We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i \ge \alpha$ for some known parameter $\alpha$, and each $P_i$ has unknown covariance $\Sigma_i \preceq \sigma^2_i \cdot I_d$ for some unknown $\sigma_i$, the goal is to cluster the samples assuming a pairwise mean separation in the order of $(\sigma_i+\sigma_j)/\sqrt{\alpha}$ between every pair of components $P_i$ and $P_j$. Our contributions are as follows: For the special case of nearly uniform mixtures, we give the first poly-time algorithm for this clustering task. Prior work either required separation scaling with the maximum cluster standard deviation (i.e. $\max_i \sigma_i$) [DKK+22b] or required both additional structural assumptions and mean separation scaling as a large degree polynomial in $1/\alpha$ [BKK22]. For general-weight mixtures, we point out that accurate clustering is information-theoretically impossible under our fine-grained mean separation assumptions. We introduce the notion of a clustering refinement -- a list of not-too-small subsets satisfying a similar separation, and which can be merged into a clustering approximating the ground truth -- and show that it is possible to efficiently compute an accurate clustering refinement of the samples. Furthermore, under a variant of the "no large sub-cluster'' condition from in prior work [BKK22], we show that our algorithm outputs an accurate clustering, not just a refinement, even for general-weight mixtures. As a corollary, we obtain efficient clustering algorithms for mixtures of well-conditioned high-dimensional log-concave distributions. Moreover, our algorithm is robust to $\Omega(\alpha)$-fraction of adversarial outliers.

Dirichlet Process Mixture Models (DPMMs) are widely used to address clustering problems. Their main advantage lies in their ability to automatically estimate the number of clusters during the inference process through the Bayesian non-parametric framework. However, the inference becomes considerably slow as the dataset size increases. This paper proposes a new distributed Markov Chain Monte Carlo (MCMC) inference method for DPMMs (DisCGS) using sufficient statistics. Our approach uses the collapsed Gibbs sampler and is specifically designed to work on distributed data across independent and heterogeneous machines, which habilitates its use in horizontal federated learning. Our method achieves highly promising results and notable scalability. For instance, with a dataset of 100K data points, the centralized algorithm requires approximately 12 hours to complete 100 iterations while our approach achieves the same number of iterations in just 3 minutes, reducing the execution time by a factor of 200 without compromising clustering performance. The code source is publicly available at https://github.com/redakhoufache/DisCGS.

This paper uses clustering algorithms to introduce a shape framework for deformable objects. Until now, the shape detection of the deformable objects has faced several challenges: 1) unable to form a unified framework for multiple shapes; 2) the calculation burden as a large number of calculations; 3) the inability to solve the 3D point-cloud case. A novel shape detection framework for deformable objects is presented in this paper, which only uses the input 2D-pixel data of the objects without any artificial markers. The proposed detection approach runs in a highly real-time manner. For the definitions of the shapes of the deformable objects, three shape configurations are used to describe the outlines of the objects, i.e., centerline, contour, and surface. In addition, for the obtaining of the 3D shape, Different from the traditional 3D point cloud processing method, this article uses a one-to-one mapping method between 2D-pixel points and 3D shape points. Therefore, this guarantees a one-to-one correspondence between 2D and 3D shape points. Hence, the proposed approach can enhance the autonomous capability to detect the shape of deformable objects. Detailed experimental results are conducted within the centerline configuration to evaluate the effectiveness of the proposed shape detection framework.

Semi-supervised clustering techniques have emerged as valuable tools for leveraging prior information in the form of constraints to improve the quality of clustering outcomes. Despite the proliferation of such methods, the ability to seamlessly integrate various types of constraints remains limited. While structural entropy has proven to be a powerful clustering approach with wide-ranging applications, it has lacked a variant capable of accommodating these constraints. In this work, we present Semi-supervised clustering via Structural Entropy (SSE), a novel method that can incorporate different types of constraints from diverse sources to perform both partitioning and hierarchical clustering. Specifically, we formulate a uniform view for the commonly used pairwise and label constraints for both types of clustering. Then, we design objectives that incorporate these constraints into structural entropy and develop tailored algorithms for their optimization. We evaluate SSE on nine clustering datasets and compare it with eleven semi-supervised partitioning and hierarchical clustering methods. Experimental results demonstrate the superiority of SSE on clustering accuracy with different types of constraints. Additionally, the functionality of SSE for biological data analysis is demonstrated by cell clustering experiments conducted on four single-cell RNAseq datasets.

With increasingly volatile market conditions and rapid product innovations, operational decision-making for large-scale systems entails solving thousands of problems with limited data. Data aggregation is proposed to combine the data across problems to improve the decisions obtained by solving those problems individually. We propose a novel cluster-based Shrunken-SAA approach that can exploit the cluster structure among problems when implementing the data aggregation approaches. We prove that, as the number of problems grows, leveraging the given cluster structure among problems yields additional benefits over the data aggregation approaches that neglect such structure. When the cluster structure is unknown, we show that unveiling the cluster structure, even at the cost of a few data points, can be beneficial, especially when the distance between clusters of problems is substantial. Our proposed approach can be extended to general cost functions under mild conditions. When the number of problems gets large, the optimality gap of our proposed approach decreases exponentially in the distance between the clusters. We explore the performance of the proposed approach through the application of managing newsvendor systems via numerical experiments. We investigate the impacts of distance metrics between problem instances on the performance of the cluster-based Shrunken-SAA approach with synthetic data. We further validate our proposed approach with real data and highlight the advantages of cluster-based data aggregation, especially in the small-data large-scale regime, compared to the existing approaches.

This makes us ponder the key factors behind this revolution: is it the availability of the large datasets, the actual learning algorithms, or both? ML models rely on very deep networks and enormous labeled datasets, requiring exorbitant computational and human labeling efforts. For example, the market for data annotation costs have crossed one billion US dollars in 2020, and it is estimated to hit seven billion in 2027. Human annotation of semantic segmentation labels takes about 45-60 minutes [BGC10] for a single image. In most vision and NLP applications, unlabeled data is unlimited and is usually available at no cost. To directly reduce the human annotation costs, this paper focuses on identifying smaller subsets of training data that can lead to accurate models with marginal or no loss in performance compared to the ones trained on the full dataset. Among the several approaches for subset selection, two are shown to achieve impressive results: (1) the classical margin sampling algorithm that selects points based on the uncertainty in the class prediction scores [RS06b], and (2) the k-center clustering algorithm [SS18] based on core sets. One may wonder about the natural extension of these two powerful algorithms: is there a principled method that jointly uses both these measures for computing more informative subsets?

Federated Learning (FL) has emerged as a promising solution to perform deep learning on different data owners without exchanging raw data. However, non-IID data has been a key challenge in FL, which could significantly degrade the accuracy of the final model. Among different non-IID types, label skews have been challenging and common in image classification and other tasks. Instead of averaging the local models in most previous studies, we propose FedConcat, a simple and effective approach that concatenates these local models as the base of the global model to effectively aggregate the local knowledge. To reduce the size of the global model, we adopt the clustering technique to group the clients by their label distributions and collaboratively train a model inside each cluster. We theoretically analyze the advantage of concatenation over averaging by analyzing the information bottleneck of deep neural networks. Experimental results demonstrate that FedConcat achieves significantly higher accuracy than previous state-of-the-art FL methods in various heterogeneous label skew distribution settings and meanwhile has lower communication costs. Our code is publicly available at https://github.com/sjtudyq/FedConcat.

Existing multi-stage clustering methods independently learn the salient features from multiple views and then perform the clustering task. Particularly, multi-view clustering (MVC) has attracted a lot of attention in multi-view or multi-modal scenarios. MVC aims at exploring common semantics and pseudo-labels from multiple views and clustering in a self-supervised manner. However, limited by noisy data and inadequate feature learning, such a clustering paradigm generates overconfident pseudo-labels that mis-guide the model to produce inaccurate predictions. Therefore, it is desirable to have a method that can correct this pseudo-label mistraction in multi-stage clustering to avoid the bias accumulation. To alleviate the effect of overconfident pseudo-labels and improve the generalization ability of the model, this paper proposes a novel multi-stage deep MVC framework where multi-view self-distillation (DistilMVC) is introduced to distill dark knowledge of label distribution. Specifically, in the feature subspace at different hierarchies, we explore the common semantics of multiple views through contrastive learning and obtain pseudo-labels by maximizing the mutual information between views. Additionally, a teacher network is responsible for distilling pseudo-labels into dark knowledge, supervising the student network and improving its predictive capabilities to enhance the robustness. Extensive experiments on real-world multi-view datasets show that our method has better clustering performance than state-of-the-art methods.

Hyperspectral image (HSI) clustering is gaining considerable attention owing to recent methods that overcome the inefficiency and misleading results from the absence of supervised information. Contrastive learning methods excel at existing pixel level and super pixel level HSI clustering tasks. The pixel-level contrastive learning method can effectively improve the ability of the model to capture fine features of HSI but requires a large time overhead. The super pixel-level contrastive learning method utilizes the homogeneity of HSI and reduces computing resources; however, it yields rough classification results. To exploit the strengths of both methods, we present a pixel super pixel contrastive learning and pseudo-label correction (PSCPC) method for the HSI clustering. PSCPC can reasonably capture domain-specific and fine-grained features through super pixels and the comparative learning of a small number of pixels within the super pixels. To improve the clustering performance of super pixels, this paper proposes a pseudo-label correction module that aligns the clustering pseudo-labels of pixels and super-pixels. In addition, pixel-level clustering results are used to supervise super pixel-level clustering, improving the generalization ability of the model. Extensive experiments demonstrate the effectiveness and efficiency of PSCPC.

Detecting events from social media data streams is gradually attracting researchers. The innate challenge for detecting events is to extract discriminative information from social media data thereby assigning the data into different events. Due to the excessive diversity and high updating frequency of social data, using supervised approaches to detect events from social messages is hardly achieved. To this end, recent works explore learning discriminative information from social messages by leveraging graph contrastive learning (GCL) and embedding clustering in an unsupervised manner. However, two intrinsic issues exist in benchmark methods: conventional GCL can only roughly explore partial attributes, thereby insufficiently learning the discriminative information of social messages; for benchmark methods, the learned embeddings are clustered in the latent space by taking advantage of certain specific prior knowledge, which conflicts with the principle of unsupervised learning paradigm. In this paper, we propose a novel unsupervised social media event detection method via hybrid graph contrastive learning and reinforced incremental clustering (HCRC), which uses hybrid graph contrastive learning to comprehensively learn semantic and structural discriminative information from social messages and reinforced incremental clustering to perform efficient clustering in a solidly unsupervised manner. We conduct comprehensive experiments to evaluate HCRC on the Twitter and Maven datasets. The experimental results demonstrate that our approach yields consistent significant performance boosts. In traditional incremental setting, semi-supervised incremental setting and solidly unsupervised setting, the model performance has achieved maximum improvements of 53%, 45%, and 37%, respectively.