Semi-supervised learning with regularized Laplacian

Graph-based semi-supervised learning algorithms have attracted a lot of attention. Constructing a good graph is playing an essential role for all these algorithms. Many existing graph construction methods(e.g. Gaussian Kernel etc.) require user input parameter, which is hard to configure manually. In this paper, we propose a parameter-free similarity measure Adaptive Similarity Estimation (ASE), which constructs the graph by adaptively optimizing linear combination of its neighbors. Experimental results show the effectiveness of our proposed method.

Computer Aided Geometric Design, 2020

Semi-supervised learning (SSL) is fundamentally a geometric task: in order to classify high-dimensional point sets when only a small fraction of data points are labeled, the geometry of the unlabeled data points is exploited to gain better classifying accuracy. A number of state-of-the-art SSL techniques rely on label propagation through graphbased diffusion, with edge weights that are evaluated either analytically from the data or through compute-intensive training based on nonlinear and nonconvex optimization. In this paper, we bring discrete differential geometry to bear on this problem by introducing a graph-based SSL approach where label diffusion uses a Laplacian operator learned from the geometry of the input data. From a data-dependent graph of the input, we formulate a biconvex loss function in terms of graph edge weights and inferred labels. Its minimization is achieved through alternating rounds of optimization of the Laplacian and diffusion-based inference of labels. The resulting optimized Laplacian diffusion directionally adapts to the intrinsic geometric structure of the data which often concentrates in clusters or around low-dimensional manifolds within the high-dimensional representation space. We show on a range of classical datasets that our variational classification is more accurate than current graph-based SSL techniques. The algorithmic simplicity and efficiency of our discrete differential geometric approach (limited to basic linear algebra operations) also make it attractive, despite the seemingly complex task of optimizing all the edge weights of a graph.

arXiv: Learning, 2016

Semi-supervised learning (SSL) is an indispensable tool when there are few labeled entities and many unlabeled entities for which we want to predict labels. With graph-based methods, entities correspond to nodes in a graph and edges represent strong relations. At the heart of SSL algorithms is the specification of a dense {\em kernel} of pairwise affinity values from the graph structure. A learning algorithm is then trained on the kernel together with labeled entities. The most popular kernels are {\em spectral} and include the highly scalable "symmetric" Laplacian methods, that compute a soft labels using Jacobi iterations, and "asymmetric" methods including Personalized Page Rank (PPR) which use short random walks and apply with directed relations, such as like, follow, or hyperlinks. We introduce {\em Reach diffusion} and {\em Distance diffusion} kernels that build on powerful social and economic models of centrality and influence in networks and capture the d...

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.

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 (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of the available data by identifying classes or groups regardless data distribution and representing submanifold in Euclidean space. Most of methods used in literature for SSL classification do not worry about graph construction. However, regular graphs can obtain better classification accuracy compared to traditional methods such as k-nearest neighbor (kNN), since kNN benefits the generation of hubs and it is not appropriate for high-dimensionality data. Nevertheless, methods commonly used for generating regular graphs have high computational cost. We tackle this problem introducing an alternative method for generation of regular graphs with better runtime performance compared to methods usually find in the area. Our technique is based on the preferential selection of vertices according some topological measures, like closeness, generating at the end of the process a regular graph. Experiments using the global and local consistency method for label propagation show that our method provides better or equal classification rate in comparison with kNN.

International Journal on Bioinformatics & Biosciences, 2013

Protein function prediction is the important problem in modern biology. In this paper, the un-normalized, symmetric normalized, and random walk graph Laplacian based semi-supervised learning methods will be applied to the integrated network combined from multiple networks to predict the functions of all yeast proteins in these multiple networks. These multiple networks are network created from Pfam domain structure, co-participation in a protein complex, protein-protein interaction network, genetic interaction network, and network created from cell cycle gene expression measurements. Multiple networks are combined with fixed weights instead of using convex optimization to determine the combination weights due to high time complexity of convex optimization method. This simple combination method will not affect the accuracy performance measures of the three semi-supervised learning methods. Experiment results show that the un-normalized and symmetric normalized graph Laplacian based methods perform slightly better than random walk graph Laplacian based method for integrated network. Moreover, the accuracy performance measures of these three semi-supervised learning methods for integrated network are much better than the best accuracy performance measures of these three methods for the individual network.

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.

Computation, 2019

In semi-supervised label propagation (LP), the data manifold is approximated by a graph, which is considered as a similarity metric. Graph estimation is a crucial task, as it affects the further processes applied on the graph (e.g., LP, classification). As our knowledge of data is limited, a single approximation cannot easily find the appropriate graph, so in line with this, multiple graphs are constructed. Recently, multi-metric fusion techniques have been used to construct more accurate graphs which better represent the data manifold and, hence, improve the performance of LP. However, most of these algorithms disregard use of the information of label space in the LP process. In this article, we propose a new multi-metric graph-fusion method, based on the Flexible Manifold Embedding algorithm. Our proposed method represents a unified framework that merges two phases: graph fusion and LP. Based on one available view, different simple graphs were efficiently generated and used as inp...