Constrained Clustering With Nonnegative Matrix Factorization

Zhang, Xianchao; Zong, Linlin; Liu, Xinyue; Luo, Jiebo

doi:10.1109/tnnls.2015.2448653

Cited by 54 publications

(24 citation statements)

References 34 publications

(39 reference statements)

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“…W and H are the latent feature matrices(basis matrix and coefficient matrix), with the size of n × C and C × n , respectively, C is the number of latent features or the inner rank of X . f ( W , H ) is the penalty function about W and H , such as L 1 or L 2 norm 24 .…”

Section: Resultsmentioning

confidence: 99%

Link predication based on matrix factorization by fusion of multi class organizations of the network

Jiao

Cai

Feng

et al. 2017

Sci Rep

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Link predication aims at forecasting the latent or unobserved edges in the complex networks and has a wide range of applications in reality. Almost existing methods and models only take advantage of one class organization of the networks, which always lose important information hidden in other organizations of the network. In this paper, we propose a link predication framework which makes the best of the structure of networks in different level of organizations based on nonnegative matrix factorization, which is called NMF 3 here. We first map the observed network into another space by kernel functions, which could get the different order organizations. Then we combine the adjacency matrix of the network with one of other organizations, which makes us obtain the objective function of our framework for link predication based on the nonnegative matrix factorization. Third, we derive an iterative algorithm to optimize the objective function, which converges to a local optimum, and we propose a fast optimization strategy for large networks. Lastly, we test the proposed framework based on two kernel functions on a series of real world networks under different sizes of training set, and the experimental results show the feasibility, effectiveness, and competitiveness of the proposed framework.

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Section: Resultsmentioning

confidence: 99%

Link predication based on matrix factorization by fusion of multi class organizations of the network

Jiao

Cai

Feng

et al. 2017

Sci Rep

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“…In the context of this paper, it is important to address the matrix decomposition problem for clustering purposes. In the CF field, the use of MF provides some relevant clustering advantages [40]: 1) MF accurately models sparse data variations [41], 2) It can implement both hard and soft clustering: e.g. : by means of Nonnegative Matrix Factorization (NMF) and BNMF, and 3) MF simultaneously factorizes users and items.…”

Section: Matrix Decomposition-based Clusteringmentioning

confidence: 99%

A Collaborative Filtering Probabilistic Approach for Recommendation to Large Homogeneous and Automatically Detected Groups

Bobadilla¹,

Gutiérrez²,

Alonso³

et al. 2020

IJIMAI

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In the collaborative filtering recommender systems (CFRS) field, recommendation to group of users is mainly focused on stablished, occasional or random groups. These groups have a little number of users: relatives, friends, colleagues, etc. Our proposal deals with large numbers of automatically detected groups. Marketing and electronic commerce are typical targets of large homogenous groups. Large groups present a major difficulty in terms of automatically achieving homogeneity, equilibrated size and accurate recommendations. We provide a method that combines diverse machine learning algorithms in an original way: homogeneous groups are detected by means of a clustering based on hidden factors instead of ratings. Predictions are made using a virtual user model, and virtual users are obtained by performing a hidden factors aggregation. Additionally, this paper selects the most appropriate dimensionality reduction for the explained RS aim. We conduct a set of experiments to catch the maximum cumulative deviation of the ratings information. Results show an improvement on recommendations made to large homogeneous groups. It is also shown the desirability of designing specific methods and algorithms to deal with automatically detected groups.

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“…It is possible to formulate clustering as a matrix decomposition problem [11], [29]. According to [31] and [32] MF has important advantages when used as a clustering method:…”

Section: Introductionmentioning

confidence: 99%

A New Recommendation Approach Based on Probabilistic Soft Clustering Methods: A Scientific Documentation Case Study

et al. 2019

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Recommender system (RS) clustering is an important issue, both for the improvement of the collaborative filtering (CF) accuracy and to obtain analytical information from their high sparse datasets. RS items and users usually share features belonging to different clusters, e.g., a musical-comedy movie. Soft clustering, therefore, is the CF clustering's most natural approach. In this paper, we propose a new prediction approach for probabilistic soft clustering methods. In addition, we put to test a not traditional scientific documentation CF dataset: SD4AI, and we compare results with the MovieLens baseline. Not traditional CF datasets have challenging features, such as not regular rating frequency distributions, broad range of rating values, and a particularly high sparsity. The results show the suitability of using soft-clustering approaches, where their probabilistic overlapping parameters find optimum values when balanced hard/soft clustering is used. This paper opens some promising lines of research, such as RSs' use in the scientific documentation field, the Internet of Things-based datasets processing, and design of new model-based soft clustering methods. INDEX TERMSSoft clustering, scientific documentation, collaborative filtering, recommender systems. JESÚS BOBADILLA received the B.S. degree in computer science from the Universidad Politécnica de Madrid and the Ph.D. degree in computer science from Universidad Carlos III.

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Constrained Clustering With Nonnegative Matrix Factorization

Cited by 54 publications

References 34 publications

Link predication based on matrix factorization by fusion of multi class organizations of the network

Link predication based on matrix factorization by fusion of multi class organizations of the network

A Collaborative Filtering Probabilistic Approach for Recommendation to Large Homogeneous and Automatically Detected Groups

A New Recommendation Approach Based on Probabilistic Soft Clustering Methods: A Scientific Documentation Case Study

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