Higher-order Correlations Research Articles

CORONet: A Cross-Sequence Joint Representation and Hypergraph Convolutional Network for Classifying Molecular Subtypes of Breast Cancer Using Incomplete DCE-MRI.

Breast cancer, the predominant malignancy among women, is characterized by significant heterogeneity, leading to the emergence of distinct molecular subtypes. Accurate differentiation of these molecular subtypes holds paramount clinical significance, owing to substantial variations in prognosis, therapeutic strategies, and survival outcomes. In this study, we propose a cross-sequence joint representation and hypergraph convolution network (CORONet) for classifying molecular subtypes of breast cancer using incomplete DCE-MRI. Specifically, we first build a cross-sequence joint representation (COR) module to integrate image imputation and feature representation into a unified framework, encouraging effective feature extraction for subsequent classification. Then, we fuse multiple COR features and applied feature selection to reduce the redundant information between sequences. Finally, we deploy hypergraph structures to model high-order correlation among different subjects and extracted high-level semantic features by hypergraph convolutions for molecular subtyping. Extensive experiments on incomplete DCE-MRIs of 395 patients from the TCIA repository showed a significant improvement of our CORONet over state of the arts, with the area under the curve (AUC) of 0.891 and 0.903 for luminal and triple-negative (TN) subtype prediction, respectively. Similar advantages of CORONet were also confirmed in partial complete DCE-MRIs of 144 patients, achieving an AUC of 0.858 and 0.832 for predicting luminal and TN subtypes of breast cancer, respectively. Nevertheless, both of these values were lower compared to the scenario where DCE-MRIs from all 395 patients were utilized. Our study contributes to the precise molecular subtyping using incomplete multi-sequence DCE-MRI, thereby offering promising prospects for future risk stratification of breast cancer patients.

Identifying System Non-Linearities by Fusing Signal Bispectral Signatures

Higher-order statistics investigate the phase relationships between frequency components, an aspect which cannot be treated using conventional spectral measures such as the power spectrum. Among the widely used higher-order statistics, the bispectrum ranks prominently. By delving into higher-order correlations, the bispectrum offers a means of extracting additional merits and insights from frequency coupling, enhancing our understanding of complex signal interactions. This analytical approach overcomes the limitations of traditional methods, providing a more comprehensive view of the complex relationships within the frequency domain. In this paper, the extensive use of the bispectrum in various scientific and technical areas is firstly emphasized by presenting very recent applications. The main scope of this work is to investigate the consequences of various non-linearities in the creation of phase couplings. Specifically, the quadratic, the cubic and the logarithmic non-linearities are examined. In addition, simple recommendations are given on how the underlying nonlinearity could be detected. The total approach is novel, considering the capability to distinguish from the bispectral content if two non-linearities are simultaneously present.

Generalized latent multi-view clustering with tensorized bipartite graph

Tensor-based multi-view spectral clustering algorithms use tensors to model the structure of multi-dimensional data to take advantage of the complementary information and high-order correlations embedded in the graph, thus achieving impressive clustering performance. However, these algorithms use linear models to obtain consensus, which prevents the learned consensus from adequately representing the nonlinear structure of complex data. In order to address this issue, we propose a method called Generalized Latent Multi-View Clustering with Tensorized Bipartite Graph (GLMC-TBG). Specifically, in this paper we introduce neural networks to learn highly nonlinear mappings that encode nonlinear structures in graphs into latent representations. In addition, multiple views share the same latent consensus through nonlinear interactions. In this way, a more comprehensive common representation from multiple views can be achieved. An Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) framework is designed to optimize the model. Experiments on seven real-world data sets verify that the proposed algorithm is superior to state-of-the-art algorithms.

Non-Gaussian Correlations in the Steady State of Driven-Dissipative Clouds of Two-Level Atoms.

We report experimental measurements of the second-order coherence function g^{(2)}(τ) of the light emitted by a laser-driven dense ensemble of ^{87}Rb atoms. We observe a clear departure from the Siegert relation valid for Gaussian chaotic light. Measuring intensity and first-order coherence, we conclude that the violation is not due to the emergence of a coherent field. This indicates that the light obeys non-Gaussian statistics, stemming from non-Gaussian correlations in the atomic medium. More specifically, the steady state of this driven-dissipative many-body system sustains high-order correlations in the absence of first-order coherence. These findings call for new theoretical and experimental explorations to uncover their origin, and they open new perspectives for the realization of non-Gaussian states of light.

Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models.

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.

CHL-DTI: A Novel High-Low Order Information Convergence Framework for Effective Drug-Target Interaction Prediction.

Recognizing drug-target interactions (DTI) stands as a pivotal element in the expansive field of drug discovery. Traditional biological wet experiments, although valuable, are time-consuming and costly as methods. Recently, computational methods grounded in network learning have demonstrated great advantages by effective topological feature extraction and attracted extensive research attention. However, most existing network-based learning methods only consider the low-order binary correlation between individual drug and target, neglecting the potential higher-order correlation information derived from multiple drugs and targets. High-order information, as an essential component, exhibits complementarity with low-order information. Hence, the incorporation of higher-order associations between drugs and targets, while adequately integrating them with the existing lower-order information, could potentially yield substantial breakthroughs in predicting drug-target interactions. We propose a novel dual channels network-based learning model CHL-DTI that converges high-order information from hypergraphs and low-order information from ordinary graph for drug-target interaction prediction. The convergence of high-loworder information in CHL-DTI is manifested in two key aspects. First, during the feature extraction stage, the model integrates both high-level semantic information and low-level topological information by combining hypergraphs and ordinary graph. Second, CHL-DTI fully fuse the innovative introduced drug-protein pairs (DPP) hypergraph network structure with ordinary topological network structure information. Extensive experimentation conducted on three public datasets showcases the superior performance of CHL-DTI in DTI prediction tasks when compared to SOTA methods. The source code of CHL-DTI is available at https://github.com/UPCLyy/CHL-DTI .

Joint contrastive learning of structural and semantic for graph collaborative filtering

Recently, graph collaborative filtering has been proposed as a superior recommendation technique, due to its outstanding capability of capturing high-order correlations from user–item interactions. Despite effectiveness, it still suffers from two limitations on representation learning: (1) imbalanced data distribution. User/item nodes with high-degree usually interfere with the representation learning process of low-degree nodes, deteriorating the recommendation accuracy; (2) structural noise vulnerability. The neighborhood aggregation scheme for the node representing could easily amplify structural noises, damaging the robustness of recommenders. The latest studies have made progress in overcoming the two limitations by capturing self-supervision signals via contrastive learning. Nevertheless, they somehow rely on heuristics to design, at a certain distance from a more comprehensive settlement.To make contrastive learning more entrenched with graph collaborative filtering, this paper proposes a multi-task framework JCG that integrates joint contrastive learning strategies with a backbone of graph-based recommender. Specifically, (1) we design six contrastive learning tasks categorized as structural and semantic, and obtain nine joint strategies by combining two tasks from each category; (2) we systematically study the effect of joint strategies on graph collaborative filtering, finding that JCG with feasible strategies could achieve up to 18.5% and 17.9% performance gain over the backbone on datasets of Yelp and ML, respectively; (3) performance comparison with other competitive baselines demonstrates the superiority of our JCG, especially that on mitigating the two limitations of data imbalance and noise vulnerability. We hope that our conclusion could provide new insight for future studies.

Online multi-hypergraph fusion learning for cross-subject emotion recognition

Multimodal fusion for emotion recognition has received increasing attention from researchers because of its ability to effectively leverage multimodal complementary information. However, there are two main challenges lead to performance degradation of existing emotion recognition models, which limits the practical use of existing models. One is that multimodal signals are difficult to fuse effectively to respond to the complexity of emotions. The other is that the individual variability and non-stationarity of physiological signals lead to poor performance of the model on new subjects. In particular, existing methods will not work well when faced with emotion recognition of new subjects in online scenarios. In this paper, we propose a novel online multi-hypergraph fusion learning method (OnMHF) to effectively fuse multimodal information and to reduce the difference between training data and test data for online cross-subject emotion recognition. Specifically, in a training phase, a multi-hypergraph fusion is proposed to fuse multimodal physiological signals to effectively obtain emotion-aware information via leveraging multimodal complementary information and high-order correlations among multimodal signals. In an online recognizing phase, an online multi-hypergraph learning is designed to learn online multimodal information from online multimodal data by updating hypergraph structure. As a result, the proposed method can be more effective for emotion recognition of target subjects when target data arrive in an online manner. Experimental results have demonstrated that the proposed method outperforms the baselines and compared state-of-the-art methods in online emotion recognition tasks.

Non-Gaussianities and the large |η| approach to inflation

The physics of primordial black holes can be affected by the non-Gaussian statistics of the density fluctuations that generate them. Therefore, it is important to have good theoretical control of the higher-order correlation functions for primordial curvature perturbations. By working at leading order in a 1/|η| expansion, we analytically determine the bispectrum of curvature fluctuations for single field inflationary scenarios producing primordial black holes. The bispectrum has a rich scale and shape dependence, and its features depend on the dynamics of the would-be decaying mode. We apply our analytical results to study gravitational waves induced at second order by enhanced curvature fluctuations. Their statistical properties are derived in terms of convolution integrals over wide momentum ranges, and they are sensitive on the scale and shape dependence of the curvature bispectrum we analytically computed. Published by the American Physical Society 2024

The effects of nonlinear approximation to mass operator on the wave propagation in polycrystalline materials

Existing theoretical models utilize the first or third-order smoothing approximations (FOSA and TOSA) to predict attenuation and wavespeed in polycrystalline materials. The FOSA-based model involves a Born approximation, limiting its application to the stochastic (low-frequency) scattering regime. This restriction is a significant factor contributing to its disagreement with FE-based models. The model based on TOSA was subsequently developed, incorporating two additional multiple scattering terms, and increasing the degree of heterogeneity. To extend into the high-frequency regime, the TOSA-based model was solved using numerical integrations. This presentation highlights the analytical solution of the Dyson equation based on the non-linear approximation, wherein the mass operator expression incorporates the mean dyadic Green’s function. Evaluating this equation with consideration of higher-order correlations addresses potential truncation errors associated with FOSA and TOSA approximations and encompasses the full range of frequencies from Rayleigh to the geometric asymptote. This presentation will also demonstrate a comparison of the results obtained from the nonlinear approximation with those from FOSA and TOSA across a range of polycrystalline metals.

Learning All-In Collaborative Multiview Binary Representation for Clustering.

Multiview clustering via binary representation has attracted intensive attention due to its effectiveness in handling large-scale multiple view data. However, these kind of clustering approaches usually ignore a very important potential high-order correlation in discrete representation learning. In this article, we propose a novel all-in collaborative multiview binary representation for clustering (AC-MVBC) framework, where multiview collaborative binary representation and clustering structure are learned in a joint manner. Specifically, using a new type of tensor low-rank constraint, the high-order collaborations, i.e., cross-view and inner view collaborations, can be effectively captured in our model. Moreover, by incorporating the Bregman discrepancy, the projective consistency among different views can be guaranteed to achieve a more powerful binary representation. An efficient optimization algorithm is also proposed to solve the objective function with fast convergence empirically. Experimental results on several challenge datasets demonstrate that the proposed method has achieved highly competent performance compared with the state-of-the-art multiview clustering (MVC) methods while maintaining low computational and memory requirements.

Toward Improving the Generation Quality of Autoregressive Slot VAEs.

Unconditional scene inference and generation are challenging to learn jointly with a single compositional model. Despite encouraging progress on models that extract object-centric representations ("slots") from images, unconditional generation of scenes from slots has received less attention. This is primarily because learning the multiobject relations necessary to imagine coherent scenes is difficult. We hypothesize that most existing slot-based models have a limited ability to learn object correlations. We propose two improvements that strengthen object correlation learning. The first is to condition the slots on a global, scene-level variable that captures higher-order correlations between slots. Second, we address the fundamental lack of a canonical order for objects in images by proposing to learn a consistent order to use for the autoregressive generation of scene objects. Specifically, we train an autoregressive slot prior to sequentially generate scene objects following a learned order. Ordered slot inference entails first estimating a randomly ordered set of slots using existing approaches for extracting slots from images, then aligning those slots to ordered slots generated autoregressively with the slot prior. Our experiments across three multiobject environments demonstrate clear gains in unconditional scene generation quality. Detailed ablation studies are also provided that validate the two proposed improvements.

Multi-Channel Hypergraph Collaborative Filtering with Attribute Inference

In the field of collaborative filtering, attribute information is often integrated to improve recommendations. However, challenges remain unaddressed. Firstly, existing data modeling methods often fall short of appropriately handling attribute information. Secondly, attribute data are often sparse and can potentially impact recommendation performance due to the challenge of incomplete correspondence between the attribute information and the recommendations. To tackle these challenges, we propose a hypergraph collaborative filtering with attribute inference (HCFA) framework, which segregates attribute and user behavior information into distinct channels and leverages hypergraphs to capture high-order correlations among vertices, offering a more natural approach to modeling. Furthermore, we introduce behavior-based attribute confidence (BAC) for assessing the reliability of inferred attributes concerning the corresponding behaviors and update the most credible portions to enhance recommendation quality. Extensive experiments conducted on three public benchmarks demonstrate the superiority of our model. It consistently outperforms other state-of-the-art approaches, with ablation experiments further confirming the effectiveness of our proposed method.

HSG-MGAF Net: Heterogeneous subgraph-guided multiscale graph attention fusion network for interpretable prediction of whole-slide image

Background and objectivePathological whole slide image (WSI) prediction and region of interest (ROI) localization are important issues in computer-aided diagnosis and postoperative analysis in clinical applications. Existing computer-aided methods for predicting WSI are mainly based on multiple instance learning (MIL) and its variants. However, most of the methods are based on instance independence and identical distribution assumption and performed at a single scale, which not fully exploit the hierarchical multiscale heterogeneous information contained in WSI. MethodsHeterogeneous Subgraph-Guided Multiscale Graph Attention Fusion Network (HSG-MGAF Net) is proposed to build the topology of critical image patches at two scales for adaptive WSI prediction and lesion localization. The HSG-MGAF Net simulates the hierarchical heterogeneous information of WSI through graph and hypergraph at two scales, respectively. This framework not only fully exploits the low-order and potential high-order correlations of image patches at each scale, but also leverages the heterogeneous information of the two scales for adaptive WSI prediction. ResultsWe validate the superiority of the proposed method on the CAMELYON16 and the TCGA- NSCLC, and the results show that HSG-MGAF Net outperforms the state-of-the-art method on both datasets. The average ACC, AUC and F1 score of HSG-MGAF Net can reach 92.7 %/0.951/0.892 and 92.2 %/0.957/0.919, respectively. The obtained heatmaps can also localize the positive regions more accurately, which have great consistency with the pixel-level labels. ConclusionsThe results demonstrate that HSG-MGAF Net outperforms existing weakly supervised learning methods by introducing critical heterogeneous information between the two scales. This approach paves the way for further research on light weighted heterogeneous graph-based WSI prediction and ROI localization.

View-specific anchors coupled tensorial bipartite graph learning for incomplete multi-view clustering

The incomplete multi-view clustering (IMVC) aims to explore the consensus and complementary information embedded in incomplete multi-view data, so as to accurately aggregate all samples into different clusters. Existing IMVC methods still have the following issues that need to be further solved: how to efficiently (1) alleviate the computational complexity; (2) capture the complementary information from views; (3) uncover the high-order correlations underlying incomplete multi-view data. To address these problems, a new method, called view-specific anchors coupled tensorial bipartite graph learning for incomplete multi-view clustering (VA-TBGIMC), is proposed in this paper. Specifically, view-specific anchors are learned from non-missing samples to represent the distribution of all samples including missing ones. With the help of high-quality anchors, the bipartite graph between all samples and anchors is constructed, which can preserve the complementary information. Meanwhile, these bipartite graphs are stacked into a tensor which is imposed with a low-rank constraint to adequately capture the inter-view and inter-sample correlations from incomplete multi-view data. Further, the augmented graph of bipartite graph is constrained by Laplacian rank to learn a consensus cluster indicator. A large number of experiments validate the superiority and efficiency of the proposed method in terms of clustering performance and time consumption.

The Use of Data Mining for Obtaining Deeper Insights into the Fabrication of Prednisolone-Loaded Chitosan Nanoparticles.

The present work explores a data mining approach to study the fabrication of prednisolone-loaded chitosan nanoparticles and their properties. Eight PLC formulations were prepared using an automated adaptation of the antisolvent precipitation method. The PLCs were characterized using dynamic light scattering, infrared spectroscopy, and drug release studies. Results showed that that the effective diameter, loading capacity, encapsulation efficiency, zeta potential, and polydispersity of the PLCs were influenced by the concentration and molecular weight of chitosan. The drug release studies showed that PLCs exhibited significant dissolution enhancement compared to pure prednisolone crystals. Principal components analysis and partial least squares regression were applied to the infrared spectra and the DLS data to extract higher-order interactions and correlations between the critical quality attributes and the diameter of the PLCs. Principal components revealed that the spectra clustered according to the type of material, with PLCs forming a separate cluster from the raw materials and the physical mix. PLS was successful in predicting the ED of the PLCs from the FTIR spectra with R2 = 0.98 and RMSE = 27.18. The present work demonstrates that data mining techniques can be useful tools for obtaining deeper insights into the fabrication and properties of PLCs, and for optimizing their quality and performance. It also suggests that FTIR spectroscopy can be a rapid and non-destructive method for predicting the ED of PLCs.

A method for evaluation of the probability density function of white noise filtered non-Gaussian stochastic process

Passing non-Gaussian white noises through a pre-designed linear filter can generate non-Gaussian stochastic processes with desired probabilistic and spectral properties. This linear filtering methodology has been extensively employed in non-Gaussian signal processing and simulation. At present, the investigation of probability properties for the output non-Gaussian processes is primarily concentrated on the higher-order statistics, spectra, and correlation functions. However, evaluating the probability density function (PDF) of the output process remains a challenging task. In order to address this issue, this short communication commences with the theoretical derivation of the PDF formula for the white noise filtered non-Gaussian stochastic process. The derived PDF is the result of a convolution of multiple PDFs, each obtained by applying a scaling transformation to the input white noise PDF. Subsequently, a discretized numerical calculation method is proposed to overcome the analytical difficulties associated with the computation of multiple convolutions. Finally, the accuracy and efficiency of the proposed method are demonstrated through several numerical examples.

A Tensor Approach for Uncoupled Multiview Clustering.

Multiview clustering plays an important part in unsupervised learning. Although the existing methods have shown promising clustering performances, most of them assume that the data is completely coupled between different views, which is unfortunately not always ensured in real-world applications. The clustering performance of these methods drops dramatically when handling the uncoupled data. The main reason is that: 1) cross-view correlation of uncoupled data is unclear, which limits the existing multiview clustering methods to explore the complementary information between views and 2) features from different views are uncoupled with each other, which may mislead the multiview clustering methods to partition data into wrong clusters. To address these limitations, we propose a tensor approach for uncoupled multiview clustering (T-UMC) in this article. Instead of pairwise correlation, T-UMC chooses a most reliable view by view-specific silhouette coefficient (VSSC) at first, and then couples the self-representation matrix of each view with it by pairwise cross-view coupling learning. After that, by integrating recoupled self-representation matrices into a third-order tensor, the high-order correlations of all views are explored with tensor singular value decomposition (t-SVD)-based tensor nuclear norm (TNN). And the view-specific local structures of each individual view are also preserved with the local structure learning scheme with manifold learning. Besides, the physical meaning of view-specific coupling matrix is also discussed in this article. Extensive experiments on six commonly used benchmark datasets have demonstrated the superiority of the proposed method compared with the state-of-the-art multiview clustering methods.

A novel complex-high-order graph convolutional network paradigm: ChyGCN

Abstract In recent years, there has been a growing interest in Graph Convolutional Networks (GCN). However, existing GCN and variants are predominantly based on simple graph or hypergraph structures, which restricts their ability to handle complex data correlations in practical applications. These limitations stem from the difficulty in establishing multiple hierarchies and acquiring adaptive weights for each of them. To address this issue, this paper introduces the latest concept of complex hypergraphs and constructs a versatile high-order multi-level data correlation model. This model is realized by establishing a three-tier structure of complexes-hypergraphs-vertices. Specifically, we start by establishing hyperedge clusters on the foundational network, utilizing a second-order hypergraph structure to depict potential correlations. For this second-order structure, truncation methods are applied to assess and generate a three-layer composite structure. During the construction of the composite structure, an adaptive learning strategy is implemented to merge correlations across different levels. We evaluate this model on several popular datasets and compare it with recent state-of-the-art methods. The comprehensive assessment results demonstrate that the proposed model surpasses existing methods, particularly in modeling implicit data correlations (the classification accuracy of nodes on five public datasets Cora, Citeseer, Pubmed, Github Web ML, and Facebook is 86.1±0.33, 79.2±0.35, 83.1±0.46, 83.8±0.23, and 80.1±0.37, respectively). This indicates that our approach holds advantages when handling datasets with implicit multi-level structures.

PML-ED: A method of partial multi-label learning by using encoder-decoder framework and exploring label correlation

Partial multi-label learning (PML) addresses problems where each instance is assigned a candidate label set and only a subset of these candidate labels is correct. The major challenge of PML is that the training procedure can be easily misguided by noisy labels. Current studies on PML have revealed two significant drawbacks. First, most of them do not sufficiently explore complex label correlations, which could improve the effectiveness of label disambiguation. Second, PML models heavily rely on prior assumptions, limiting their applicability to specific scenarios. In this work, we propose a novel method of PML based on the Encoder-Decoder Framework (PML-ED) to address the drawbacks. PML-ED initially achieves the distribution of label probability through a KNN label attention mechanism. It then adopts Conditional Layer Normalization (CLN) to extract the high-order label correlation and relaxes the prior assumption of label noise by introducing a universal Encoder-Decoder framework. This approach makes PML-ED not only more efficient compared to the state-of-the-art methods, but also capable of handling the data with large noisy labels across different domains. Experimental results on 28 benchmark datasets demonstrate that the proposed PML-ED model, when benchmarked against nine leading-edge PML algorithms, achieves the highest average ranking across five evaluation criteria.