Robust Graph Learning From Noisy Data

Robust Supervised Spline Embedding

High-dimensional data present significant challenges such as inadequate sample size, abundance of noise, and the curse of dimensionality, which make many traditional classification algorithms inapplicable. To provide valid inference for such data, it requires finding a noise-free low-dimensional representation that preserves both the underlying manifold structure and discriminative information. However, the existing methods often fail to take full consideration of these requirements. In this article, we introduce a robust supervised spline embedding (RS2E) algorithm for high-dimensional classification. The proposed approach is highlighted in four aspects: 1) it preserves the class-aware submanifold structure in the thin plate spline embedding space; 2) it eliminates noise and outliers to recover the clean manifold by exploiting its intrinsic low complexity; 3) it separates the class-aware submanifolds by maximizing the distance between each data point and the marginal data points of other class-aware submanifolds; and 4) it applies the alternating direction method of multipliers with generalized power iteration to solve the objective function. Promising experimental results on the real-world, generative adversarial network (GAN)-generated and artificially corrupted datasets demonstrate that RS2E outperforms other supervised dimensionality reduction algorithms in terms of classification accuracy.

Robust Subcluster Search and Mergence Clustering

In recent years, graph-based clustering presents outstanding performance and has been widely investigated. It segments the data similarity graph into multiple subgraphs as final clusters. Many methods integrate graph learning and segmentation into a unified optimization problem to explore the graph structure. However, existing research 1) attempts to derive the final clusters from the learned graph directly, which relies on a highly tight internal distribution within each cluster, and is too strict for the real-world data; 2) generally constructs a holistic full sample graph, which means the outliers are involved in graph learning explicitly, and may corrupt the graph quality. To overcome the above limitations, a new clustering model called robust subcluster search and mergence (RSSM) is established in this article. Inspired by the positive-incentive noise (Pi-Noise), RSSM assumes that the outliers are useful for learning the data structure. Considering a few samples with large errors as outliers, RSSM finds the subcentroids by searching an imbalanced residue distribution. In this way, the subcentroids pull the normal samples together and push the outliers far away. Compared with the traditional clusters, the subclusters indicated by the subcentroids are more explicit, where the normal samples are tightly connected. After that, a subcluster similarity graph is constructed to guide the mergence of subclusters. To sum up, RSSM performs the search and mergence of subclusters simultaneously with the help of outliers, and generates a graph that is more suitable for clustering. Experiments on several datasets demonstrate the rationality and superiority of RSSM.

A Novel Composite Graph Neural Network

Graph neural networks (GNNs) have achieved great success in many fields due to their powerful capabilities of processing graph-structured data. However, most GNNs can only be applied to scenarios where graphs are known, but real-world data are often noisy or even do not have available graph structures. Recently, graph learning has attracted increasing attention in dealing with these problems. In this article, we develop a novel approach to improving the robustness of the GNNs, called composite GNN. Different from existing methods, our method uses composite graphs (C-graphs) to characterize both sample and feature relations. The C-graph is a unified graph that unifies these two kinds of relations, where edges between samples represent sample similarities, and each sample has a tree-based feature graph to model feature importance and combination preference. By jointly learning multiaspect C-graphs and neural network parameters, our method improves the performance of semisupervised node classification and ensures robustness. We conduct a series of experiments to evaluate the performance of our method and the variants of our method that only learn sample relations or feature relations. Extensive experimental results on nine benchmark datasets demonstrate that our proposed method achieves the best performance on almost all the datasets and is robust to feature noises.

aKNNO: single-cell and spatial transcriptomics clustering with an optimized adaptive k-nearest neighbor graph

Typical clustering methods for single-cell and spatial transcriptomics struggle to identify rare cell types, while approaches tailored to detect rare cell types gain this ability at the cost of poorer performance for grouping abundant ones. Here, we develop aKNNO to simultaneously identify abundant and rare cell types based on an adaptive k-nearest neighbor graph with optimization. Benchmarking on 38 simulated and 20 single-cell and spatial transcriptomics datasets demonstrates that aKNNO identifies both abundant and rare cell types more accurately than general and specialized methods. Using only gene expression aKNNO maps abundant and rare cells more precisely compared to integrative approaches.

Partial Tubal Nuclear Norm-Regularized Multiview Subspace Learning

In this article, a unified multiview subspace learning model, called partial tubal nuclear norm-regularized multiview subspace learning (PTN2MSL), was proposed for unsupervised multiview subspace clustering (MVSC), semisupervised MVSC, and multiview dimension reduction. Unlike most of the existing methods which treat the above three related tasks independently, PTN2MSL integrates the projection learning and the low-rank tensor representation to promote each other and mine their underlying correlations. Moreover, instead of minimizing the tensor nuclear norm which treats all singular values equally and neglects their differences, PTN2MSL develops the partial tubal nuclear norm (PTNN) as a better alternative solution by minimizing the partial sum of tubal singular values. The PTN2MSL method was applied to the above three multiview subspace learning tasks. It demonstrated that these tasks organically benefited from each other and PTN2MSL has achieved better performance in comparison to state-of-the-art methods.

Multi-View Graph Learning by Joint Modeling of Consistency and Inconsistency

Graph learning has emerged as a promising technique for multi-view clustering due to its ability to learn a unified and robust graph from multiple views. However, existing graph learning methods mostly focus on the multi-view consistency issue, yet often neglect the inconsistency between views, which makes them vulnerable to possibly low-quality or noisy datasets. To overcome this limitation, we propose a new multi-view graph learning framework, which for the first time simultaneously and explicitly models multi-view consistency and inconsistency in a unified objective function, through which the consistent and inconsistent parts of each single-view graph as well as the unified graph that fuses the consistent parts can be iteratively learned. Though optimizing the objective function is NP-hard, we design a highly efficient optimization algorithm that can obtain an approximate solution with linear time complexity in the number of edges in the unified graph. Furthermore, our multi-view graph learning approach can be applied to both similarity graphs and dissimilarity graphs, which lead to two graph fusion-based variants in our framework. Experiments on 12 multi-view datasets have demonstrated the robustness and efficiency of the proposed approach. The code is available at https://github.com/youweiliang/Multi-view_Graph_Learning.

Single-cell and Spatial Transcriptomics Clustering with an Optimized Adaptive K-Nearest Neighbor Graph

Single-cell and spatial transcriptomics have been widely used to characterize cellular landscape in complex tissues. To understand cellular heterogeneity, one essential step is to define cell types through unsupervised clustering. While typical clustering methods have difficulty in identifying rare cell types, approaches specifically tailored to detect rare cell types gain their ability at the cost of poorer performance for grouping abundant ones. Here, we developed aKNNO, a method to identify abundant and rare cell types simultaneously based on an adaptive k-nearest neighbor graph with optimization. Benchmarked on 38 simulated and 20 single-cell and spatial transcriptomics datasets, aKNNO identified both abundant and rare cell types accurately. Without sacrificing performance for clustering abundant cell types, aKNNO discovered known and novel rare cell types that those typical and even specifically tailored methods failed to detect. aKNNO, using transcriptome alone, stereotyped fine-grained anatomical structures more precisely than those integrative approaches combining expression with spatial locations and histology image.

An Integrated Multi-Omics and Artificial Intelligence Framework for Advance Plant Phenotyping in Horticulture

This review discusses the transformative potential of integrating multi-omics data and artificial intelligence (AI) in advancing horticultural research, specifically plant phenotyping. The traditional methods of plant phenotyping, while valuable, are limited in their ability to capture the complexity of plant biology. The advent of (meta-)genomics, (meta-)transcriptomics, proteomics, and metabolomics has provided an opportunity for a more comprehensive analysis. AI and machine learning (ML) techniques can effectively handle the complexity and volume of multi-omics data, providing meaningful interpretations and predictions. Reflecting the multidisciplinary nature of this area of research, in this review, readers will find a collection of state-of-the-art solutions that are key to the integration of multi-omics data and AI for phenotyping experiments in horticulture, including experimental design considerations with several technical and non-technical challenges, which are discussed along with potential solutions. The future prospects of this integration include precision horticulture, predictive breeding, improved disease and stress response management, sustainable crop management, and exploration of plant biodiversity. The integration of multi-omics and AI holds immense promise for revolutionizing horticultural research and applications, heralding a new era in plant phenotyping.

Link-Information Augmented Twin Autoencoders for Network Denoising

Removing noisy links from an observed network is a task commonly required for preprocessing real-world network data. However, containing both noisy and clean links, the observed network cannot be treated as a trustworthy information source for supervised learning. Therefore, it is necessary but also technically challenging to detect noisy links in the context of data contamination. To address this issue, in the present article, a two-phased computational model is proposed, called link-information augmented twin autoencoders, which is able to deal with: 1) link information augmentation; 2) link-level contrastive denoising; 3) link information correction. Extensive experiments on six real-world networks verify that the proposed model outperforms other comparable methods in removing noisy links from the observed network so as to recover the real network from the corrupted one very accurately. Extended analyses also provide interpretable evidence to support the superiority of the proposed model for the task of network denoising.

Multiview Clustering via Proximity Learning in Latent Representation Space

Most existing multiview clustering methods are based on the original feature space. However, the feature redundancy and noise in the original feature space limit their clustering performance. Aiming at addressing this problem, some multiview clustering methods learn the latent data representation linearly, while performance may decline if the relation between the latent data representation and the original data is nonlinear. The other methods which nonlinearly learn the latent data representation usually conduct the latent representation learning and clustering separately, resulting in that the latent data representation might be not well adapted to clustering. Furthermore, none of them model the intercluster relation and intracluster correlation of data points, which limits the quality of the learned latent data representation and therefore influences the clustering performance. To solve these problems, this article proposes a novel multiview clustering method via proximity learning in latent representation space, named multiview latent proximity learning (MLPL). For one thing, MLPL learns the latent data representation in a nonlinear manner which takes the intercluster relation and intracluster correlation into consideration simultaneously. For another, through conducting the latent representation learning and consensus proximity learning simultaneously, MLPL learns a consensus proximity matrix with k connected components to output the clustering result directly. Extensive experiments are conducted on seven real-world datasets to demonstrate the effectiveness and superiority of the MLPL method compared with the state-of-the-art multiview clustering methods.

Multiple Kernel Clustering With Compressed Subspace Alignment

Multiple kernel clustering (MKC) has recently achieved remarkable progress in fusing multisource information to boost the clustering performance. However, the O(n²) memory consumption and O(n³) computational complexity prohibit these methods from being applied into median- or large-scale applications, where n denotes the number of samples. To address these issues, we carefully redesign the formulation of subspace segmentation-based MKC, which reduces the memory and computational complexity to O(n) and O(n²) , respectively. The proposed algorithm adopts a novel sampling strategy to enhance the performance and accelerate the speed of MKC. Specifically, we first mathematically model the sampling process and then learn it simultaneously during the procedure of information fusion. By this way, the generated anchor point set can better serve data reconstruction across different views, leading to improved discriminative capability of the reconstruction matrix and boosted clustering performance. Although the integrated sampling process makes the proposed algorithm less efficient than the linear complexity algorithms, the elaborate formulation makes our algorithm straightforward for parallelization. Through the acceleration of GPU and multicore techniques, our algorithm achieves superior performance against the compared state-of-the-art methods on six datasets with comparable time cost to the linear complexity algorithms.

Parameter-Free Consensus Embedding Learning for Multiview Graph-Based Clustering

Finding a consensus embedding from multiple views is the mainstream task in multiview graph-based clustering, in which the key problem is to handle the inconsistence among multiple views. In this article, we consider clustering effectiveness and practical applicability collectively, and propose a parameter-free model to alleviate the inconsistence of multiple views cleverly. To be specific, the proposed model considers the diversities of multiple views as two-layers. The first layer considers the inconsistence among different features of each view and the second layer considers linking the preembeddings of multiple views attentively. By this way, a consensus embedding can be learned via kernel method effectively and the whole learning procedure is parameter-free. To solve the optimization problem involved in the proposed model, we propose an alternative algorithm which is efficient and easy to implement in practice. In the experiments, we evaluate the proposed model on synthetic and real datasets and the experimental results demonstrate its effectiveness.

The Real Eigenpairs of Symmetric Tensors and Its Application to Independent Component Analysis

It has been proved that the determination of independent components (ICs) in the independent component analysis (ICA) can be attributed to calculating the eigenpairs of high-order statistical tensors of the data. However, previous works can only obtain approximate solutions, which may affect the accuracy of the ICs. In addition, the number of ICs would need to be set manually. Recently, an algorithm based on semidefinite programming (SDP) has been proposed, which utilizes the first-order gradient information of the Lagrangian function and can obtain all the accurate real eigenpairs. In this article, for the first time, we introduce this into the ICA field, which tends to further improve the accuracy of the ICs. Note that the number of eigenpairs of symmetric tensors is usually larger than the number of ICs, indicating that the results directly obtained by SDP are redundant. Thus, in practice, it is necessary to introduce second-order derivative information to identify local extremum solutions. Therefore, originating from the SDP method, we present a new modified version, called modified SDP (MSDP), which incorporates the concept of the projected Hessian matrix into SDP and, thus, can intellectually exclude redundant ICs and select true ICs. Some cases that have been tested in the experiments demonstrate its effectiveness. Experiments on the image/sound blind separation and real multi/hyperspectral image also show its superiority in improving the accuracy of ICs and automatically determining the number of ICs. In addition, the results on hyperspectral simulation and real data also demonstrate that MSDP is also capable of dealing with cases, where the number of features is less than the number of ICs.

Structured Graph Learning for Scalable Subspace Clustering: From Single View to Multiview

Graph-based subspace clustering methods have exhibited promising performance. However, they still suffer some of these drawbacks: they encounter the expensive time overhead, they fail to explore the explicit clusters, and cannot generalize to unseen data points. In this work, we propose a scalable graph learning framework, seeking to address the above three challenges simultaneously. Specifically, it is based on the ideas of anchor points and bipartite graph. Rather than building an n×n graph, where n is the number of samples, we construct a bipartite graph to depict the relationship between samples and anchor points. Meanwhile, a connectivity constraint is employed to ensure that the connected components indicate clusters directly. We further establish the connection between our method and the K -means clustering. Moreover, a model to process multiview data is also proposed, which is linearly scaled with respect to n . Extensive experiments demonstrate the efficiency and effectiveness of our approach with respect to many state-of-the-art clustering methods.

Adaptive Transition Probability Matrix Learning for Multiview Spectral Clustering

Multiview clustering as an important unsupervised method has been gathering a great deal of attention. However, most multiview clustering methods exploit the self-representation property to capture the relationship among data, resulting in high computation cost in calculating the self-representation coefficients. In addition, they usually employ different regularizers to learn the representation tensor or matrix from which a transition probability matrix is constructed in a separate step, such as the one proposed by Wu et al.. Thus, an optimal transition probability matrix cannot be guaranteed. To solve these issues, we propose a unified model for multiview spectral clustering by directly learning an adaptive transition probability matrix (MCA²M), rather than an individual representation matrix of each view. Different from the one proposed by Wu et al., MCA²M utilizes the one-step strategy to directly learn the transition probability matrix under the robust principal component analysis framework. Unlike existing methods using the absolute symmetrization operation to guarantee the nonnegativity and symmetry of the affinity matrix, the transition probability matrix learned from MCA²M is nonnegative and symmetric without any postprocessing. An alternating optimization algorithm is designed based on the efficient alternating direction method of multipliers. Extensive experiments on several real-world databases demonstrate that the proposed method outperforms the state-of-the-art methods.

Large-Scale Subspace Clustering by Independent Distributed and Parallel Coding

Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS²C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS²C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/ l₁ -norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS²C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS²C methods, our approach achieves better clustering results in public datasets, including a million images and videos.

Feature-Attention Graph Convolutional Networks for Noise Resilient Learning

Noise and inconsistency commonly exist in real-world information networks, due to the inherent error-prone nature of human or user privacy concerns. To date, tremendous efforts have been made to advance feature learning from networks, including the most recent graph convolutional networks (GCNs) or attention GCN, by integrating node content and topology structures. However, all existing methods consider networks as error-free sources and treat feature content in each node as independent and equally important to model node relations. Noisy node content, combined with sparse features, provides essential challenges for existing methods to be used in real-world noisy networks. In this article, we propose feature-based attention GCN (FA-GCN), a feature-attention graph convolution learning framework, to handle networks with noisy and sparse node content. To tackle noise and sparse content in each node, FA-GCN first employs a long short-term memory (LSTM) network to learn dense representation for each node feature. To model interactions between neighboring nodes, a feature-attention mechanism is introduced to allow neighboring nodes to learn and vary feature importance, with respect to their connections. By using a spectral-based graph convolution aggregation process, each node is allowed to concentrate more on the most determining neighborhood features aligned with the corresponding learning task. Experiments and validations, w.r.t. different noise levels, demonstrate that FA-GCN achieves better performance than the state-of-the-art methods in both noise-free and noisy network environments.

A Clustering Ensemble Framework with Integration of Data Characteristics and Structure Information: A Graph Neural Networks Approach

Clustering ensemble is a research hotspot of data mining that aggregates several base clustering results to generate a single output clustering with improved robustness and stability. However, the validity of the ensemble result is usually affected by unreliability in the generation and integration of base clusterings. In order to address this issue, we develop a clustering ensemble framework viewed from graph neural networks that generates an ensemble result by integrating data characteristics and structure information. In this framework, we extract structure information from base clustering results of the data set by using a coupling affinity measure After that, we combine structure information with data characteristics by using a graph neural network (GNN) to learn their joint embeddings in latent space. Then, we employ a Gaussian mixture model (GMM) to predict the final cluster assignment in the latent space. Finally, we construct the GNN and GMM as a unified optimization model to integrate the objectives of graph embedding and consensus clustering. Our framework can not only elegantly combine information in feature space and structure space, but can also achieve suitable representations for final cluster partitioning. Thus, it can produce an outstanding result. Experimental results on six synthetic benchmark data sets and six real world data sets show that the proposed framework yields a better performance compared to 12 reference algorithms that are developed based on either clustering ensemble architecture or a deep clustering strategy.

Robust semi-supervised non-negative matrix factorization for binary subspace learning

Non-negative matrix factorization and its extensions were applied to various areas (i.e., dimensionality reduction, clustering, etc.). When the original data are corrupted by outliers and noise, most of non-negative matrix factorization methods cannot achieve robust factorization and learn a subspace with binary codes. This paper puts forward a robust semi-supervised non-negative matrix factorization method for binary subspace learning, called RSNMF, for image clustering. For better clustering performance on the dataset contaminated by outliers and noise, we propose a weighted constraint on the noise matrix and impose manifold learning into non-negative matrix factorization. Moreover, we utilize the discrete hashing learning method to constrain the learned subspace, which can achieve a binary subspace from the original data. Experimental results validate the robustness and effectiveness of RSNMF in binary subspace learning and image clustering on the face dataset corrupted by Salt and Pepper noise and Contiguous Occlusion.

ARCANE-ROG: Algorithm for Reconstruction of Cancer Evolution from single-cell data using Robust Graph Learning

Tumor heterogeneity, marked by the presence of divergent clonal subpopulations of tumor cells, impedes the treatment response in cancer patients. Single-cell sequencing technology provides substantial prospects to gain an in-depth understanding of the cellular phenotypic variability driving tumor progression. A comprehensive insight into the intra-tumor heterogeneity may further assist in dealing with the treatment-resistant clones in cancer patients, thereby improving their overall survival. However, this task is hampered due to the challenges associated with the single-cell data, such as false positives, false negatives and missing bases, and the increase in their size. As a result, the computational cost of the existing methods increases, thereby limiting their usage. In this work, we propose a robust graph learning-based method, ARCANE-ROG (Algorithm for Reconstruction of CANcer Evolution via RObust Graph learning), for inferring clonal evolution from single-cell datasets. The first step of the proposed method is a joint framework of denoising with data imputation for the noisy and incomplete matrix while simultaneously learning an adjacency graph. Both the operations in the joint framework boost each other such that the overall performance of the denoising algorithm is improved. In the second step, an optimal number of clusters are identified via the Leiden method. In the last step, clonal evolution trees are inferred via a minimum spanning tree algorithm. The method has been benchmarked against a state-of-the-art method, RobustClone, using simulated datasets of varying sizes and five real datasets. The performance of our proposed method is found to be significantly superior (p-value < 0.05) in terms of reconstruction error, False Positive to False Negative (FPFN) ratio, tree distance error and V-measure compared to the other method. Overall, the proposed method is an improvement over the existing methods as it enhances cluster assignment and inference on clonal hierarchies.

A Survey on Multi-View Clustering

Clustering is a machine learning paradigm of dividing sample subjects into a number of groups such that subjects in the same groups are more similar to those in other groups. With advances in information acquisition technologies, samples can frequently be viewed from different angles or in different modalities, generating multi-view data. Multi-view clustering, that clusters subjects into subgroups using multi-view data, has attracted more and more attentions. Although MVC methods have been developed rapidly, there has not been enough survey to summarize and analyze the current progress. Therefore, we propose a novel taxonomy of the MVC approaches. Similar to other machine learning methods, we categorize them into generative and discriminative classes. In discriminative class, based on the way of view integration, we split it further into five groups: Common Eigenvector Matrix, Common Coefficient Matrix, Common Indicator Matrix, Direct Combination and Combination After Projection. Furthermore, we relate MVC to other topics: multi-view representation, ensemble clustering, multi-task clustering, multi-view supervised and semi-supervised learning. Several representative real-world applications are elaborated for practitioners. Some benchmark multi-view datasets are introduced and representative MVC algorithms from each group are empirically evaluated to analyze how they perform on benchmark datasets. To promote future development of MVC approaches, we point out several open problems that may require further investigation and thorough examination.

Multiview Clustering: A Scalable and Parameter-Free Bipartite Graph Fusion Method

Multiview clustering partitions data into different groups according to their heterogeneous features. Most existing methods degenerate the applicability of models due to their intractable hyper-parameters triggered by various regularization terms. Moreover, traditional spectral based methods always encounter the expensive time overheads and fail in exploring the explicit clusters from graphs. In this paper, we present a scalable and parameter-free graph fusion framework for multiview clustering, seeking for a joint graph compatible across multiple views in a self-supervised weighting manner. Our formulation coalesces multiple view-wise graphs straightforward and learns the weights as well as the joint graph interactively, which could actively release the model from any weight-related hyper-parameters. Meanwhile, we manipulate the joint graph by a connectivity constraint such that the connected components indicate clusters directly. The designed algorithm is initialization-independent and time-economical which obtains the stable performance and scales well with the data size. Substantial experiments on toy data as well as real datasets are conducted that verify the superiority of the proposed method compared to the state-of-the-arts over the clustering performance and time expenditure.