Contemporary datasets sourced from the web often adopt a multiview format, collecting data from diverse sources, domains, or modules.Existing methodologies employed to analyze such datasets frequently overlook or inaccurately allocate the view-weights, pivotal metrics reflecting each view's significance.This work introduces EVA-MVC, a simple yet effective algorithm designed for Equitable View-weight Allocation (EVA) seamlessly integrated with arbitrary Multi-view Clustering (MVC) methods.Within the EVA module, we establish theoretical connections between view supplementarity and Multi-view Subspace Learning (MSL), leading to the partition of views into View Communities (VCs) based on these foundational principles.These VCs exhibit internal supplementarity similarities, facilitating Equitable View-weights Allocation through VCspecific MSL.The proposed EVA process precedes and operates independently of traditional or SOTA MVC approaches, requiring no additional processing or specialized design, making it an ideal preprocessing step for MVC applications.Through comprehensive evaluations across diverse multi-view datasets, our findings reveal that our EVA significantly enhances the effectiveness of mainstream MVC frameworks, resulting in a notable performance improvement.

In the domain of Multi-view Subspace Clustering (MSC) in Latent Embedding Space (LES), existing methods aim to capture and leverage critical multi-view information by mapping it into a low-dimensional LES. However, several aspects can be further improved: (i) Fusion Strategy: Existing methods adopt either early fusion or late fusion to integrate multi-view information, limiting the effectiveness of the fusion. (ii) Diversity: Current methods often overlook the inherent diversity in the multi-view data by focusing on a single LES. (iii) Efficiency: LES-based methods exhibit high computational complexity, with cubic time and quadratic space requirements based on the number of samples. To address these issues, we propose a novel framework called MSC-DOLES (Multi-view Subspace Clustering in Diverse Orthogonal Latent Embedding Spaces), a novel framework designed to tackle these challenges. MSC-DOLES incorporates a two-stage fusion approach that generates and learns from multiple LES to maximize cross-view diversity. Orthogonality constraints on individual LES ensure view-internal diversity, resulting in a set of Diverse Orthogonal Latent Embedding Spaces (DOLES). The DOLES are then fused into a consensus anchor graph using learnable anchors. The final clustering is induced by partitioning the obtained graph without pre-processing. We develop an eight-step optimization algorithm for MSC-DOLES, which exhibits nearly linear time and space complexities relative to the number of samples. Extensive experiments demonstrate the superiority of MSC-DOLES over state-of-the-art methods.

Although robust tensor completion has been extensively studied, the effect of incorporating side information has not been explored. In this article, we fill this gap by developing a novel high-order robust tensor completion model that incorporates both latent and explicit side information. We base our model on the transformed t-product because the corresponding tensor tubal rank can characterize the inherent low-rank structure of a tensor. We study the effect of side information on sample complexity and prove that our model needs fewer observations than other tensor recovery methods when side information is perfect. This theoretically shows that informative side information is beneficial for learning. Extensive experimental results on synthetic and real data further demonstrate the superiority of the proposed method over several popular alternatives. In particular, we evaluate the performance of our solution based on two important applications, namely, link prediction in signed networks and rating prediction in recommender systems. We show that the proposed model, which manages to exploit side information in learning, outperforms other methods in the learning of such low-rank tensor data. Furthermore, when dealing with varying dimensions, we also design an online robust tensor completion with side information algorithm and validate its effectiveness using a real-world traffic dataset in the supplementary material. The source code is available athttps://github.com/yyyancy/RTCF.

In this paper, we aim to build a novel bandits algorithm that is capable of fully harnessing the power of multi-dimensional data and the inherent non-linearity of reward functions to provide high-usable and accountable decision-making services. To this end, we introduce a generalized low-rank tensor contextual bandits model in which an action is formed from three feature vectors, and thus is represented by a tensor. In this formulation, the reward is determined through a generalized linear function applied to the inner product of the action’s feature tensor and a fixed but unknown parameter tensor with low-rank structure. To effectively achieve the trade-off between exploration and exploitation, we introduce an algorithm called “Generalized Low-Rank Tensor Exploration Subspace then Refine” (G-LowTESTR). This algorithm first collects data to explore the intrinsic low-rank tensor subspace information embedded in the scenario, and then converts the original problem into a lower-dimensional generalized linear contextual bandits problem. Rigorous theoretical analysis shows that the regret bound of G-LowTESTR is superior to those in vectorization and matricization cases. We conduct a series of synthetic and real data experiments to further highlight the effectiveness of G-LowTESTR, leveraging its ability to capitalize on the low-rank tensor structure for enhanced learning.

Spectral Clustering (SC) is an effective clustering method for its excellent performance in partitioning non-linearly distributed data. On the other hand, Ensemble Clustering (EC), a different clustering technology, can promote cluster quality by ensembling the results of base clusterings. In this work, we concentrate on an EC framework that utilizes SC as the base method. Nevertheless, SC suffers from scalability due to its high computational complexity in constructing the Laplacian graph and computing the corresponding eigendecomposition. In the past decades, many efforts have been made to it. However, SC suffers from the scalability issue in processing extensive data, especially in web-scale scenarios. Additionally, EC requires multiple clustering results as the ensemble bases, which further aggravates resource consumption. To address this issue, LiteWSEC, a simple yet efficient Lightweight Framework for Web-scale Spectral Ensemble Clustering, is proposed to cluster web-scale data with limited resource requirements. It adopts the Web-scale Spectral Clustering (WSC) as the base method, which has minimal space overhead without computing overall embedding explicitly. LiteWSEC is highly flexible in the memory requirement, which is adaptive to the available resource. It can partition web-scale data (e.g.,$n $= 8,000 k) in an resource-limited host (e.g., memory is restricted to 1 GB). Experiments on real-world, large-scale, and web-scale datasets demonstrate both the efficiency and effectiveness of LiteWSEC over state-of-the-art SC and EC methods.

Many achievements have been made by studying how to visualize large-scale and high-dimensional data in typically 2D or 3D space. Normally, such a process is performed through a non-parametric (unsupervised) approach which is limited in handling the unseen data. In this work, we study the parametric (supervised) model which is capable to learn a mapping between high-dimensional data space Rd and low-dimensional latent space Rs with similarity structure in Rd preserved where s l d. The GNNVis is proposed, a framework that applies the idea of Graph Neural Networks (GNNs) to the parametric learning process and the learned mapping serves as a Visualizer (Vis) to compute the low-dimensional embeddings of unseen data online. In our framework, the features of data nodes, as well as the (hidden) information of their neighbors are fused to conduct Dimension Reduction. To the best of our knowledge, none of the existing visualization works have studied how to combine such information into the learning representation. Moreover, the learning process of GNNVis is designed as an end-to-end manner and can easily be extended to arbitrary Dimension Reduction methods if the corresponding objective function is given. Based on GNNVis, several typical dimension reduction methods t-SNE, LargeVis, and UMAP are investigated. As a parametric framework, GNNVis is an inherently efficient Visualizer capable of computing the embeddings of large-scale unseen data. To guarantee its scalability in the Training Stage, a novel training strategy with Subgraph Negative Sampling (SNS) is conducted to reduce the corresponding cost. Experimental results in real datasets demonstrate the advantages of GNNVis. The visualization quality of GNNVis outperforms the state-of-the-art parametric models, and is comparable to that of the non-parametric models.

Deducing trip-related information from web-scale datasets has received large amounts of attention recently. Identifying points of interest (POIs) in geo-tagged photos is one of these problems. The problem can be viewed as a standard clustering problem of partitioning two-dimensional objects. In this work, we study spectral clustering, which is the first attempt for the identification of POIs. However, there is no unified approach to assigning the subjective clustering parameters, and these parameters vary immensely in different metropolitans and locations. To address this issue, we study a self-tuning technique that can properly determine the parameters for the clustering needed. Besides geographical information, web photos inherently store other rich information. Such heterogenous information can be used to enhance the identification accuracy. Thereby, we study a novel refinement framework that is based on the tightness and cohesion degree of the additional information. We thoroughly demonstrate our findings by web-scale datasets collected from Flickr.

Deducing trip related information from web-scale datasets has received very large amounts of attention recently. Identifying points of interest (POIs) in geo-tagged photos is one of these problems. The problem can be viewed as a standard clustering problem of partitioning two dimensional objects. In this work, we study spectral clustering which is the first attempt for the POIs identification. However, there is no unified approach to assign the clustering parameters; especially the features of POIs are immensely varying in different metropolitans and locations. To address this, we are intent to study a self-tuning technique which can properly assign the parameters for the clustering needed. Besides geographical information, web photos inherently store rich information. These information are mutually influenced each others and should be taken into trip related mining tasks. To address this, we study reinforcement which constructs the relationship over multiple sources by iterative learning. At last, we thoroughly demonstrate our findings by web scale datasets collected from Flickr.