Probabilistic Matrix Research Articles

Hysteresis constitutive model of C/SiC composites considering probabilistic matrix fragmentations

Hysteresis constitutive model of C/SiC composites considering probabilistic matrix fragmentations

Decentralized Federated Recommendation with Privacy-aware Structured Client-level Graph

Recommendation models are deployed in a variety of commercial applications to provide personalized services for users. However, most of them rely on the users’ original rating records that are often collected by a centralized server for model training, which may cause privacy issues. Recently, some centralized federated recommendation models are proposed for the protection of users’ privacy, which however requires a server for coordination in the whole process of model training. As a response, we propose a novel privacy-aware decentralized federated recommendation (DFedRec) model, which is lossless compared with the traditional model in recommendation performance and is thus more accurate than other models in this line. Specifically, we design a privacy-aware structured client-level graph for the sharing of the model parameters in the process of model training, which is a one-stone-two-bird strategy, i.e., it protects users’ privacy via some randomly sampled fake entries and reduces the communication cost by sharing the model parameters only with the related neighboring users. With the help of the privacy-aware structured client-level graph, we propose two novel collaborative training mechanisms in the setting without a server, including a batch algorithm DFedRec(b) and a stochastic one DFedRec(s), where the former requires the anonymity mechanism while the latter does not. They are both equivalent to probabilistic matrix factorization trained in a centralized server and are thus lossless. We then provide formal analysis of privacy guarantee of our methods and conduct extensive empirical studies on three public datasets with explicit feedback, which show the effectiveness of our DFedRec, i.e., it is privacy aware, communication efficient, and lossless.

Trilateration-based indoor localization utilizing the matrix completion method by probabilistic matrix factorization and stochastic gradient

Trilateration-based indoor localization utilizing the matrix completion method by probabilistic matrix factorization and stochastic gradient

PMF-GRN: a variational inference approach to single-cell gene regulatory network inference using probabilistic matrix factorization.

Inferring gene regulatory networks (GRNs) from single-cell data is challenging due to heuristic limitations. Existing methods also lack estimates of uncertainty. Here we present Probabilistic Matrix Factorization for Gene Regulatory Network Inference (PMF-GRN). Using single-cell expression data, PMF-GRN infers latent factors capturing transcription factor activity and regulatory relationships. Using variational inference allows hyperparameter search for principled model selection and direct comparison to other generative models. We extensively test and benchmark our method using real single-cell datasets and synthetic data. We show that PMF-GRN infers GRNs more accurately than current state-of-the-art single-cell GRN inference methods, offering well-calibrated uncertainty estimates.

Size-invariant two-in-one image secret sharing scheme based on gray mixing model

TiOISSS (Two-in-One Image Secret Sharing Scheme) can reconstruct the secret through computation and realize secret preview recovery when the power system is destroyed or the network is paralyzed. However, the visual quality of previewing images obtained by the existing TiOISSS is not satisfactory and usually affected by pixel expansion. To resolve the two problems, this paper introduces multiple gray values in the share image generation stage and establishes an optimization model to obtain the grayscale probabilistic matrix needed in the encoding stage. By using the probability matrix, a secret sharing algorithm is designed to obtain size-invariant shares with multiple gray values. Then, the secret information of another image can be shared and embedded into the multi-level gray shares through Lagrange polynomials over finite fields. In the decryption stage, the electronic shares can be directly superimposed based on a gray mixing model, or they can be printed to transparent films by a multi-level gray printer and then superimposed to obtain the preview image. If computational devices are available, a high-resolution gray image can be obtained by Lagrange interpolation over finite fields. Experimental results indicate that the proposed scheme is effective for generating shares without pixel expansion and improving the preview image quality.

Improved collaborative filtering for cross-store demand forecasting

Accurate and reliable demand forecasting is crucial for decision-making in assortment planning, store location, and various operational aspects. This study proposes a hybrid TS-SimPMF framework for multi-store multi-product demand forecasting, employing probabilistic matrix factorization (PMF) with time-series similarity measures to capture product and store heterogeneity. The heterogeneity enables the framework to achieve multi-step demand forecasting under unknown item-store combinations through an adaptive integration strategy. We first employ a hybrid dynamic regularization approach to measure the similarity of product sales simultaneously, and then the PMF framework is applied to generate latent vectors of products and stores. The performance of the proposed framework is verified by the real-world retail data, in which the dataset includes all sales records with 50 SKUs in 10 locations, totaling over 180,000 sales records. These experimental results demonstrate the superior performance of the proposed hybrid model compared to state-of-the-art methods.

MFAI: A Scalable Bayesian Matrix Factorization Approach to Leveraging Auxiliary Information

In various practical situations, matrix factorization methods suffer from poor data quality, such as high data sparsity and low signal-to-noise ratio (SNR). Here, we consider a matrix factorization problem by utilizing auxiliary information, which is massively available in real-world applications, to overcome the challenges caused by poor data quality. Unlike existing methods that mainly rely on simple linear models to combine auxiliary information with the main data matrix, we propose to integrate gradient boosted trees in the probabilistic matrix factorization framework to effectively leverage auxiliary information (MFAI). Thus, MFAI naturally inherits several salient features of gradient boosted trees, such as the capability of flexibly modeling nonlinear relationships and robustness to irrelevant features and missing values in auxiliary information. The parameters in MFAI can be automatically determined under the empirical Bayes framework, making it adaptive to the utilization of auxiliary information and immune to overfitting. Moreover, MFAI is computationally efficient and scalable to large datasets by exploiting variational inference. We demonstrate the advantages of MFAI through comprehensive numerical results from simulation studies and real data analyses. Our approach is implemented in the R package mfair available at https://github.com/YangLabHKUST/mfair.

Probabilistic Matrix Factorization for Data With Attributes Based on Finite Mixture Modeling.

Matrix factorization (MF) methods decompose a data matrix into a product of two-factor matrices (denoted as U and V ) which are with low ranks. In this article, we propose a generative latent variable model for the data matrix, in which each entry is assumed to be a Gaussian with mean to be the inner product of the corresponding columns of U and V . The prior of each column of U and V is assumed to be as a finite mixture of Gaussians. Further, we propose to model the attribute matrix with the data matrix jointly by considering them as conditional independence with respect to the factor matrix U , building upon previously defined model for the data matrix. Due to the intractability of the proposed models, we employ variational Bayes to infer the posteriors of the factor matrices and the clustering relationships, and to optimize for the model parameters. In our development, the posteriors and model parameters can be readily computed in closed forms, which is much more computationally efficient than existing sampling-based probabilistic MF models. Comprehensive experimental studies of the proposed methods on collaborative filtering and community detection tasks demonstrate that the proposed methods achieve the state-of-the-art performance against a great number of MF-based and non-MF-based algorithms.

Double-ConvMF: probabilistic matrix factorization with user and item characteristic text

Double-ConvMF: probabilistic matrix factorization with user and item characteristic text

Research on personalized recommendation of teaching resources based on joint probability matrix decomposition model and CNN improvement algorithm

Abstract This study proposes a teaching resource recommendation method (TRRDLMF) based on deep learning and probabilistic matrix decomposition, aiming to improve teaching resource recommendation’s accuracy and personalization level. The study combines hybrid neural network feature extraction of teaching resources and user feature extraction based on extended noise-reducing self-encoder and extended probabilistic matrix decomposition-based teaching resource recommendation technique. The study validates the model’s effectiveness by conducting empirical analyses on four online learning platform datasets of different sizes. The recommendation system can effectively track learners’ knowledge mastery status and learning preferences, and provide corresponding teaching resources. Test question similarity and difficulty analysis results show that the model can accurately capture the correlation between test questions and provide complementary data in education. The personalized recommendation analysis reveals the learners’ knowledge preference states that change with learning, demonstrating the model’s ability to give explanations at the level of learners’ knowledge preferences. The analysis of the impact of data size on recommendation results shows that the recommender system can achieve up to 73.12% accuracy and 97.89% recall for different TOP-K recommendation lists, with the best F-value at TOP-6. The personalized recommendation system for teaching resources based on the joint probability matrix decomposition model and CNN improvement algorithm proposed by the research demonstrates significant effects in improving the accuracy and personalization level of teaching resources recommendation, which helps learners to acquire suitable learning resources more efficiently, and has high practical value and promotion potential.

AI-Assisted Emotion Recognition: Impacts on Mental Health Education and Learning Motivation

With the rapid advancements in artificial intelligence (AI) technology, its deployment in the field of education has gained considerable attention, particularly in the context of mental health education. Addressing the mounting academic and social pressures faced by contemporary students necessitates the utilization of cutting-edge techniques to accurately discern their emotional states and deliver customized learning resources. Existing methodologies for mental health education often fall short due to an over-reliance on educators’ experience and observations, as well as challenges in handling complex multimodal data. This research aims to investigate the integration of multimodal audio-visual features using a transformer architecture for emotion recognition. An enhanced probabilistic matrix factorization (PMF) model has been concurrently developed to facilitate tailored content recommendations for students. The goal is to provide a more accurate and effective approach to health education.

The Recommendation Algorithm Based on Improved Conditional Variational Autoencoder and Constrained Probabilistic Matrix Factorization

An improved recommendation algorithm based on Conditional Variational Autoencoder (CVAE) and Constrained Probabilistic Matrix Factorization (CPMF) is proposed to address the issues of poor recommendation performance in traditional user-based collaborative filtering algorithms caused by data sparsity and suboptimal feature extraction. Firstly, in the data preprocessing stage, a hidden layer is added to CVAE, and random noise is introduced into the hidden layer to constrain the data features, thereby obtaining more accurate latent features and improving the model’s robustness and generative capability. Secondly, the category of items is incorporated as auxiliary information in CVAE to supervise the encoding and decoding of item data. By learning the distribution characteristics of the data, missing values in the rating data can be effectively reconstructed, thereby reducing the sparsity of the rating matrix. Subsequently, the reconstructed data is processed using CPMF, which optimizes the feature extraction performance by imposing constraints on user features. Finally, the prediction rating of a user for an item can be obtained through the matrix product of user and item feature matrices. Experimental results on the MovieLens-100K and MovieLens-1M datasets demonstrate the effectiveness and superiority of the proposed algorithm over four comparative algorithms, as it exhibits significant advantages in terms of root mean square error and mean absolute error metrics.

Fast and accurate computational E-field dosimetry for group-level transcranial magnetic stimulation targeting

Transcranial magnetic stimulation (TMS) is used to study brain function and treat mental health disorders. During TMS, a coil placed on the scalp induces an E-field in the brain that modulates its activity. TMS is known to stimulate regions that are exposed to a large E-field. Clinical TMS protocols prescribe a coil placement based on scalp landmarks. There are inter-individual variations in brain anatomy that result in variations in the TMS-induced E-field at the targeted region and its outcome. These variations across individuals could in principle be minimized by developing a large database of head subjects and determining scalp landmarks that maximize E-field at the targeted brain region while minimizing its variation using computational methods. However, this approach requires repeated execution of a computational method to determine the E-field induced in the brain for a large number of subjects and coil placements. We developed a probabilistic matrix decomposition-based approach for rapidly evaluating the E-field induced during TMS for a large number of coil placements due to a pre-defined coil model. Our approach can determine the E-field induced in over 1 Million coil placements in 9.5 h, in contrast, to over 5 years using a brute-force approach. After the initial set-up stage, the E-field can be predicted over the whole brain within 2–3 ms and to 2% accuracy. We tested our approach in over 200 subjects and achieved an error of <2% in most and <3.5% in all subjects. We will present several examples of bench-marking analysis for our tool in terms of accuracy and speed. Furthermore, we will show the methods’ applicability for group-level optimization of coil placement for illustration purposes only. The software implementation link is provided in the appendix.

A Recommendation Engine Model for Giant Social Media Platforms using a Probabilistic Approach

Existing recommender system algorithms often find it difficult to interpret and, as a result, to extract meaningful recommendations from social media. Because of this, there is a growing demand for more powerful algorithms that are able to extract information from low-dimensional spaces. One such approach would be the cutting-edge matrix factorization technique. Facebook is one of the most widely used social networking platforms. It has more than one billion monthly active users who engage with each other on the platform by sharing status updates, images, events, and other types of content. Facebook's mission includes fostering stronger connections between individuals, and to that end, the platform employs techniques from recommender systems in an effort to better comprehend the actions and patterns of its users, after which it suggests forming new connections with other users. However, relatively little study has been done in this area to investigate the low-dimensional spaces included within the black box system by employing methods such as matrix factorization. Using a probabilistic matrix factorization approach, the interactions that users have with the posts of other users, such as liking, commenting, and other similar activities, were utilized in an effort to generate a list of potential friends that the user who is the focus of this work may not yet be familiar with. The proposed model performed better in terms of suggestion accuracy in comparison to the original matrix factorization, which resulted in the creation of a recommendation list that contained more correct information.

Predicting Student Performance in Future Exams via Neutrosophic Cognitive Diagnosis in Personalized E-Learning Environment

To provide intelligent learning guidance for students in e-learning systems, it is necessary to accurately predict their performance in future exams by analyzing score data in past exams. However, existing research has not addressed the uncertain and dynamic features of students' cognitive status, whereas these features are essential for improving the accuracy of performance prediction. A novel approach via neutrosophic cognitive diagnosis is proposed to predict student performance in a personalized e-learning environment. This approach innovatively employs the neutrosophic set (NS) theory to comprehensively measure the students' cognitive status on knowledge concepts from three features, i.e., understanding level, degree of misunderstanding, and uncertainty. A new measurement method of NS similarity is used to identify top- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> neighboring students for one student. Then, we predict a student's performance on exercises in future exams by integrating a neighborhood-based collaborative filtering algorithm with a probabilistic matrix factorization method to address the data sparsity problem. Finally, the experiments based on real-world datasets demonstrate that the proposed approach provides higher prediction accuracy than the existing ones with a low execution cost.

The impact of modern Internet technology on the teaching of American voice in colleges and universities

Abstract In this paper, firstly, the average prediction rating of interest points is performed by a recommendation model incorporating multiple factors through probabilistic matrix decomposition to improve the accuracy of the beauty teaching features obtained by matrix decomposition. Then, we combine the collaborative filtering recommendation algorithm and propose a recommendation model called TGSS-MF, and optimize the TGSS-MF recommendation model through the model of neural network for the sparse data problem faced by the interest point recommendation and the hidden feature vector representation problem of users and interest points, and finally use the TGSS-MF recommendation model to analyze the user needs of teachers, students and system administrators who are involved in teaching and learning. Finally, the TGSS-MF recommendation model is used to analyze the needs of users such as teachers, students, and system administrators involved in teaching and learning. A mobile teaching platform is designed to meet the characteristics of American voice teaching in colleges and universities. The performance analysis of the TGSS-MF recommendation model shows that when k=10, the accuracy and recall of the TGSS-MF model in the two data sets are 0.095 and 0.113, respectively, which are better than the other three algorithms in both accuracy and recall. This study can present more rich resources to students through modern Internet technology, which can help students learn effectiveness.

Mashup-Oriented Web API Recommendation Via Full-Text Semantic Mining of Developer Requirements

API recommendation differs from conventional recommendation systems in that it integrates the characteristics of development requirements, mashup, and API, where there are two primary challenges, i.e., how to effectively mine the personalized development requirements of developers and the sparseness of interaction data. This research proposes a novel model framework, called Bayesian Probabilistic Matrix Factorization Model with Text Similarity and Adversarial Training (SAMF), to address these two issues. Utilizing natural language processing technology to extract the full-text semantics of requirements documents, mashup descriptions, and API descriptions, fully mining personalized development requirements, and contextual information of mashups and APIs, and calculating text similarity, is our fundamental idea. Simultaneously, the collaborative filtering method is used to mine user needs, mashup, and API information from historical data, and the obtained text similarity is added to the training as auxiliary information. Furthermore, adversarial training is further incorporated to supplement data in order to minimize data sparsity and enhance model robustness and generalization. To assess the performance of SAMF, we run thorough experiments that illustrate the efficacy of each module of the model and explain the influence of hyperparameter settings. Specifically, compared to the baseline, the experimental findings demonstrate that SAMF can basically achieve better performance.

A decentralized trust inference approach with intelligence to improve data collection quality for mobile crowd sensing

Mobile Crowd Sensing (MCS) has been recognized as a promising param to construct numerous applications by employing enormous workers to perceive and collect data. The quality of MCS depends on the quality of the data submitted by the workers. Therefore, there is an urgent need to gain the trust of workers. In this paper, we propose a Decentralized Trust Inference (DTI) approach to improve data collection quality for MCS, mainly including the following components: (a) A trust evaluation method is proposed to obtain trust baselines of different levels, which can be used to assess the trust of workers. In addition, a data filling scheme on the basis of Bayesian Probabilistic Matrix Factorization (BPMF) is adopted to fill data when there is no credible baseline in the region. (b) Based on the DTI approach, we propose a worker recruitment method according to the priority of trust and bid ratio. Then, by preferentially selecting reliable and low-bid workers, we can improve data quality and reduce costs. Finally, theoretical analysis and experimental results demonstrate the effectiveness of our proposed scheme.

Imputing missing data in plant traits: A guide to improve gap‐filling

AbstractAimGlobally distributed plant trait data are increasingly used to understand relationships between biodiversity and ecosystem processes. However, global trait databases are sparse because they are compiled from many, mostly small databases. This sparsity in both trait space completeness and geographical distribution limits the potential for both multivariate and global analyses. Thus, ‘gap‐filling’ approaches are often used to impute missing trait data. Recent methods, like Bayesian hierarchical probabilistic matrix factorization (BHPMF), can impute large and sparse data sets using side information. We investigate whether BHPMF imputation leads to biases in trait space and identify aspects influencing bias to provide guidance for its usage.InnovationWe use a fully observed trait data set from which entries are randomly removed, along with extensive but sparse additional data. We use BHPMF for imputation and evaluate bias by: (1) accuracy (residuals, RMSE, trait means), (2) correlations (bi‐ and multivariate) and (3) taxonomic and functional clustering (valuewise, uni‐ and multivariate). BHPMF preserves general patterns of trait distributions but induces taxonomic clustering. Data set–external trait data had little effect on induced taxonomic clustering and stabilized trait–trait correlations.Main ConclusionsOur study extends the criteria for the evaluation of gap‐filling beyond RMSE, providing insight into statistical data structure and allowing better informed use of imputed trait data, with improved practice for imputation. We expect our findings to be valuable beyond applications in plant ecology, for any study using hierarchical side information for imputation.

Graph Regularized Probabilistic Matrix Factorization for Drug-Drug Interactions Prediction.

Co-administration of two or more drugs simultaneously can result in adverse drug reactions. Identifying drug-drug interactions (DDIs) is necessary, especially for drug development and for repurposing old drugs. DDI prediction can be viewed as a matrix completion task, for which matrix factorization (MF) appears as a suitable solution. This paper presents a novel Graph Regularized Probabilistic Matrix Factorization (GRPMF) method, which incorporates expert knowledge through a novel graph-based regularization strategy within an MF framework. An efficient and sounded optimization algorithm is proposed to solve the resulting non-convex problem in an alternating fashion. The performance of the proposed method is evaluated through the DrugBank dataset, and comparisons are provided against state-of-the-art techniques. The results demonstrate the superior performance of GRPMF when compared to its counterparts.