characterizing the potentially stochastic nature of facial motions has been to date rarely studied. While generative modeling approaches can easily handle the one-to-many mapping by repeatedly drawing samples, ensuring a diverse mode coverage of plausible facial motions on small-scale datasets remains challenging and less explored. In this article, we propose predicting multiple samples conditioned on the same audio signal and then explicitly encouraging sample diversity to address diverse facial animation synthesis. Our core insight is to guide our model to explore the expressive facial latent space with a diversity-promoting loss such that the desired latent codes for diversification can be ideally identified. To this end, building upon the rich facial prior learned with vector-quantized variational auto-encoding mechanism, our model temporally queries multiple stochastic codes which can be flexibly decoded into a diverse yet plausible set of speech-faithful facial motions. To further allow for control over different facial parts during generation, the proposed model is designed to predict different facial portions of interest in a sequential manner, and compose them to eventually form full-face motions. Our paradigm realizes both diverse and controllable facial animation synthesis in a unified formulation. We experimentally demonstrate that our method yields state-of-the-art performance both quantitatively and qualitatively, especially regarding sample diversity.

Subspace clustering methods which embrace a self-expressive model that represents each data point as a linear combination of other data points in the dataset provide powerful unsupervised learning techniques. However, when dealing with large datasets, representation of each data point by referring to all data points via a dictionary suffers from high computational complexity. To alleviate this issue, we introduce a parallelizable multi-subset based self-expressive model (PMS) which represents each data point by combining multiple subsets, with each consisting of only a small proportion of the samples. The adoption of PMS in subspace clustering (PMSSC) leads to computational advantages because the optimization problems decomposed over each subset are small, and can be solved efficiently in parallel. Furthermore, PMSSC is able to combine multiple self-expressive coefficient vectors obtained from subsets, which contributes to an improvement in self-expressiveness. Extensive experiments on synthetic and real-world datasets show the efficiency and effectiveness of our approach in comparison to other methods.

Abstract In this paper, the problem of clustering data points that lie near or on a union of independent low‐dimensional subspaces is addressed. To this end, the popular spectral clustering‐based algorithms usually follow a two‐stage strategy that initially builds an affinity matrix and then applies spectral clustering. However, an inappropriate affinity matrix that does not sufficiently connect data points lying on the same subspace will easily lead to the issue of over‐segmentation. To alleviate this issue, building the affinity matrix based on subspace hypotheses generated by an iterative sampling operation according to the Random Cluster Model under the framework of energy minimisation is proposed. Specifically, each hypothesis is generated from a large number of data points by sampling a component in a K ‐nearest neighbour graph. Extensive experiments on synthetic data and real‐world datasets show that the proposed method can improve the connectivity of the affinity matrix and provide competitive results against state‐of‐the‐art methods.

In this paper we address the problem of geometric multi-model fitting using a few weakly annotated data points, which has been little studied so far. In weak annotating (WA), most manual annotations are supposed to be correct yet inevitably mixed with incorrect ones. Such WA data can naturally arise through interaction in various tasks. For example, in the case of homography estimation, one can easily annotate points on the same plane or object with a single label by observing the image. Motivated by this, we propose a novel method to make full use of WA data to boost multi-model fitting performance. Specifically, a graph for model proposal sampling is first constructed using the WA data, given the prior that WA data annotated with the same weak label has a high probability of belonging to the same model. By incorporating this prior knowledge into the calculation of edge probabilities, vertices (i.e., data points) lying on or near the latent model are likely to be associated and further form a subset or cluster for effective proposal generation. Having generated proposals, o-expansion is used for labeling, and our method in return updates the proposals. This procedure works in an iterative way. Extensive experiments validate our method and show that it produces noticeably better results than state-of-the-art techniques in most cases.