Multi-view spectral clustering (MVSC) has garnered growing interest across various real-world applications, owing to its flexibility in managing diverse data space structures. Nevertheless, the fusion of multiple $n\times n$n×n similarity matrices and the separate post-discretization process hinder the utilization of MVSC in large-scale tasks, where $n$n denotes the number of samples. Moreover, noise in different similarity matrices, along with the two-stage mismatch caused by the post-discretization, results in a reduction in clustering effectiveness. To overcome these challenges, we establish a novel fast multi-view discrete clustering (FMVDC) model via spectral embedding fusion, which integrates spectral embedding matrices ($n\times c$n×c, $c\ll n$c≪n) to directly obtain discrete sample categories, where $c$c indicates the number of clusters, bypassing the need for both similarity matrix fusion and post-discretization. To further enhance clustering efficiency, we employ an anchor-based spectral embedding strategy to decrease the computational complexity of spectral analysis from cubic to linear. Since gradient descent methods are incapable of discrete models, we propose a fast optimization strategy based on the coordinate descent method to solve the FMVDC model efficiently. Extensive studies demonstrate that FMVDC significantly improves clustering performance compared to existing state-of-the-art methods, particularly in large-scale clustering tasks.

In light of their capability to capture structural information while reducing computing complexity, anchor graph-based multi-view clustering (AGMC) methods have attracted considerable attention in large-scale clustering problems. Nevertheless, existing AGMC methods still face the following two issues: 1) They directly embedded diverse anchor graphs into a consensus anchor graph (CAG), and hence ignore redundant information and numerous noises contained in these anchor graphs, leading to a decrease in clustering effectiveness; 2) They drop effectiveness and efficiency due to independent post-processing to acquire clustering indicators. To overcome the aforementioned issues, we deliver a novel one-step multi-view clustering method with adaptive low-rank anchor-graph learning (OMCAL). To construct a high-quality CAG, OMCAL provides a nuclear norm-based adaptive CAG learning model against information redundancy and noise interference. Then, to boost clustering effectiveness and efficiency substantially, we incorporate category indicator acquisition and CAG learning into a unified framework. Numerous studies conducted on ordinary and large-scale datasets indicate that OMCAL outperforms existing state-of-the-art methods in terms of clustering effectiveness and efficiency.

Hypergraph clustering has garnered considerable attention in complex learning tasks due to its powerful capacity for modeling high-order relationships among samples. Nevertheless, existing methods encounter two fundamental challenges: 1) The need for an additional discretization step following low-dimensional spectral embedding, which introduces a suboptimal mismatch between continuous embeddings and discrete cluster assignments, thereby impairing clustering performance; and 2) the susceptibility to diverse and complex noise are commonly present in real-world scenarios, which significantly compromises clustering robustness. To address these issues, we propose a novel correntropy-induced hypergraph spectral clustering (CIHSC) model. Different from current spectral clustering methods, CIHSC integrates a correntropy-based framework to enable direct discrete spectral decomposition on hypergraphs, eliminating the need for post discretization and thereby enhancing clustering fidelity and robustness. To effectively address the non-convex optimization arising from the correntropy-induced objective, we develop a half-quadratic optimization strategy tailored to the CIHSC model. Extensive experiments conducted on both real-world and noise-contaminated datasets demonstrate that CIHSC consistently outperforms state-of-the-art clustering methods in terms of performance and robustness.

Multi-view spectral clustering has attracted considerable attention since it can explore common geometric structures from diverse views. Nevertheless, existing min-min framework-based models adopt internal minimization to find the view combination with the minimized within-cluster variance, which will lead to effectiveness loss since the real clusters often exhibit high within-cluster variance. To address this issue, we provide a novel scalable min-max multi-view spectral clustering (SMMSC) model to improve clustering performance. Besides, anchor graphs, rather than full sample graphs, are utilized to reduce the computational complexity of graph construction and singular value decomposition, thereby enhancing the applicability of SMMSC to large-scale applications. Then, we rewrite the min-max model as a minimized optimal value function, demonstrate its differentiability, and develop an efficient gradient descent-based algorithm to optimize it with linear computational complexity. Moreover, we demonstrate that the resultant solution of the proposed algorithm is the global optimum. Numerous experiments on different real-world datasets, including some large-scale datasets, demonstrate that SMMSC outperforms existing state-of-the-art multi-view clustering methods regarding clustering performance.

Due to its high computational complexity, graph-based methods have limited applicability in large-scale multiview clustering tasks. To address this issue, many accelerated algorithms, especially anchor graph-based methods and indicator learning-based methods, have been developed and made a great success. Nevertheless, since the restrictions of the optimization strategy, these accelerated methods still need to approximate the discrete graph-cutting problem to a continuous spectral embedding problem and utilize different discretization strategies to obtain discrete sample categories. To avoid the loss of effectiveness and efficiency caused by the approximation and discretization, we establish a discrete fast multiview anchor graph clustering (FMAGC) model that first constructs an anchor graph of each view and then generates a discrete cluster indicator matrix by solving the discrete multiview graph-cutting problem directly. Since the gradient descent-based method makes it hard to solve this discrete model, we propose a fast coordinate descent-based optimization strategy with linear complexity to solve it without approximating it as a continuous one. Extensive experiments on widely used normal and large-scale multiview datasets show that FMAGC can improve clustering effectiveness and efficiency compared to other state-of-the-art baselines.

Self-supervised learning (SSL) models confront challenges of abrupt informational collapse or slow dimensional collapse. We propose TriNet, which introduces a novel triple-branch architecture for preventing collapse and stabilizing the pretraining. TriNet learns the SSL latent embedding space and incorporates it to a higher level space for predicting pseudo target vectors generated by a frozen teacher. Our experimental results show that the proposed method notably stabilizes and accelerates pre-training and achieves a relative word error rate reduction (WERR) of 6.06% compared to the state-of- the-art (SOTA) Data2vec for a downstream benchmark ASR task. We will release our code at https://github.com/tencent-ailab/.

Three-dimensional geospatial thinking is an important skillset used by earth scientists and students to analyze and interpret data [1]. This method of inquiry is useful in glaciology, where traditional geophysical survey techniques have been adapted to map three-dimensional (3D) ice sheet structures and inform studies of ice flow, mass change, and history in both Greenland and Antarctica. Ice-penetrating radar images the ice in two-dimensional (2D) cross-sections from the surface to the base. Analysis of this data often requires visual inspection and 3D interpretation, but is hindered by data visualization tools and techniques that rarely transcend the two-dimensionality of the computer screen [2]. Recent advances in Augmented Reality (AR) and Virtual Reality (VR), together referred to as Extended Reality (XR), offer a glimpse into the future of 3D ice-sheet data analysis [3]. These technologies offer users an immersive experience where 3D geospatial datasets can be understood more immediately than with 2D maps, and gestural user interfaces can enhance understanding. Here we present Pol-XR, an XR application that supports both visualization and interpretation of ice-penetrating radar in Antarctica and Greenland.

Multi-view clustering has attracted a lot of attention due to its ability to integrate information from distinct views, but how to improve efficiency is still a hot research topic. Anchor graph-based methods and k-means-based methods are two current popular efficient methods, however, both have limitations. Clustering on the derived anchor graph takes a while for anchor graph-based methods, and the efficiency of k-means-based methods drops significantly when the data dimension is large. To emphasize these issues, we developed an efficient multi-view k-means clustering method with multiple anchor graphs (EMKMC). It first constructs anchor graphs for each view and then integrates these anchor graphs using an improved k-means strategy to obtain sample categories without any extra post-processing. Since EMKMC combines the high-efficiency portions of anchor graph-based methods and k-means-based methods, its efficiency is substantially higher than current fast methods, especially when dealing with large-scale high-dimensional multi-view data. Extensive experiments demonstrate that, compared to other state-of-the-art methods, EMKMC can boost clustering efficiency by several to thousands of times while maintaining comparable or even exceeding clustering effectiveness.

One of the hottest topics in unsupervised learning is how to efficiently and effectively cluster large amounts of unlabeled data. To address this issue, we propose an orthogonal conceptual factorization (OCF) model to increase clustering effectiveness by restricting the degree of freedom of matrix factorization. In addition, for the OCF model, a fast optimization algorithm containing only a few low-dimensional matrix operations is given to improve clustering efficiency, as opposed to the traditional CF optimization algorithm, which involves dense matrix multiplications. To further improve the clustering efficiency while suppressing the influence of the noises and outliers distributed in real-world data, an efficient correntropy-based clustering algorithm (ECCA) is proposed in this article. Compared with OCF, an anchor graph is constructed and then OCF is performed on the anchor graph instead of directly performing OCF on the original data, which can not only further improve the clustering efficiency but also inherit the advantages of the high performance of spectral clustering. In particular, the introduction of the anchor graph makes ECCA less sensitive to changes in data dimensions and still maintains high efficiency at higher data dimensions. Meanwhile, for various complex noises and outliers in real-world data, correntropy is introduced into ECCA to measure the similarity between the matrix before and after decomposition, which can greatly improve the clustering effectiveness and robustness. Subsequently, a novel and efficient half-quadratic optimization algorithm was proposed to quickly optimize the ECCA model. Finally, extensive experiments on different real-world datasets and noisy datasets show that ECCA can archive promising effectiveness and robustness while achieving tens to thousands of times the efficiency compared with other state-of-the-art baselines.

Multi-view clustering has received widespread attention owing to its effectiveness by integrating multi-view data appropriately, but traditional algorithms have limited applicability to large-scale real-world data due to their high computational complexity and low robustness. Focusing on the aforementioned issues, we propose an efficient and robust multi-view clustering algorithm with anchor graph regularization (ERMC-AGR). In this work, a novel anchor graph regularization (ARG) is designed to improve the quality of the learned embedded anchor graph (EAG), and the obtained EAG is decomposed by nonnegative matrix factorization (NMF) under correntropy criterion to acquire clustering results directly. Different from the traditional graph regularization that needs to construct a large-scale Laplacian matrix pertaining to the all-sample graph, our lightweight AGR, constructed from the perspective of anchors, can reduce the computational complexity significantly while improving the EAG quality. Moreover, a factor matrix of NMF is constrained to be the cluster indicator matrix to omit additional k-means after optimization. Subsequently, correntropy is utilized to improve the effectiveness and robustness of ERMC-AGR owing to its promising performance to complex noises and outliers. Extensive experiments on real-world datasets and noisy datasets show that ERMC-ARG can improve the clustering efficiency and robustness while ensuring comparable or even better effectiveness.

Spectral clustering has been a hot topic in unsupervised learning owing to its remarkable clustering effectiveness and well-defined framework. Despite this, due to its high computation complexity, it is unable of handling large-scale or high-dimensional data, particularly multi-view large-scale data. To address this issue, in this paper, we propose a fast multi-view clustering algorithm with spectral embedding (FMCSE), which speeds up both the spectral embedding and spectral analysis stages of multi-view spectral clustering. Furthermore, unlike conventional spectral clustering, FMCSE can acquire all sample categories directly after optimization without extra k-means, which can significantly enhance efficiency. Moreover, we also provide a fast optimization strategy for solving the FMCSE model, which divides the optimization problem into three decoupled small-scale sub-problems that can be solved in a few iteration steps. Finally, extensive experiments on a variety of real-world datasets (including large-scale and high-dimensional datasets) show that, when compared to other state-of-the-art fast multi-view clustering baselines, FMCSE can maintain comparable or even better clustering effectiveness while significantly improving clustering efficiency.

The rapid growth of the number of data brings great challenges to clustering, especially the introduction of multi-view data, which collected from multiple sources or represented by multiple features, makes these challenges more arduous. How to clustering large-scale data efficiently has become the hottest topic of current large-scale clustering tasks. Although several accelerated multi-view methods have been proposed to improve the efficiency of clustering large-scale data, they still cannot be applied to some scenarios that require high efficiency because of the high computational complexity. To cope with the issue of high computational complexity of existing multi-view methods when dealing with large-scale data, a fast multi-view clustering model via nonnegative and orthogonal factorization (FMCNOF) is proposed in this paper. Instead of constraining the factor matrices to be nonnegative as traditional nonnegative and orthogonal factorization (NOF), we constrain a factor matrix of this model to be cluster indicator matrix which can assign cluster labels to data directly without extra post-processing step to extract cluster structures from the factor matrix. Meanwhile, the F-norm instead of the L2-norm is utilized on the FMCNOF model, which makes the model very easy to optimize. Furthermore, an efficient optimization algorithm is proposed to solve the FMCNOF model. Different from the traditional NOF optimization algorithm requiring dense matrix multiplications, our algorithm can divide the optimization problem into three decoupled small size subproblems that can be solved by much less matrix multiplications. Combined with the FMCNOF model and the corresponding fast optimization method, the efficiency of the clustering process can be significantly improved, and the computational complexity is nearly O(n) . Extensive experiments on various benchmark data sets validate our approach can greatly improve the efficiency when achieve acceptable performance.

ABSTRACT We present a novel procedural synthesis method to improve small‐scale turbulence details for controllable smoke animation constrained by shapes and paths. In order to enhance fluid details without introducing unpleasing fluid control effects, we propose a spatial–temporal varying synthesis parameter to control turbulence behaviors and compute it from control force and the vorticity velocity. Our approach can control enhanced turbulence behaviors efficiently and produces visually plausible realistic fine‐scale details while reducing artifacts of large‐scale noises on fluid control. We compare our algorithm to existing procedural synthesis ones to validate its efficiency and controllability. Copyright © 2014 John Wiley & Sons, Ltd.