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 prominence 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 graph formation with average degree around 2 and hub formation from the labeled points, which facilitates the propagation of labels.Sao Paulo Research Foundation (FAPESP) (Grant 2011/21880-3 and 2011/22749-8

Self-weighted Multiple Kernel Learning for Graph-based Clustering and Semi-supervised Classification

Multiple kernel learning (MKL) method is generally believed to perform better than single kernel method. However, some empirical studies show that this is not always true: the combination of multiple kernels may even yield an even worse performance than using a single kernel. There are two possible reasons for the failure: (i) most existing MKL methods assume that the optimal kernel is a linear combination of base kernels, which may not hold true; and (ii) some kernel weights are inappropriately assigned due to noises and carelessly designed algorithms. In this paper, we propose a novel MKL framework by following two intuitive assumptions: (i) each kernel is a perturbation of the consensus kernel; and (ii) the kernel that is close to the consensus kernel should be assigned a large weight. Impressively, the proposed method can automatically assign an appropriate weight to each kernel without introducing additional parameters, as existing methods do. The proposed framework is integrated into a unified framework for graph-based clustering and semi-supervised classification. We have conducted experiments on multiple benchmark datasets and our empirical results verify the superiority of the proposed framework.Comment: Accepted by IJCAI 2018, Code is availabl

A Graph-Based Semi-Supervised k Nearest-Neighbor Method for Nonlinear Manifold Distributed Data Classification

$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially when a very limited amount of labeled samples are available. In this paper, we propose a new graph-based $k$NN algorithm which can effectively handle both Gaussian distributed data and nonlinear manifold distributed data. To achieve this goal, we first propose a constrained Tired Random Walk (TRW) by constructing an $R$-level nearest-neighbor strengthened tree over the graph, and then compute a TRW matrix for similarity measurement purposes. After this, the nearest neighbors are identified according to the TRW matrix and the class label of a query point is determined by the sum of all the TRW weights of its nearest neighbors. To deal with online situations, we also propose a new algorithm to handle sequential samples based a local neighborhood reconstruction. Comparison experiments are conducted on both synthetic data sets and real-world data sets to demonstrate the validity of the proposed new $k$NN algorithm and its improvements to other version of $k$NN algorithms. Given the widespread appearance of manifold structures in real-world problems and the popularity of the traditional $k$NN algorithm, the proposed manifold version $k$NN shows promising potential for classifying manifold-distributed data.Comment: 32 pages, 12 figures, 7 table