Bayesian tensor network structure search and its application to tensor completion.

Tensor network (TN) has demonstrated remarkable efficacy in the compact representation of high-order data. In contrast to the TN methods with pre-determined structures, the recently introduced tensor network structure search (TNSS) methods automatically learn a compact TN structure from the data, gaining increasing attention. Nonetheless, TNSS requires time-consuming manual adjustments of the penalty parameters that control the model complexity to achieve better performance, especially in the presence of missing or noisy data. To provide an effective solution to this problem, in this paper, we propose a parameters tuning-free TNSS algorithm based on Bayesian modeling, aiming at conducting TNSS in a fully data-driven manner. Specifically, the uncertainty in the data corruption is well-incorporated in the prior setting of the probabilistic model. For TN structure determination, we reframe it as a rank learning problem of the fully-connected tensor network (FCTN), integrating the generalized inverse Gaussian (GIG) distribution for low-rank promotion. To eliminate the need for hyperparameter tuning, we adopt a fully Bayesian approach and propose an efficient Markov chain Monte Carlo (MCMC) algorithm for posterior distribution sampling. Compared with the previous TNSS method, experiment results demonstrate the proposed algorithm can effectively and efficiently find the latent TN structures of the data under various missing and noise conditions and achieves the best recovery results. Furthermore, our method exhibits superior performance in tensor completion with real-world data compared to other state-of-the-art tensor-decomposition-based completion methods.

Balanced Unfolding Induced Tensor Nuclear Norms for High-Order Tensor Completion.

The recently proposed tensor tubal rank has been witnessed to obtain extraordinary success in real-world tensor data completion. However, existing works usually fix the transform orientation along the third mode and may fail to turn multidimensional low-tubal-rank structure into account. To alleviate these bottlenecks, we introduce two unfolding induced tensor nuclear norms (TNNs) for the tensor completion (TC) problem, which naturally extends tensor tubal rank to high-order data. Specifically, we show how multidimensional low-tubal-rank structure can be captured by utilizing a novel balanced unfolding strategy, upon which two TNNs, namely, overlapped TNN (OTNN) and latent TNN (LTNN), are developed. We also show the immediate relationship between the tubal rank of unfolding tensor and the existing tensor network (TN) rank, e.g., CANDECOMP/PARAFAC (CP) rank, Tucker rank, and tensor ring (TR) rank, to demonstrate its efficiency and practicality. Two efficient TC models are then proposed with theoretical guarantees by analyzing a unified nonasymptotic upper bound. To solve optimization problems, we develop two alternating direction methods of multipliers (ADMM) based algorithms. The proposed models have been demonstrated to exhibit superior performance based on experimental findings involving synthetic and real-world tensors, including facial images, light field images, and video sequences.

Nuclear autoantigenic sperm protein facilitates glioblastoma progression and radioresistance by regulating the ANXA2/STAT3 axis.

AIMS: Although radiotherapy is a core treatment modality for various human cancers, including glioblastoma multiforme (GBM), its clinical effects are often limited by radioresistance. The specific molecular mechanisms underlying radioresistance are largely unknown, and the reduction of radioresistance is an unresolved challenge in GBM research. METHODS: We analyzed and verified the expression of nuclear autoantigenic sperm protein (NASP) in gliomas and its relationship with patient prognosis. We also explored the function of NASP in GBM cell lines. We performed further mechanistic experiments to investigate the mechanisms by which NASP facilitates GBM progression and radioresistance. An intracranial mouse model was used to verify the effectiveness of combination therapy. RESULTS: NASP was highly expressed in gliomas, and its expression was negatively correlated with the prognosis of glioma. Functionally, NASP facilitated GBM cell proliferation, migration, invasion, and radioresistance. Mechanistically, NASP interacted directly with annexin A2 (ANXA2) and promoted its nuclear localization, which may have been mediated by phospho-annexin A2 (Tyr23). The NASP/ANXA2 axis was involved in DNA damage repair after radiotherapy, which explains the radioresistance of GBM cells that highly express NASP. NASP overexpression significantly activated the signal transducer and activator of transcription 3 (STAT3) signaling pathway. The combination of WP1066 (a STAT3 pathway inhibitor) and radiotherapy significantly inhibited GBM growth in vitro and in vivo. CONCLUSION: Our findings indicate that NASP may serve as a potential biomarker of GBM radioresistance and has important implications for improving clinical radiotherapy.

A Novel Tensor Ring Sparsity Measurement for Image Completion.

As a promising data analysis technique, sparse modeling has gained widespread traction in the field of image processing, particularly for image recovery. The matrix rank, served as a measure of data sparsity, quantifies the sparsity within the Kronecker basis representation of a given piece of data in the matrix format. Nevertheless, in practical scenarios, much of the data are intrinsically multi-dimensional, and thus, using a matrix format for data representation will inevitably yield sub-optimal outcomes. Tensor decomposition (TD), as a high-order generalization of matrix decomposition, has been widely used to analyze multi-dimensional data. In a direct generalization to the matrix rank, low-rank tensor modeling has been developed for multi-dimensional data analysis and achieved great success. Despite its efficacy, the connection between TD rank and the sparsity of the tensor data is not direct. In this work, we introduce a novel tensor ring sparsity measurement (TRSM) for measuring the sparsity of the tensor. This metric relies on the tensor ring (TR) Kronecker basis representation of the tensor, providing a unified interpretation akin to matrix sparsity measurements, wherein the Kronecker basis serves as the foundational representation component. Moreover, TRSM can be efficiently computed by the product of the ranks of the mode-2 unfolded TR-cores. To enhance the practical performance of TRSM, the folded-concave penalty of the minimax concave penalty is introduced as a nonconvex relaxation. Lastly, we extend the TRSM to the tensor completion problem and use the alternating direction method of the multipliers scheme to solve it. Experiments on image and video data completion demonstrate the effectiveness of the proposed method.

Radiomic profiling for insular diffuse glioma stratification with distinct biologic pathway activities.

Current literature emphasizes surgical complexities and customized resection for managing insular gliomas; however, radiogenomic investigations into prognostic radiomic traits remain limited. We aimed to develop and validate a radiomic model using multiparametric magnetic resonance imaging (MRI) for prognostic prediction and to reveal the underlying biological mechanisms. Radiomic features from preoperative MRI were utilized to develop and validate a radiomic risk signature (RRS) for insular gliomas, validated through paired MRI and RNA-seq data (N = 39), to identify core pathways underlying the RRS and individual prognostic radiomic features. An 18-feature-based RRS was established for overall survival (OS) prediction. Gene set enrichment analysis (GSEA) and weighted gene coexpression network analysis (WGCNA) were used to identify intersectional pathways. In total, 364 patients with insular gliomas (training set, N = 295; validation set, N = 69) were enrolled. RRS was significantly associated with insular glioma OS (log-rank p = 0.00058; HR = 3.595, 95% CI:1.636-7.898) in the validation set. The radiomic-pathological-clinical model (R-P-CM) displayed enhanced reliability and accuracy in prognostic prediction. The radiogenomic analysis revealed 322 intersectional pathways through GSEA and WGCNA fusion; 13 prognostic radiomic features were significantly correlated with these intersectional pathways. The RRS demonstrated independent predictive value for insular glioma prognosis compared with established clinical and pathological profiles. The biological basis for prognostic radiomic indicators includes immune, proliferative, migratory, metabolic, and cellular biological function-related pathways.

Biological underpinnings of radiomic magnetic resonance imaging phenotypes for risk stratification in IDH wild-type glioblastoma.

BACKGROUND: To develop and validate a conventional MRI-based radiomic model for predicting prognosis in patients with IDH wild-type glioblastoma (GBM) and reveal the biological underpinning of the radiomic phenotypes. METHODS: A total of 801 adult patients (training set, N = 471; internal validation set, N = 239; external validation set, N = 91) diagnosed with IDH wild-type GBM were included. A 20-feature radiomic risk score (Radscore) was built for overall survival (OS) prediction by univariate prognostic analysis and least absolute shrinkage and selection operator (LASSO) Cox regression in the training set. GSEA and WGCNA were applied to identify the intersectional pathways underlying the prognostic radiomic features in a radiogenomic analysis set with paired MRI and RNA-seq data (N = 132). The biological meaning of the conventional MRI sequences was revealed using a Mantel test. RESULTS: Radscore was demonstrated to be an independent prognostic factor (P < 0.001). Incorporating the Radscore into a clinical model resulted in a radiomic-clinical nomogram predicting survival better than either the Radscore model or the clinical model alone, with better calibration and classification accuracy (a total net reclassification improvement of 0.403, P < 0.001). Three pathway categories (proliferation, DNA damage response, and immune response) were significantly correlated with the prognostic radiomic phenotypes. CONCLUSION: Our findings indicated that the prognostic radiomic phenotypes derived from conventional MRI are driven by distinct pathways involved in proliferation, DNA damage response, and immunity of IDH wild-type GBM.

Neuropathologist-level integrated classification of adult-type diffuse gliomas using deep learning from whole-slide pathological images.

Current diagnosis of glioma types requires combining both histological features and molecular characteristics, which is an expensive and time-consuming procedure. Determining the tumor types directly from whole-slide images (WSIs) is of great value for glioma diagnosis. This study presents an integrated diagnosis model for automatic classification of diffuse gliomas from annotation-free standard WSIs. Our model is developed on a training cohort (n = 1362) and a validation cohort (n = 340), and tested on an internal testing cohort (n = 289) and two external cohorts (n = 305 and 328, respectively). The model can learn imaging features containing both pathological morphology and underlying biological clues to achieve the integrated diagnosis. Our model achieves high performance with area under receiver operator curve all above 0.90 in classifying major tumor types, in identifying tumor grades within type, and especially in distinguishing tumor genotypes with shared histological features. This integrated diagnosis model has the potential to be used in clinical scenarios for automated and unbiased classification of adult-type diffuse gliomas.

Radiomic features from multiparametric magnetic resonance imaging predict molecular subgroups of pediatric low-grade gliomas.

BACKGROUND: We aimed to develop machine learning models for prediction of molecular subgroups (low-risk group and intermediate/high-risk group) and molecular marker (KIAA1549-BRAF fusion) of pediatric low-grade gliomas (PLGGs) based on radiomic features extracted from multiparametric MRI. METHODS: 61 patients with PLGGs were included in this retrospective study, which were divided into a training set and an internal validation set at a ratio of 2:1 based on the molecular subgroups or the molecular marker. The patients were classified into low-risk and intermediate/high-risk groups, BRAF fusion positive and negative groups, respectively. We extracted 5929 radiomic features from multiparametric MRI. Thereafter, we removed redundant features, trained random forest models on the training set for predicting the molecular subgroups or the molecular marker, and validated their performance on the internal validation set. The performance of the prediction model was verified by 3-fold cross-validation. RESULTS: We constructed the classification model differentiating low-risk PLGGs from intermediate/high-risk PLGGs using 4 relevant features, with an AUC of 0.833 and an accuracy of 76.2% in the internal validation set. In the prediction model for predicting KIAA1549-BRAF fusion using 4 relevant features, an AUC of 0.818 and an accuracy of 81.0% were achieved in the internal validation set. CONCLUSIONS: The current study demonstrates that MRI radiomics is able to predict molecular subgroups of PLGGs and KIAA1549-BRAF fusion with satisfying sensitivity. TRIAL REGISTRATION: This study was retrospectively registered at clinicaltrials.gov (NCT04217018).

Diffusion tensor imaging-based machine learning for IDH wild-type glioblastoma stratification to reveal the biological underpinning of radiomic features.

INTRODUCTION: This study addresses the lack of systematic investigation into the prognostic value of hand-crafted radiomic features derived from diffusion tensor imaging (DTI) in isocitrate dehydrogenase (IDH) wild-type glioblastoma (GBM), as well as the limited understanding of the biological interpretation of individual DTI radiomic features and metrics. AIMS: To develop and validate a DTI-based radiomic model for predicting prognosis in patients with IDH wild-type GBM and reveal the biological underpinning of individual DTI radiomic features and metrics. RESULTS: The DTI-based radiomic signature was an independent prognostic factor (p < 0.001). Incorporating the radiomic signature into a clinical model resulted in a radiomic-clinical nomogram that predicted survival better than either the radiomic model or clinical model alone, with a better calibration and classification accuracy. Four categories of pathways (synapse, proliferation, DNA damage response, and complex cellular functions) were significantly correlated with the DTI-based radiomic features and DTI metrics. CONCLUSION: The prognostic radiomic features derived from DTI are driven by distinct pathways involved in synapse, proliferation, DNA damage response, and complex cellular functions of GBM.

Radiomic features from dynamic susceptibility contrast perfusion-weighted imaging improve the three-class prediction of molecular subtypes in patients with adult diffuse gliomas.

OBJECTIVES: To investigate whether radiomic features extracted from dynamic susceptibility contrast perfusion-weighted imaging (DSC-PWI) can improve the prediction of the molecular subtypes of adult diffuse gliomas, and to further develop and validate a multimodal radiomic model by integrating radiomic features from conventional and perfusion MRI. METHODS: We extracted 1197 radiomic features from each sequence of conventional MRI and DSC-PWI, respectively. The Boruta algorithm was used for feature selection and combination, and a three-class random forest method was applied to construct the models. We also constructed a combined model by integrating radiomic features and clinical metrics. The models' diagnostic performance for discriminating the molecular subtypes (IDH wild type [IDHwt], IDH mutant and 1p/19q-noncodeleted [IDHmut-noncodel], and IDH mutant and 1p/19q-codeleted [IDHmut-codel]) was compared using AUCs in the validation set. RESULTS: We included 272 patients (training set, n = 166; validation set, n = 106) with grade II-IV gliomas (mean age, 48.7 years; range, 19-77 years). The proportions of the molecular subtypes were 66.2% IDHwt, 15.1% IDHmut-noncodel, and 18.8% IDHmut-codel. Nineteen radiomic features (13 from conventional MRI and 6 from DSC-PWI) were selected to build the multimodal radiomic model. In the validation set, the multimodal radiomic model showed better performance than the conventional radiomic model did in predicting the IDHwt and IDHmut-codel subtypes, which was comparable to the conventional radiomic model in predicting the IDHmut-noncodel subtype. The multimodal radiomic model yielded similar performance as the combined model in predicting the three molecular subtypes. CONCLUSIONS: Adding DSC-PWI to conventional MRI can improve molecular subtype prediction in patients with diffuse gliomas. KEY POINTS: • The multimodal radiomic model outperformed conventional MRI when predicting both the IDH wild type and IDH mutant and 1p/19q-codeleted subtypes of gliomas. • The multimodal radiomic model showed comparable performance to the combined model in the prediction of the three molecular subtypes. • Radiomic features from T1-weighted gadolinium contrast-enhanced and relative cerebral blood volume images played an important role in the prediction of molecular subtypes.

Graph-Regularized Non-Negative Tensor-Ring Decomposition for Multiway Representation Learning.

Tensor-ring (TR) decomposition is a powerful tool for exploiting the low-rank property of multiway data and has been demonstrated great potential in a variety of important applications. In this article, non-negative TR (NTR) decomposition and graph-regularized NTR (GNTR) decomposition are proposed. The former equips TR decomposition with the ability to learn the parts-based representation by imposing non-negativity on the core tensors, and the latter additionally introduces a graph regularization to the NTR model to capture manifold geometry information from tensor data. Both of the proposed models extend TR decomposition and can be served as powerful representation learning tools for non-negative multiway data. The optimization algorithms based on an accelerated proximal gradient are derived for NTR and GNTR. We also empirically justified that the proposed methods can provide more interpretable and physically meaningful representations. For example, they are able to extract parts-based components with meaningful color and line patterns from objects. Extensive experimental results demonstrated that the proposed methods have better performance than state-of-the-art tensor-based methods in clustering and classification tasks.

Image-based deep learning identifies glioblastoma risk groups with genomic and transcriptomic heterogeneity: a multi-center study.

OBJECTIVES: To develop and validate a deep learning imaging signature (DLIS) for risk stratification in patients with multiforme (GBM), and to investigate the biological pathways and genetic alterations underlying the DLIS. METHODS: The DLIS was developed from multi-parametric MRI based on a training set (n = 600) and validated on an internal validation set (n = 164), an external test set 1 (n = 100), an external test set 2 (n = 161), and a public TCIA set (n = 88). A co-profiling framework based on a radiogenomics analysis dataset (n = 127) using multiscale high-dimensional data, including imaging, transcriptome, and genome, was established to uncover the biological pathways and genetic alterations underpinning the DLIS. RESULTS: The DLIS was associated with survival (log-rank p < 0.001) and was an independent predictor (p < 0.001). The integrated nomogram incorporating the DLIS achieved improved C indices than the clinicomolecular nomogram (net reclassification improvement 0.39, p < 0.001). DLIS significantly correlated with core pathways of GBM (apoptosis and cell cycle-related P53 and RB pathways, and cell proliferation-related RTK pathway), as well as key genetic alterations (del_CDNK2A). The prognostic value of DLIS-correlated genes was externally confirmed on TCGA/CGGA sets (p < 0.01). CONCLUSIONS: Our study offers a biologically interpretable deep learning predictor of survival outcomes in patients with GBM, which is crucial for better understanding GBM patient's prognosis and guiding individualized treatment. KEY POINTS: • MRI-based deep learning imaging signature (DLIS) stratifies GBM into risk groups with distinct molecular characteristics. • DLIS is associated with P53, RB, and RTK pathways and del_CDNK2A mutation. • The prognostic value of DLIS-correlated pathway genes is externally demonstrated.

Imbalanced low-rank tensor completion via latent matrix factorization.

Tensor completion has been widely used in computer vision and machine learning. Most existing tensor completion methods empirically assume the intrinsic tensor is simultaneous low-rank in all over modes. However, tensor data recorded from real-world applications may conflict with these assumptions, e.g., face images taken from different subjects often lie in a union of low-rank subspaces, which may result in a quite high rank or even full rank structure in its sample mode. To this aim, in this paper, we propose an imbalanced low-rank tensor completion method, which can flexibly estimate the low-rank incomplete tensor via decomposing it into a mixture of multiple latent tensor ring (TR) rank components. Specifically, each latent component is approximated using low-rank matrix factorization based on TR unfolding matrix. In addition, an effective proximal alternating minimization algorithm is developed and theoretically proved to maintain the global convergence property, that is, the whole sequence of iterates is convergent and converges to a critical point. Extensive experiments on both synthetic and real-world tensor data demonstrate that the proposed method achieves more favorable completion results with less computational cost when compared to the state-of-the-art tensor completion methods.

Noisy Tensor Completion via Low-Rank Tensor Ring.

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries are noise-free to provide a theoretical guarantee of exact recovery of missing entries, which is quite restrictive in practice. To remedy such drawback, this article proposes a novel noisy tensor completion model, which complements the incompetence of existing works in handling the degeneration of high-order and noisy observations. Specifically, the tensor ring nuclear norm (TRNN) and least-squares estimator are adopted to regularize the underlying tensor and the observed entries, respectively. In addition, a nonasymptotic upper bound of estimation error is provided to depict the statistical performance of the proposed estimator. Two efficient algorithms are developed to solve the optimization problem with convergence guarantee, one of which is specially tailored to handle large-scale tensors by replacing the minimization of TRNN of the original tensor equivalently with that of a much smaller one in a heterogeneous tensor decomposition framework. Experimental results on both synthetic and real-world data demonstrate the effectiveness and efficiency of the proposed model in recovering noisy incomplete tensor data compared with state-of-the-art tensor completion models.

A Generalized Graph Regularized Non-Negative Tucker Decomposition Framework for Tensor Data Representation.

Non-negative Tucker decomposition (NTD) is one of the most popular techniques for tensor data representation. To enhance the representation ability of NTD by multiple intrinsic cues, that is, manifold structure and supervisory information, in this article, we propose a generalized graph regularized NTD (GNTD) framework for tensor data representation. We first develop the unsupervised GNTD (UGNTD) method by constructing the nearest neighbor graph to maintain the intrinsic manifold structure of tensor data. Then, when limited must-link and cannot-link constraints are given, unlike most existing semisupervised learning methods that only use the pregiven supervisory information, we propagate the constraints through the entire dataset and then build a semisupervised graph weight matrix by which we can formulate the semisupervised GNTD (SGNTD). Moreover, we develop a fast and efficient alternating proximal gradient-based algorithm to solve the optimization problem and show its convergence and correctness. The experimental results on unsupervised and semisupervised clustering tasks using four image datasets demonstrate the effectiveness and high efficiency of the proposed methods.