Un-normalized hypergraph p-Laplacian based semi-supervised learning methods (original) (raw)
Related papers
ArXiv, 2018
Most network-based speech recognition methods are based on the assumption that the labels of two adjacent speech samples in the network are likely to be the same. However, assuming the pairwise relationship between speech samples is not complete. The information a group of speech samples that show very similar patterns and tend to have similar labels is missed. The natural way overcoming the information loss of the above assumption is to represent the feature data of speech samples as the hypergraph. Thus, in this paper, the three un-normalized, random walk, and symmetric normalized hypergraph Laplacian based semi-supervised learning methods applied to hypergraph constructed from the feature data of speech samples in order to predict the labels of speech samples are introduced. Experiment results show that the sensitivity performance measures of these three hypergraph Laplacian based semi-supervised learning methods are greater than the sensitivity performance measures of the Hidden...
Journal of Automation and Control Engineering, 2015
Abstract-A successful classification of different tumor types is essential for successful treatment of cancer. However, most prior cancer classification methods are clinical-based and have inadequate diagnostic ability. Cancer classification using gene expression data is very important in cancer diagnosis and drug discovery. The introduction of DNA microarray techniques has made simultaneous monitoring of thousands of gene expression probable. With this abundance of gene expression data nowadays, the researchers have the opportunity to do cancer classification using gene expression data. In recent years, a lot of machine learning methods have been proposed to do cancer classification using gene expression data such as clustering-based methods, k-nearest neighbor method, artificial neural network method, and support vector machine method, to name a few. In this paper, we present the un-normalized graph p-Laplacian semisupervised learning methods. These methods will be applied to the patient-patient network constructed from the gene expression data to predict the tumor types of all patients in the network. These methods are based on the assumption that the labels of two adjacent patients in the network are likely to be the same. The experiments show that that the un-normalized graph p-Laplacian semi-supervised learning methods are at least as good as the current state of the art network-based method (the un-normalized graph Laplacian based semi-supervised learning method) but often lead to better classification accuracy performance measures.
Un-normlized and Random Walk Hypergraph Laplacian Un-supervised Learning
Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2015
Most network-based clustering methods are based on the assumption that the labels of two adjacent vertices in the network are likely to be the same. However, assuming the pairwise relationship between vertices is not complete. The information a group of vertices that show very similar patterns and tend to have similar labels is missed. The natural way overcoming the information loss of the above assumption is to represent the given data as the hypergraph. Thus, in this paper, the two unnormalized and random walk hypergraph Laplacian based un-supervised learning methods are introduced. Experiment results show that the accuracy performance measures of these two hypergraph Laplacian based un-supervised learning methods are greater than the accuracy performance measure of symmetric normalized graph Laplacian based un-supervised learning method (i.e. the baseline method of this paper) applied to simple graph created from the incident matrix of hypergraph.
2017
Speech recognition is the classical problem in pattern recognition research field. However, just a few graph based machine learning methods have been applied to this classical problem. In this paper, we propose the un-normalized graph p-Laplacian semi-supervised learning methods and these methods will be applied to the speech network constructed from the MFCC speech dataset to predict the labels of all speech samples in the speech network. These methods are based on the assumption that the labels of two adjacent speech samples in the network are likely to be the same. The experiments show that that the un-normalized graph p-Laplacian semi-supervised learning methods are at least as good as the current state of the art method (the un-normalized graph Laplacian based semi-supervised learning method) but often lead to better classification sensitivity performance measures.
Influence of Graph Construction on Semi-supervised Learning
Advanced Information Systems Engineering, 2013
A variety of graph-based semi-supervised learning (SSL) algorithms and graph construction methods have been proposed in the last few years. Despite their apparent empirical success, the field of SSL lacks a detailed study that empirically evaluates the influence of graph construction on SSL. In this paper we provide such an experimental study. We combine a variety of graph construction methods as well as a variety of graph-based SSL algorithms and empirically compare them on a number of benchmark data sets widely used in the SSL literature. The empirical evaluation proposed in this paper is subdivided into four parts: (1) best case analysis; (2) classifiers' stability evaluation; (3) influence of graph construction; and (4) influence of regularization parameters. The purpose of our experiments is to evaluate the trade-off between classification performance and stability of the SSL algorithms on a variety of graph construction methods and parameter values. The obtained results show that the mutual k-nearest neighbors (mutKNN) graph may be the best choice for adjacency graph construction while the RBF kernel may be the best choice for weighted matrix generation. In addition, mutKNN tends to generate smoother error surfaces than other adjacency graph construction methods. However, mutKNN is unstable for a relatively small value of k. Our results indicate that the classification performance of the graph-based SSL algorithms are heavily influenced by the parameters setting and we found no evident explorable pattern to relay to future practitioners. We discuss the consequences of such instability in research and practice.
Semi-supervised learning with regularized Laplacian
Optimization Methods and Software
We study a semi-supervised learning method based on the similarity graph and Regularized Laplacian. We give convenient optimization formulation of the Regularized Laplacian method and establish its various properties. In particular, we show that the kernel of the method can be interpreted in terms of discrete and continuous time random walks and possesses several important properties of proximity measures. Both optimization and linear algebra methods can be used for efficient computation of the classification functions. We demonstrate on numerical examples that the Regularized Laplacian method is competitive with respect to the other state of the art semi-supervised learning methods.
Generalized Optimization Framework for Graph-based Semi-supervised Learning
Proceedings of the 2012 SIAM International Conference on Data Mining, 2012
We develop a generalized optimization framework for graph-based semi-supervised learning. The framework gives as particular cases the Standard Laplacian, Normalized Laplacian and PageRank based methods. We have also provided new probabilistic interpretation based on random walks and characterized the limiting behaviour of the methods. The random walk based interpretation allows us to explain differences between the performances of methods with different smoothing kernels. It appears that the PageRank based method is robust with respect to the choice of the regularization parameter and the labelled data. We illustrate our theoretical results with two realistic datasets, characterizing different challenges: Les Miserables characters social network and Wikipedia hyper-link graph. The graph-based semi-supervised learning classifies the Wikipedia articles with very good precision and perfect recall employing only the information about the hyper-text links.
Hyperparameter and Kernel Learning for Graph Based Semi-Supervised Classification
2005
There have been many graph-based approaches for semi-supervised classification. One problem is that of hyperparameter learning: performance depends greatly on the hyperparameters of the similarity graph, transformation of the graph Laplacian and the noise model. We present a Bayesian framework for learning hyperparameters for graph-based semisupervised classification. Given some labeled data, which can contain inaccurate labels, we pose the semi-supervised classification as an inference problem over the unknown labels. Expectation Propagation is used for approximate inference and the mean of the posterior is used for classification. The hyperparameters are learned using EM for evidence maximization. We also show that the posterior mean can be written in terms of the kernel matrix, providing a Bayesian classifier to classify new points. Tests on synthetic and real datasets show cases where there are significant improvements in performance over the existing approaches.
High-quality Training Data Selection using Latent Topics for Graph-based Semi-supervised Learning
In a multi-class document categorization using graph-based semi-supervised learning (GBSSL), it is essential to construct a proper graph expressing the relation among nodes and to use a reasonable categorization algorithm. Furthermore, it is also important to provide high-quality correct data as training data. In this context, we propose a method to construct a similarity graph by employing both surface information and latent information to express similarity between nodes and a method to select high-quality training data for GBSSL by means of the PageRank algorithm. Experimenting on Reuters-21578 corpus, we have confirmed that our proposed methods work well for raising the accuracy of a multi-class document categorization.
Graph construction based on labeled instances for semi-supervised learning
Semi-Supervised Learning (SSL) techniques have become very relevant since they require a small set of labeled data. In this context, graph-based algorithms have gained promi- nence in the area due to their capacity to exploiting, besides information about data points, the relationships among them. Moreover, data represented in graphs allow the use of collective inference (vertices can affect each other), propagation of labels (autocorrelation among neighbors) and use of neighborhood characteristics of a vertex. An important step in graph-based SSL methods is the conversion of tabular data into a weighted graph. The graph construction has a key role in the quality of the classification in graph-based methods. This paper explores a method for graph construction that uses available labeled data. We provide extensive experiments showing the proposed method has many advantages: good classification accuracy, quadratic time complexity, no sensitivity to the parameter k>10, sparse graphformationwithaveragedegreearound 2 andhubformation from the labeled points, which facilitates the propagation of labels.