Orthogonal Nonnegative Matrix Tri-factorization Research Articles

Community Detection in Multiplex Networks Using Orthogonal Non-Negative Matrix Tri-Factorization Based on Graph Regularization and Diversity

In recent years, community detection has received increasing interest. In network analysis, community detection refers to the identification of tightly connected subsets of nodes, which are called “communities” or “groups”, in the network. Non-negative matrix factorization models are often used to solve the problem. Orthogonal non-negative matrix tri-factorization (ONMTF) exhibits significant potential as an approach for community detection within multiplex networks. This paper explores the application of ONMTF in multiplex networks, aiming to detect both shared and exclusive communities simultaneously. The model decomposes each layer within the multiplex network into two low-rank matrices. One matrix corresponds to shared communities across all layers, and the other to unique communities within each layer. Additionally, graph regularization and the diversity of private communities are taken into account in the algorithm. The Hilbert Schmidt Independence Criterion (HSIC) is used to constrain the independence of private communities. The results prove that ONMTF effectively addresses community detection in multiplex networks. It also offers strong interpretability and feature extraction capabilities. Therefore, it is an advanced method for community detection in multiplex networks.

Community Detection in Multiplex Networks Based on Orthogonal Nonnegative Matrix Tri-Factorization

Community Detection in Multiplex Networks Based on Orthogonal Nonnegative Matrix Tri-Factorization

TCD-CF: Triple cross-domain collaborative filtering recommendation

• A triple cross-domain collaborative filtering recommendation method is proposed. • An extended codebook construction algorithm is designed. • A transfer learning method based on extended codebook is presented. • Empirical results show the proposed method is superior to state-of-the-art methods. Recently, data sparsity is still one of the critical problems faced by recommendation systems. Although many existing methods based on cross-domain can alleviate it to a certain extent, these methods only use the information of single-domain (e.g., user-side, item-side and rating-side) or dual-domain (e.g., user-rating-side, user-item-side and item-rating-side) to make recommendations, which results in performance degradation . In this paper, we propose a triple cross-domain collaborative filtering method to alleviate data sparsity, named TCD-CF. In TCD-CF method, the triple-side intrinsic characteristics are first obtained by using the joint nonnegative matrix factorization to integrate the user-side, item-side and rating-side domain knowledge. Then the extended codebook (as knowledge to transfer) based on these intrinsic characteristics is constructed by using the orthogonal nonnegative matrix tri-factorization. Finally, the codebook-based transfer method for cross-system CF is applied into the source domain and target domain to predict the missing ratings and perform recommendation in the target domain. Extensive experiments on two real-world datasets demonstrate that the proposed method outperforms the state-of-the-art methods for the cross-domain recommendation task.

A Privacy-Preserving Cross-Domain Healthcare Wearables Recommendation Algorithm Based on Domain-Dependent and Domain-Independent Feature Fusion.

Recently, recommender systems are applied to provide personalized recomendation for healthcare wearables. However, due to the sparsity problem, traditional recommendation algorithms are difficult to achieve desired performance. Considering that consumers often buy and rate other types of items on E-commerce platforms, we can leverage significant information in the auxiliary domains to improve the recommendation performance of healthcare wearables, which can be regarded as cross-domain recommendation. However, traditional cross-domain recommendation model cannot fully represent user's characteristics and fail to consider the leaks of original auxiliary domain ratings during the information transfer process. To overcome the two shortcomings, this paper proposes a Privacy-Preserving Cross-Domain Healthcare Wearables Recommendation algorithm (PPCDHWRec). Firstly, user's characteristics are divided into domain-dependent features and domain-independent features, which complement each other and fully depict the user's characteristics. Secondly, inspired by the latent factor model, we factorize the original rating information of each auxiliary domain by Funk-SVD and Orthogonal Nonnegative Matrix Tri-Factorization (ONMTF) model, to obtain user's domain-dependent and domain-independent features, respectively. Finally, the Factorization Machine algorithm is used to fuse the obtained user's features with the target domain information to provide the recommendation results. By hiding the item latent factors obtained in the factorization process, PPCDHWRec ensures that the original information cannot be inferred from the transferred user hidden vector. Hence, PPCDHWRec is a privacy-preserving recommendation model. Experiments on two groups of auxiliary domains, having high and low correlations with target domain, show the effectiveness of PPCDHWRec.

Semi-supervised Co-Clustering on Attributed Heterogeneous Information Networks

Node clustering on heterogeneous information networks (HINs) plays an important role in many real-world applications. While previous research mainly clusters same-type nodes independently via exploiting structural similarity search, they ignore the correlations of different-type nodes. In this paper, we focus on the problem of co-clustering heterogeneous nodes where the goal is to mine the latent relevance of heterogeneous nodes and simultaneously partition them into the corresponding type-aware clusters. This problem is challenging in two aspects. First, the similarity or relevance of nodes is not only associated with multiple meta-path-based structures but also related to numerical and categorical attributes. Second, clusters and similarity/relevance searches usually promote each other.To address this problem, we first design a learnable overall relevance measure that integrates the structural and attributed relevance by employing meta-paths and attribute projection. We then propose a novel approach, called SCCAIN, to co-cluster heterogeneous nodes based on constrained orthogonal non-negative matrix tri-factorization. Furthermore, an end-to-end framework is developed to jointly optimize the relevance measures and co-clustering. Extensive experiments on real-world datasets not only demonstrate that SCCAIN consistently outperforms state-of-the-art methods but also validate the effectiveness of integrating attributed and structural information for co-clustering.

Robust orthogonal nonnegative matrix tri-factorization for data representation

Nonnegative matrix factorization (NMF) has been a vital data representation technique, and has demonstrated significant potential in the field of machine learning and data mining. Nonnegative matrix tri-factorization (NMTF) is an extension of NMF, and provides more degrees of freedom than NMF. In this paper, we propose the correntropy based orthogonal nonnegative matrix tri-factorization (CNMTF) algorithm, which is robust to noisy data contaminated by non-Gaussian noise and outliers. Different from previous NMF algorithms, CNMTF firstly applies correntropy to NMTF to measure the similarity, and preserves double orthogonality conditions and dual graph regularization. We adopt the half-quadratic technique to solve the optimization problem of CNMTF, and derive the multiplicative update rules. The complexity issue of CNMTF is also presented. Furthermore, the robustness of the proposed algorithm is analyzed, and the relationships between CNMTF and several previous NMF based methods are discussed. Experimental results demonstrate that the proposed CNMTF method has better performance on real world image and text datasets for clustering tasks, compared with several state-of-the-art methods.

Constrained Dual Graph Regularized Orthogonal Nonnegative Matrix Tri-Factorization for Co-Clustering

Coclustering approaches for grouping data points and features have recently been receiving extensive attention. In this paper, we propose a constrained dual graph regularized orthogonal nonnegative matrix trifactorization (CDONMTF) algorithm to solve the coclustering problems. The new method improves the clustering performance obviously by employing hard constraints to retain the priori label information of samples, establishing two nearest neighbor graphs to encode the geometric structure of data manifold and feature manifold, and combining with biorthogonal constraints as well. In addition, we have also derived the iterative optimization scheme of CDONMTF and proved its convergence. Clustering experiments on 5 UCI machine-learning data sets and 7 image benchmark data sets show that the achievement of the proposed algorithm is superior to that of some existing clustering algorithms.

Orthogonal nonnegative matrix tri-factorization based on Tweedie distributions

Orthogonal nonnegative matrix tri-factorization (ONMTF) is a biclustering method using a given nonnegative data matrix and has been applied to document-term clustering, collaborative filtering, and so on. In previously proposed ONMTF methods, it is assumed that the error distribution is normal. However, the assumption of normal distribution is not always appropriate for nonnegative data. In this paper, we propose three new ONMTF methods, which respectively employ the following error distributions: normal, Poisson, and compound Poisson. To develop the new methods, we adopt a k-means based algorithm but not a multiplicative updating algorithm, which was the main method used for obtaining estimators in previous methods. A simulation study and an application involving document-term matrices demonstrate that our method can outperform previous methods, in terms of the goodness of clustering and in the estimation of the factor matrix.

Exploration of Web Page Structural Patterns Based on Request Dependency Graph Decomposition

This article first proposed a Bipartite Request Dependency Graph (BRDG) that describes the object-level interrelationships between user click requests and embedded web object requests. These two kinds of requests are classified from HTTP data by an identification algorithm. The interrelationships between user click requests and embedded web object reflect the web page structural, which contain latent web information. Exploring structural patterns is crucial for many aspects like web security analysis and web information visualization. Accordingly, the article also proposed a novel graph decomposition method called orthogonal nonnegative matrix tri-factorization (tNMF) to the BRDG. Compared to traditional web graph analysis focus on statistical and structural properties of the whole graph, the proposed method is dedicated to mine latent web structural patterns. Decomposition results demonstrate that several interesting structures exist in the BRDG. The article aims at classifying these subgraphs as several structural patterns and shedding light on the causes of these patterns.

Orthogonal nonnegative matrix tri-factorization for co-clustering: Multiplicative updates on Stiefel manifolds

Matrix factorization-based methods become popular in dyadic data analysis, where a fundamental problem, for example, is to perform document clustering or co-clustering words and documents given a term-document matrix. Nonnegative matrix tri-factorization (NMTF) emerges as a promising tool for co-clustering, seeking a 3-factor decomposition X ≈ USV ⊤ with all factor matrices restricted to be nonnegative, i.e., U ⩾ 0 , S ⩾ 0 , V ⩾ 0 . In this paper we develop multiplicative updates for orthogonal NMTF where X ≈ USV ⊤ is pursued with orthogonality constraints, U ⊤ U = I , and V ⊤ V = I , exploiting true gradients on Stiefel manifolds. Experiments on various document data sets demonstrate that our method works well for document clustering and is useful in revealing polysemous words via co-clustering words and documents.

Unveiling core network-wide communication patterns through application traffic activity graph decomposition

As Internet communications and applications become more complex,operating, managing and securing networks have become increasingly challenging tasks. There are urgent demands for more sophisticated techniques for understanding and analyzing the behavioral characteristics of network traffic. In this paper, we study the network traffic behaviors using traffic activity graphs (TAGs), which capture the interactions among hosts engaging in certain types of communications and their collective behavior. TAGs derived from real network traffic are large, sparse, yet seemingly complex and richly connected, therefore difficult to visualize and comprehend. In order to analyze and characterize these TAGs, we propose a novel statistical traffic graph decomposition technique based on orthogonal nonnegative matrix tri-factorization (tNMF) to decompose and extract the core host interaction patterns and other structural properties. Using the real network traffic traces, we demonstrate that our tNMF-based graph decomposition technique produces meaningful and interpretable results. It enables us to characterize and quantify the key structural properties of large and sparse TAGs associated with various applications, and study their formation and evolution.

Collaborative filtering using orthogonal nonnegative matrix tri-factorization

Collaborative filtering aims at predicting a test user’s ratings for new items by integrating other like-minded users’ rating information. The key assumption is that users sharing the same ratings on past items tend to agree on new items. Traditional collaborative filtering methods can mainly be divided into two classes: memory-based and model-based. The memory-based approaches generally suffer from two fundamental problems: sparsity and scalability, and the model-based approaches usually cost too much on establishing a model and have many parameters to be tuned. In this paper, we propose a novel framework for collaborative filtering by applying orthogonal nonnegative matrix tri-factorization ( ONMTF), which (1) alleviates the sparsity problem via matrix factorization; (2) solves the scalability problem by simultaneously clustering rows and columns of the user-item matrix. Experiments on the benchmark data set show that our algorithm is indeed more tolerant against both sparsity and scalability, and achieves good performance in the mean time.