Parameter-less Auto-weighted multiple graph regularized Nonnegative Matrix Factorization for data representation
TL;DR: In GNMF, an affinity graph is constructed to encode the geometrical information and a matrix factorization is sought, which respects the graph structure, and the empirical study shows encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-world problems.
Abstract: Recently, multiple graph regularizer based methods have shown promising performances in data representation However, the parameter choice of the regularizer is crucial to the performance of clustering and its optimal value changes for different real datasets To deal with this problem, we propose a novel method called Parameter-less Auto-weighted Multiple Graph regularized Nonnegative Matrix Factorization (PAMGNMF) in this paper PAMGNMF employs the linear combination of multiple simple graphs to approximate the manifold structure of data as previous methods do Moreover, the proposed method can automatically learn an optimal weight for each graph without introducing an additive parameter Therefore, the proposed PAMGNMF method is easily applied to practical problems Extensive experimental results on different real-world datasets have demonstrated that the proposed method achieves better performance than the state-of-the-art approaches
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TL;DR: Network embedding assigns nodes in a network to low-dimensional representations and effectively preserves the network structure as discussed by the authors, and a significant amount of progress has been made toward this emerging network analysis paradigm.
Abstract: Network embedding assigns nodes in a network to low-dimensional representations and effectively preserves the network structure. Recently, a significant amount of progresses have been made toward this emerging network analysis paradigm. In this survey, we focus on categorizing and then reviewing the current development on network embedding methods, and point out its future research directions. We first summarize the motivation of network embedding. We discuss the classical graph embedding algorithms and their relationship with network embedding. Afterwards and primarily, we provide a comprehensive overview of a large number of network embedding methods in a systematic manner, covering the structure- and property-preserving network embedding methods, the network embedding methods with side information, and the advanced information preserving network embedding methods. Moreover, several evaluation approaches for network embedding and some useful online resources, including the network data sets and softwares, are reviewed, too. Finally, we discuss the framework of exploiting these network embedding methods to build an effective system and point out some potential future directions.
929 citations
Proceedings Article•
04 Feb 2017TL;DR: A novel Modularized Nonnegative Matrix Factorization (M-NMF) model is proposed to incorporate the community structure into network embedding and jointly optimize NMF based representation learning model and modularity based community detection model in a unified framework, which enables the learned representations of nodes to preserve both of the microscopic and community structures.
Abstract: Network embedding, aiming to learn the low-dimensional representations of nodes in networks, is of paramount importance in many real applications. One basic requirement of network embedding is to preserve the structure and inherent properties of the networks. While previous network embedding methods primarily preserve the microscopic structure, such as the first- and second-order proximities of nodes, the mesoscopic community structure, which is one of the most prominent feature of networks, is largely ignored. In this paper, we propose a novel Modularized Nonnegative Matrix Factorization (M-NMF) model to incorporate the community structure into network embedding. We exploit the consensus relationship between the representations of nodes and community structure, and then jointly optimize NMF based representation learning model and modularity based community detection model in a unified framework, which enables the learned representations of nodes to preserve both of the microscopic and community structures. We also provide efficient updating rules to infer the parameters of our model, together with the correctness and convergence guarantees. Extensive experimental results on a variety of real-world networks show the superior performance of the proposed method over the state-of-the-arts.
756 citations
Cites methods from "Parameter-less Auto-weighted multip..."
...We applied K-means to the learned representations of nodes and adopted accuracy (Cai et al. 2011) to assess the quality of the node clustering results....
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TL;DR: An unsupervised learning schema is constructed for the k-means algorithm so that it is free of initializations without parameter selection and can also simultaneously find an optimal number of clusters.
Abstract: The k-means algorithm is generally the most known and used clustering method. There are various extensions of k-means to be proposed in the literature. Although it is an unsupervised learning to clustering in pattern recognition and machine learning, the k-means algorithm and its extensions are always influenced by initializations with a necessary number of clusters a priori. That is, the k-means algorithm is not exactly an unsupervised clustering method. In this paper, we construct an unsupervised learning schema for the k-means algorithm so that it is free of initializations without parameter selection and can also simultaneously find an optimal number of clusters. That is, we propose a novel unsupervised k-means (U-k-means) clustering algorithm with automatically finding an optimal number of clusters without giving any initialization and parameter selection. The computational complexity of the proposed U-k-means clustering algorithm is also analyzed. Comparisons between the proposed U-k-means and other existing methods are made. Experimental results and comparisons actually demonstrate these good aspects of the proposed U-k-means clustering algorithm.
545 citations
Cites methods from "Parameter-less Auto-weighted multip..."
...in Seeds, Flowmeter D, Wine and Waveform (version 1) are distributed in different ranges and data features in Australian (credit approval) are mixed feature types, we first preprocess data matrices using matrix factorization technique [35]....
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TL;DR: A novel transfer learning framework, referred to as Adaptation Regularization based Transfer Learning (ARTL), to model adaptive classifiers in a unified way based on the structural risk minimization principle and the regularization theory, and can significantly outperform state-of-the-art learning methods on several public text and image datasets.
Abstract: Domain transfer learning, which learns a target classifier using labeled data from a different distribution, has shown promising value in knowledge discovery yet still been a challenging problem. Most previous works designed adaptive classifiers by exploring two learning strategies independently: distribution adaptation and label propagation. In this paper, we propose a novel transfer learning framework, referred to as Adaptation Regularization based Transfer Learning (ARTL), to model them in a unified way based on the structural risk minimization principle and the regularization theory. Specifically, ARTL learns the adaptive classifier by simultaneously optimizing the structural risk functional, the joint distribution matching between domains, and the manifold consistency underlying marginal distribution. Based on the framework, we propose two novel methods using Regularized Least Squares (RLS) and Support Vector Machines (SVMs), respectively, and use the Representer theorem in reproducing kernel Hilbert space to derive corresponding solutions. Comprehensive experiments verify that ARTL can significantly outperform state-of-the-art learning methods on several public text and image datasets.
537 citations
Proceedings Article•
01 Jan 2012TL;DR: Symmetric NMF is proposed as a general framework for graph clustering, which inherits the advantages of NMF by enforcing nonnegativity on the clustering assignment matrix, and serves as a potential basis for many extensions.
Abstract: Nonnegative matrix factorization (NMF) provides a lower rank approximation of a nonnegative matrix, and has been successfully used as a clustering method. In this paper, we offer some conceptual understanding for the capabilities and shortcomings of NMF as a clustering method. Then, we propose Symmetric NMF (SymNMF) as a general framework for graph clustering, which inherits the advantages of NMF by enforcing nonnegativity on the clustering assignment matrix. Unlike NMF, however, SymNMF is based on a similarity measure between data points, and factorizes a symmetric matrix containing pairwise similarity values (not necessarily nonnegative). We compare SymNMF with the widely-used spectral clustering methods, and give an intuitive explanation of why SymNMF captures the cluster structure embedded in the graph representation more naturally. In addition, we develop a Newton-like algorithm that exploits second-order information efficiently, so as to show the feasibility of SymNMF as a practical framework for graph clustering. Our experiments on artificial graph data, text data, and image data demonstrate the substantially enhanced clustering quality of SymNMF over spectral clustering and NMF. Therefore, SymNMF is able to achieve better clustering results on both linear and nonlinear manifolds, and serves as a potential basis for many extensions
411 citations
Cites background or methods from "Parameter-less Auto-weighted multip..."
...We use the GNMF algorithm and the suggested parameters in [3]....
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...[3] proposed GNMF by adding a graph-theoretic penalty term to (1....
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...NMF has received wide attention in clustering with many types of data, including documents [22], images [3], and microarray data [10]....
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References
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49,597 citations
TL;DR: Locally linear embedding (LLE) is introduced, an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs that learns the global structure of nonlinear manifolds.
Abstract: Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text.
15,106 citations
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TL;DR: A near-real-time computer system that can locate and track a subject's head, and then recognize the person by comparing characteristics of the face to those of known individuals, and that is easy to implement using a neural network architecture.
Abstract: We have developed a near-real-time computer system that can locate and track a subject's head, and then recognize the person by comparing characteristics of the face to those of known individuals. The computational approach taken in this system is motivated by both physiology and information theory, as well as by the practical requirements of near-real-time performance and accuracy. Our approach treats the face recognition problem as an intrinsically two-dimensional (2-D) recognition problem rather than requiring recovery of three-dimensional geometry, taking advantage of the fact that faces are normally upright and thus may be described by a small set of 2-D characteristic views. The system functions by projecting face images onto a feature space that spans the significant variations among known face images. The significant features are known as "eigenfaces," because they are the eigenvectors (principal components) of the set of faces; they do not necessarily correspond to features such as eyes, ears, and noses. The projection operation characterizes an individual face by a weighted sum of the eigenface features, and so to recognize a particular face it is necessary only to compare these weights to those of known individuals. Some particular advantages of our approach are that it provides for the ability to learn and later recognize new faces in an unsupervised manner, and that it is easy to implement using a neural network architecture.
14,562 citations
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TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.
Abstract: Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10(6) optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.
13,652 citations
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