On The Effect of Hyperedge Weights On Hypergraph Learning

Hypergraph is a powerful representation in several computer vision, machine learning and pattern recognition problems. In the last decade, many researchers have been keen to develop different hypergraph models. In contrast, no much attention has been paid to the design of hyperedge weights. However, many studies on pairwise graphs show that the choice of edge weight can significantly influence the performances of such graph algorithms. We argue that this also applies to hypegraphs. In this paper, we empirically discuss the influence of hyperedge weight on hypegraph learning via proposing three novel hyperedge weights from the perspectives of geometry, multivariate statistical analysis and linear regression. Extensive experiments on ORL, COIL20, JAFFE, Sheffield, Scene15 and Caltech256 databases verify our hypothesis. Similar to graph learning, several representative hyperedge weighting schemes can be concluded by our experimental studies. Moreover, the experiments also demonstrate that the combinations of such weighting schemes and conventional hypergraph models can get very promising classification and clustering performances in comparison with some recent state-of-the-art algorithms

Labeling the Features Not the Samples: Efficient Video Classification with Minimal Supervision

Feature selection is essential for effective visual recognition. We propose an efficient joint classifier learning and feature selection method that discovers sparse, compact representations of input features from a vast sea of candidates, with an almost unsupervised formulation. Our method requires only the following knowledge, which we call the \emph{feature sign}---whether or not a particular feature has on average stronger values over positive samples than over negatives. We show how this can be estimated using as few as a single labeled training sample per class. Then, using these feature signs, we extend an initial supervised learning problem into an (almost) unsupervised clustering formulation that can incorporate new data without requiring ground truth labels. Our method works both as a feature selection mechanism and as a fully competitive classifier. It has important properties, low computational cost and excellent accuracy, especially in difficult cases of very limited training data. We experiment on large-scale recognition in video and show superior speed and performance to established feature selection approaches such as AdaBoost, Lasso, greedy forward-backward selection, and powerful classifiers such as SVM.Comment: arXiv admin note: text overlap with arXiv:1411.771

Recent Advances of Manifold Regularization

Semi-supervised learning (SSL) that can make use of a small number of labeled data with a large number of unlabeled data to produce significant improvement in learning performance has been received considerable attention. Manifold regularization is one of the most popular works that exploits the geometry of the probability distribution that generates the data and incorporates them as regularization terms. There are many representative works of manifold regularization including Laplacian regularization (LapR), Hessian regularization (HesR) and p-Laplacian regularization (pLapR). Based on the manifold regularization framework, many extensions and applications have been reported. In the chapter, we review the LapR and HesR, and we introduce an approximation algorithm of graph p-Laplacian. We study several extensions of this framework for pairwise constraint, p-Laplacian learning, hypergraph learning, etc

Learning from networked examples

Many machine learning algorithms are based on the assumption that training examples are drawn independently. However, this assumption does not hold anymore when learning from a networked sample because two or more training examples may share some common objects, and hence share the features of these shared objects. We show that the classic approach of ignoring this problem potentially can have a harmful effect on the accuracy of statistics, and then consider alternatives. One of these is to only use independent examples, discarding other information. However, this is clearly suboptimal. We analyze sample error bounds in this networked setting, providing significantly improved results. An important component of our approach is formed by efficient sample weighting schemes, which leads to novel concentration inequalities

Multi-Label Dimensionality Reduction

abstract: Multi-label learning, which deals with data associated with multiple labels simultaneously, is ubiquitous in real-world applications. To overcome the curse of dimensionality in multi-label learning, in this thesis I study multi-label dimensionality reduction, which extracts a small number of features by removing the irrelevant, redundant, and noisy information while considering the correlation among different labels in multi-label learning. Specifically, I propose Hypergraph Spectral Learning (HSL) to perform dimensionality reduction for multi-label data by exploiting correlations among different labels using a hypergraph. The regularization effect on the classical dimensionality reduction algorithm known as Canonical Correlation Analysis (CCA) is elucidated in this thesis. The relationship between CCA and Orthonormalized Partial Least Squares (OPLS) is also investigated. To perform dimensionality reduction efficiently for large-scale problems, two efficient implementations are proposed for a class of dimensionality reduction algorithms, including canonical correlation analysis, orthonormalized partial least squares, linear discriminant analysis, and hypergraph spectral learning. The first approach is a direct least squares approach which allows the use of different regularization penalties, but is applicable under a certain assumption; the second one is a two-stage approach which can be applied in the regularization setting without any assumption. Furthermore, an online implementation for the same class of dimensionality reduction algorithms is proposed when the data comes sequentially. A Matlab toolbox for multi-label dimensionality reduction has been developed and released. The proposed algorithms have been applied successfully in the Drosophila gene expression pattern image annotation. The experimental results on some benchmark data sets in multi-label learning also demonstrate the effectiveness and efficiency of the proposed algorithms.Dissertation/ThesisPh.D. Computer Science 201