Learning Flexible Graph-Based Semi-Supervised Embedding

Abstract

This paper introduces a graph-based semi-supervised embedding method as well as its kernelized version for generic classification and recognition tasks. The aim is to combine the merits of flexible manifold embedding and nonlinear graph-based embedding for semi-supervised learning. The proposed linear method will be flexible since it estimates a nonlinear manifold that is the closest one to a linear embedding. The proposed kernelized method will also be flexible since it estimates a kernel-based embedding that is the closest to a nonlinear manifold. In both proposed methods, the nonlinear manifold and the mapping (linear transform for the linear method and the kernel multipliers for the kernelized method) are simultaneously estimated, which overcomes the shortcomings of a cascaded estimation. The dimension of the final embedding obtained by the two proposed methods is not limited to the number of classes. They can be used by any kind of classifiers once the data are embedded into the new subspaces. Unlike nonlinear dimensionality reduction approaches, which suffer from out-of-sample problem, our proposed methods have an obvious advantage that the learnt subspace has a direct out-of-sample extension to novel samples, and are thus easily generalized to the entire high-dimensional input space. We provide extensive experiments on seven public databases in order to study the performance of the proposed methods. These experiments demonstrate much improvement over the state-of-the-art algorithms that are based on label propagation or graph-based semi-supervised embedding.

A Semi-Supervised Method for Surveillance-Based Visual Location Recognition

“…Some cluster assumption-based methods mainly focus on looking for an optimal separation boundary that lies in the low density region of the data space, such as the transductive support vector machines [42], semi-supervised support vector machines [43], and weakly supervised latent category learning [44]. Recently, some manifold assumption based methods [45], [46] mainly consider the marginal distribution of data lying on a lowdimensional manifold embedded in a high-dimensional space, which show great success. As the discrete approximation of data manifold, the graph construction [47], [48] plays a crucial role in these kinds of learning approaches.…”

“…Recently, some manifold assumption based methods [45], [46] mainly consider the marginal distribution of data lying on a lowdimensional manifold embedded in a high-dimensional space, which show great success. As the discrete approximation of data manifold, the graph construction [47], [48] plays a crucial role in these kinds of learning approaches. Many transductive semi-supervised learning algorithms [49]- [51] have been proposed based on the graph construction and manifold preserving, but the model has to be retrained for each new test sample.…”

Ensemble Teaching for Hybrid Label Propagation

“…L ABEL propagation is an important technique in semisupervised learning [1], [2]. Given an undirected weighted graph, the target of label propagation is to iteratively transfer class labels from labeled examples to unlabeled examples so that the unlabeled examples can be accurately classified.…”

Kernel-Induced Label Propagation by Mapping for Semi-Supervised Classification

“…Note that these issues can benefit from the semi-supervised learning (SSL) methods [1][2][3] that can learn knowledge using both labeled and unlabeled data, and especially by capturing their geometrical structures over a graph [1][ [35][36][37] [48][49][50][51].…”

“…Label Propagation (LP), which is one of the most popular graph based SSL algorithms [1] [35][36][37], has aroused much attention the areas of data mining and pattern recognition in recent years because of its effectiveness and efficiency. More specifically, LP has been successfully applied to various real applications, e.g., face recognition and image segmentation.…”