S^2MVTC: a Simple yet Efficient Scalable Multi-View Tensor Clustering

Anchor-based large-scale multi-view clustering has attracted considerable attention for its effectiveness in handling massive datasets. However, current methods mainly seek the consensus embedding feature for clustering by exploring global correlations between anchor graphs or projection matrices.In this paper, we propose a simple yet efficient scalable multi-view tensor clustering (S^2MVTC) approach, where our focus is on learning correlations of embedding features within and across views. Specifically, we first construct the embedding feature tensor by stacking the embedding features of different views into a tensor and rotating it. Additionally, we build a novel tensor low-frequency approximation (TLFA) operator, which incorporates graph similarity into embedding feature learning, efficiently achieving smooth representation of embedding features within different views. Furthermore, consensus constraints are applied to embedding features to ensure inter-view semantic consistency. Experimental results on six large-scale multi-view datasets demonstrate that S^2MVTC significantly outperforms state-of-the-art algorithms in terms of clustering performance and CPU execution time, especially when handling massive data. The code of S^2MVTC is publicly available at https://github.com/longzhen520/S2MVTC.

Deep unfolding Network for Hyperspectral Image Super-Resolution with Automatic Exposure Correction

In recent years, the fusion of high spatial resolution multispectral image (HR-MSI) and low spatial resolution hyperspectral image (LR-HSI) has been recognized as an effective method for HSI super-resolution (HSI-SR). However, both HSI and MSI may be acquired under extreme conditions such as night or poorly illuminating scenarios, which may cause different exposure levels, thereby seriously downgrading the yielded HSISR. In contrast to most existing methods based on respective low-light enhancements (LLIE) of MSI and HSI followed by their fusion, a deep Unfolding HSI Super-Resolution with Automatic Exposure Correction (UHSR-AEC) is proposed, that can effectively generate a high-quality fused HSI-SR (in texture and features) even under very imbalanced exposures, thanks to the correlation between LLIE and HSI-SR taken into account. Extensive experiments are provided to demonstrate the state-of-the-art overall performance of the proposed UHSR-AEC, including comparison with some benchmark peer methods.

Inverse-Free Fast Natural Gradient Descent Method for Deep Learning

Second-order methods can converge much faster than first-order methods by incorporating second-order derivates or statistics, but they are far less prevalent in deep learning due to their computational inefficiency. To handle this, many of the existing solutions focus on reducing the size of the matrix to be inverted. However, it is still needed to perform the inverse operator in each iteration. In this paper, we present a fast natural gradient descent (FNGD) method, which only requires computing the inverse during the first epoch. Firstly, we reformulate the gradient preconditioning formula in the natural gradient descent (NGD) as a weighted sum of per-sample gradients using the Sherman-Morrison-Woodbury formula. Building upon this, to avoid the iterative inverse operation involved in computing coefficients, the weighted coefficients are shared across epochs without affecting the empirical performance. FNGD approximates the NGD as a fixed-coefficient weighted sum, akin to the average sum in first-order methods. Consequently, the computational complexity of FNGD can approach that of first-order methods. To demonstrate the efficiency of the proposed FNGD, we perform empirical evaluations on image classification and machine translation tasks. For training ResNet-18 on the CIFAR-100 dataset, FNGD can achieve a speedup of 2.05$\times$ compared with KFAC. For training Transformer on Multi30K, FNGD outperforms AdamW by 24 BLEU score while requiring almost the same training time.

TERM Model: Tensor Ring Mixture Model for Density Estimation

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a substantial number of potential tensor permutations can lead to a tensor network with the same structure but varying expressive capabilities. In this paper, we take tensor ring decomposition for density estimator, which significantly reduces the number of permutation candidates while enhancing expressive capability compared with existing used decompositions. Additionally, a mixture model that incorporates multiple permutation candidates with adaptive weights is further designed, resulting in increased expressive flexibility and comprehensiveness. Different from the prevailing directions of tensor network structure/permutation search, our approach provides a new viewpoint inspired by ensemble learning. This approach acknowledges that suboptimal permutations can offer distinctive information besides that of optimal permutations. Experiments show the superiority of the proposed approach in estimating probability density for moderately dimensional datasets and sampling to capture intricate details.

A Novel Deep Clustering Framework for Fine-Scale Parcellation of Amygdala Using dMRI Tractography

The amygdala plays a vital role in emotional processing and exhibits structural diversity that necessitates fine-scale parcellation for a comprehensive understanding of its anatomico-functional correlations. Diffusion MRI tractography is an advanced imaging technique that can estimate the brain's white matter structural connectivity to potentially reveal the topography of the amygdala for studying its subdivisions. In this work, we present a deep clustering pipeline to perform automated, fine-scale parcellation of the amygdala using diffusion MRI tractography. First, we incorporate a newly proposed deep learning approach to enable accurate segmentation of the amygdala directly on the dMRI data. Next, we design a novel streamline clustering-based structural connectivity feature for a robust representation of voxels within the amygdala. Finally, we improve the popular joint dimensionality reduction and k-means clustering approach to enable amygdala parcellation at a finer scale. With the proposed method, we obtain nine unique amygdala parcels. Experiments show that these parcels can be consistently identified across subjects and have good correspondence to the widely used coarse-scale amygdala parcellation.

Phase Guided Light Field for Spatial-Depth High Resolution 3D Imaging

On 3D imaging, light field cameras typically are of single shot, and however, they heavily suffer from low spatial resolution and depth accuracy. In this paper, by employing an optical projector to project a group of single high-frequency phase-shifted sinusoid patterns, we propose a phase guided light field algorithm to significantly improve both the spatial and depth resolutions for off-the-shelf light field cameras. First, for correcting the axial aberrations caused by the main lens of our light field camera, we propose a deformed cone model to calibrate our structured light field system. Second, over wrapped phases computed from patterned images, we propose a stereo matching algorithm, i.e. phase guided sum of absolute difference, to robustly obtain the correspondence for each pair of neighbored two lenslets. Finally, by introducing a virtual camera according to the basic geometrical optics of light field imaging, we propose a reorganization strategy to reconstruct 3D point clouds with spatial-depth high resolution. Experimental results show that, compared with the state-of-the-art active light field methods, the proposed reconstructs 3D point clouds with a spatial resolution of 1280$\times$720 with factors 10$\times$ increased, while maintaining the same high depth resolution and needing merely a single group of high-frequency patterns.

Low-Rank Multitask Learning based on Tensorized SVMs and LSSVMs

Multitask learning (MTL) leverages task-relatedness to enhance performance. With the emergence of multimodal data, tasks can now be referenced by multiple indices. In this paper, we employ high-order tensors, with each mode corresponding to a task index, to naturally represent tasks referenced by multiple indices and preserve their structural relations. Based on this representation, we propose a general framework of low-rank MTL methods with tensorized support vector machines (SVMs) and least square support vector machines (LSSVMs), where the CP factorization is deployed over the coefficient tensor. Our approach allows to model the task relation through a linear combination of shared factors weighted by task-specific factors and is generalized to both classification and regression problems. Through the alternating optimization scheme and the Lagrangian function, each subproblem is transformed into a convex problem, formulated as a quadratic programming or linear system in the dual form. In contrast to previous MTL frameworks, our decision function in the dual induces a weighted kernel function with a task-coupling term characterized by the similarities of the task-specific factors, better revealing the explicit relations across tasks in MTL. Experimental results validate the effectiveness and superiority of our proposed methods compared to existing state-of-the-art approaches in MTL. The code of implementation will be available at https://github.com/liujiani0216/TSVM-MTL.

Tensor Regression

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.

Once-Training-All-Fine: No-Reference Point Cloud Quality Assessment via Domain-relevance Degradation Description

Full-reference (FR) point cloud quality assessment (PCQA) has achieved impressive progress in recent years. However, as reference point clouds are not available in many cases, no-reference (NR) metrics have become a research hotspot. Existing NR methods suffer from poor generalization performance. To address this shortcoming, we propose a novel NR-PCQA method, Point Cloud Quality Assessment via Domain-relevance Degradation Description (D$^3$-PCQA). First, we demonstrate our model's interpretability by deriving the function of each module using a kernelized ridge regression model. Specifically, quality assessment can be characterized as a leap from the scattered perceptual domain (reflecting subjective perception) to the ordered quality domain (reflecting mean opinion score). Second, to reduce the significant domain discrepancy, we establish an intermediate domain, the description domain, based on insights from subjective experiments, by considering the domain relevance among samples located in the perception domain and learning a structured latent space. The anchor features derived from the learned latent space are generated as cross-domain auxiliary information to promote domain transformation. Furthermore, the newly established description domain decomposes the NR-PCQA problem into two relevant stages. These stages include a classification stage that gives the degradation descriptions to point clouds and a regression stage to determine the confidence degrees of descriptions, providing a semantic explanation for the predicted quality scores. Experimental results demonstrate that D$^3$-PCQA exhibits robust performance and outstanding generalization ability on several publicly available datasets. The code in this work will be publicly available at https://smt.sjtu.edu.cn.

Multi-view MERA Subspace Clustering

Tensor-based multi-view subspace clustering (MSC) can capture high-order correlation in the self-representation tensor. Current tensor decompositions for MSC suffer from highly unbalanced unfolding matrices or rotation sensitivity, failing to fully explore inter/intra-view information. Using the advanced tensor network, namely, multi-scale entanglement renormalization ansatz (MERA), we propose a low-rank MERA based MSC (MERA-MSC) algorithm, where MERA factorizes a tensor into contractions of one top core factor and the rest orthogonal/semi-orthogonal factors. Benefiting from multiple interactions among orthogonal/semi-orthogonal (low-rank) factors, the low-rank MERA has a strong representation power to capture the complex inter/intra-view information in the self-representation tensor. The alternating direction method of multipliers is adopted to solve the optimization model. Experimental results on five multi-view datasets demonstrate MERA-MSC has superiority against the compared algorithms on six evaluation metrics. Furthermore, we extend MERA-MSC by incorporating anchor learning to develop a scalable low-rank MERA based multi-view clustering method (sMREA-MVC). The effectiveness and efficiency of sMERA-MVC have been validated on three large-scale multi-view datasets. To our knowledge, this is the first work to introduce MERA to the multi-view clustering topic. The codes of MERA-MSC and sMERA-MVC are publicly available at https://github.com/longzhen520/MERA-MSC.