Unsupervised image categorization by hypergraph partition

Integrating Tensor Similarity to Enhance Clustering Performance

The performance of most clustering methods hinges on the used pairwise affinity, which is usually denoted by a similarity matrix. However, the pairwise similarity is notoriously known for its vulnerability of noise contamination or the imbalance in samples or features, and thus hinders accurate clustering. To tackle this issue, we propose to use information among samples to boost the clustering performance. We proved that a simplified similarity for pairs, denoted by a fourth order tensor, equals to the Kronecker product of pairwise similarity matrices under decomposable assumption, or provide complementary information for which the pairwise similarity missed under indecomposable assumption. Then a high order similarity matrix is obtained from the tensor similarity via eigenvalue decomposition. The high order similarity capturing spatial information serves as a robust complement for the pairwise similarity. It is further integrated with the popular pairwise similarity, named by IPS2, to boost the clustering performance. Extensive experiments demonstrated that the proposed IPS2 significantly outperformed previous similarity-based methods on real-world datasets and it was capable of handling the clustering task over under-sampled and noisy datasets.

Identifying disease-related subnetwork connectome biomarkers by sparse hypergraph learning

The functional brain network has gained increased attention in the neuroscience community because of its ability to reveal the underlying architecture of human brain. In general, majority work of functional network connectivity is built based on the correlations between discrete-time-series signals that link only two different brain regions. However, these simple region-to-region connectivity models do not capture complex connectivity patterns between three or more brain regions that form a connectivity subnetwork, or subnetwork for short. To overcome this current limitation, a hypergraph learning-based method is proposed to identify subnetwork differences between two different cohorts. To achieve our goal, a hypergraph is constructed, where each vertex represents a subject and also a hyperedge encodes a subnetwork with similar functional connectivity patterns between different subjects. Unlike previous learning-based methods, our approach is designed to jointly optimize the weights for all hyperedges such that the learned representation is in consensus with the distribution of phenotype data, i.e. clinical labels. In order to suppress the spurious subnetwork biomarkers, we further enforce a sparsity constraint on the hyperedge weights, where a larger hyperedge weight indicates the subnetwork with the capability of identifying the disorder condition. We apply our hypergraph learning-based method to identify subnetwork biomarkers in Autism Spectrum Disorder (ASD) and Attention Deficit Hyperactivity Disorder (ADHD). A comprehensive quantitative and qualitative analysis is performed, and the results show that our approach can correctly classify ASD and ADHD subjects from normal controls with 87.65 and 65.08% accuracies, respectively.

Correntropy-Induced Robust Low-Rank Hypergraph

Hypergraph learning has been widely exploited in various image processing applications, due to its advantages in modeling the high-order information. Its efficacy highly depends on building an informative hypergraph structure to accurately and robustly formulate the underlying data correlation. However, the existing hypergraph learning methods are sensitive to non- Gaussian noise, which hurts the corresponding performance. In this paper, we present a noise-resistant hypergraph learning model, which provides superior robustness against various non- Gaussian noises. In particular, our model adopts low-rank representation to construct a hypergraph, which captures the globally linear data structure as well as preserving the grouping effect of highly-correlated data. We further introduce a correntropyinduced local metric to measure the reconstruction errors, which is particularly robust to non-Gaussian noises. Finally, the Frobenious-norm based regularization is proposed to combine with the low-rank regularizer, which enables our model to regularize the singular values of the coefficient matrix. By such, the non-zero coefficients are selected to generate a hyperedge set as well as the hyperedge weights. We have evaluated the proposed hypergraph model in the tasks of image clustering and semi-supervised image classification. Quantitatively, our scheme significantly enhances the performance of the state-of-the-art hypergraph models on several benchmark datasets.

Multiview Physician-Specific Attributes Fusion for Health Seeking

Community-based health services have risen as important online resources for resolving users health concerns. Despite the value, the gap between what health seekers with specific health needs and what busy physicians with specific attitudes and expertise can offer is being widened. To bridge this gap, we present a question routing scheme that is able to connect health seekers to the right physicians. In this scheme, we first bridge the expertise matching gap via a probabilistic fusion of the physician-expertise distribution and the expertise-question distribution. The distributions are calculated by hypergraph-based learning and kernel density estimation. We then measure physicians attitudes toward answering general questions from the perspectives of activity, responsibility, reputation, and willingness. At last, we adaptively fuse the expertise modeling and attitude modeling by considering the personal needs of the health seekers. Extensive experiments have been conducted on a real-world dataset to validate our proposed scheme.

Elastic Net Hypergraph Learning for Image Clustering and Semi-Supervised Classification

Graph model is emerging as a very effective tool for learning the complex structures and relationships hidden in data. In general, the critical purpose of graph-oriented learning algorithms is to construct an informative graph for image clustering and classification tasks. In addition to the classical K-nearest-neighbor and r-neighborhood methods for graph construction, l₁-graph and its variants are emerging methods for finding the neighboring samples of a center datum, where the corresponding ingoing edge weights are simultaneously derived by the sparse reconstruction coefficients of the remaining samples. However, the pairwise links of l₁-graph are not capable of capturing the high-order relationships between the center datum and its prominent data in sparse reconstruction. Meanwhile, from the perspective of variable selection, the l₁ norm sparse constraint, regarded as a LASSO model, tends to select only one datum from a group of data that are highly correlated and ignore the others. To simultaneously cope with these drawbacks, we propose a new elastic net hypergraph learning model, which consists of two steps. In the first step, the robust matrix elastic net model is constructed to find the canonically related samples in a somewhat greedy way, achieving the grouping effect by adding the l₂ penalty to the l₁ constraint. In the second step, hypergraph is used to represent the high order relationships between each datum and its prominent samples by regarding them as a hyperedge. Subsequently, hypergraph Laplacian matrix is constructed for further analysis. New hypergraph learning algorithms, including unsupervised clustering and multi-class semi-supervised classification, are then derived. Extensive experiments on face and handwriting databases demonstrate the effectiveness of the proposed method.

Hyper-connectivity of functional networks for brain disease diagnosis

Exploring structural and functional interactions among various brain regions enables better understanding of pathological underpinnings of neurological disorders. Brain connectivity network, as a simplified representation of those structural and functional interactions, has been widely used for diagnosis and classification of neurodegenerative diseases, especially for Alzheimer's disease (AD) and its early stage - mild cognitive impairment (MCI). However, the conventional functional connectivity network is usually constructed based on the pairwise correlation among different brain regions and thus ignores their higher-order relationships. Such loss of high-order information could be important for disease diagnosis, since neurologically a brain region predominantly interacts with more than one other brain regions. Accordingly, in this paper, we propose a novel framework for estimating the hyper-connectivity network of brain functions and then use this hyper-network for brain disease diagnosis. Here, the functional connectivity hyper-network denotes a network where each of its edges representing the interactions among multiple brain regions (i.e., an edge can connect with more than two brain regions), which can be naturally represented by a hyper-graph. Specifically, we first construct connectivity hyper-networks from the resting-state fMRI (R-fMRI) time series by using sparse representation. Then, we extract three sets of brain-region specific features from the connectivity hyper-networks, and further exploit a manifold regularized multi-task feature selection method to jointly select the most discriminative features. Finally, we use multi-kernel support vector machine (SVM) for classification. The experimental results on both MCI dataset and attention deficit hyperactivity disorder (ADHD) dataset demonstrate that, compared with the conventional connectivity network-based methods, the proposed method can not only improve the classification performance, but also help discover disease-related biomarkers important for disease diagnosis.

MultiVCRank With Applications to Image Retrieval

In this paper, we propose and develop a multi-visual-concept ranking (MultiVCRank) scheme for image retrieval. The key idea is that an image can be represented by several visual concepts, and a hypergraph is built based on visual concepts as hyperedges, where each edge contains images as vertices to share a specific visual concept. In the constructed hypergraph, the weight between two vertices in a hyperedge is incorporated, and it can be measured by their affinity in the corresponding visual concept. A ranking scheme is designed to compute the association scores of images and the relevance scores of visual concepts by employing input query vectors to handle image retrieval. In the scheme, the association and relevance scores are determined by an iterative method to solve limiting probabilities of a multi-dimensional Markov chain arising from the constructed hypergraph. The convergence analysis of the iteration method is studied and analyzed. Moreover, a learning algorithm is also proposed to set the parameters in the scheme, which makes it simple to use. Experimental results on the MSRC, Corel, and Caltech256 data sets have demonstrated the effectiveness of the proposed method. In the comparison, we find that the retrieval performance of MultiVCRank is substantially better than those of HypergraphRank, ManifoldRank, TOPHITS, and RankSVM.

High-order distance-based multiview stochastic learning in image classification

How do we find all images in a larger set of images which have a specific content? Or estimate the position of a specific object relative to the camera? Image classification methods, like support vector machine (supervised) and transductive support vector machine (semi-supervised), are invaluable tools for the applications of content-based image retrieval, pose estimation, and optical character recognition. However, these methods only can handle the images represented by single feature. In many cases, different features (or multiview data) can be obtained, and how to efficiently utilize them is a challenge. It is inappropriate for the traditionally concatenating schema to link features of different views into a long vector. The reason is each view has its specific statistical property and physical interpretation. In this paper, we propose a high-order distance-based multiview stochastic learning (HD-MSL) method for image classification. HD-MSL effectively combines varied features into a unified representation and integrates the labeling information based on a probabilistic framework. In comparison with the existing strategies, our approach adopts the high-order distance obtained from the hypergraph to replace pairwise distance in estimating the probability matrix of data distribution. In addition, the proposed approach can automatically learn a combination coefficient for each view, which plays an important role in utilizing the complementary information of multiview data. An alternative optimization is designed to solve the objective functions of HD-MSL and obtain different views on coefficients and classification scores simultaneously. Experiments on two real world datasets demonstrate the effectiveness of HD-MSL in image classification.

Hyperspectral image classification through bilayer graph-based learning

Hyperspectral image classification with limited number of labeled pixels is a challenging task. In this paper, we propose a bilayer graph-based learning framework to address this problem. For graph-based classification, how to establish the neighboring relationship among the pixels from the high dimensional features is the key toward a successful classification. Our graph learning algorithm contains two layers. The first-layer constructs a simple graph, where each vertex denotes one pixel and the edge weight encodes the similarity between two pixels. Unsupervised learning is then conducted to estimate the grouping relations among different pixels. These relations are subsequently fed into the second layer to form a hypergraph structure, on top of which, semisupervised transductive learning is conducted to obtain the final classification results. Our experiments on three data sets demonstrate the merits of our proposed approach, which compares favorably with state of the art.

Including the Size of Regions in Image Segmentation by Region-Based Graph

Applying a fast over-segmentation algorithm to image and working on a region-based graph (instead of the pixel-based graph) is an efficient approach to reduce the computational complexity of graph-based image segmentation methods. Nevertheless, some undesirable effects may arise if the conventional cost functions, such as Ncut, AverageCut, and MinCut, are employed for partitioning the region-based graph. This is because these cost functions are generally tailored to pixel-based graphs. In order to resolve this problem, we first introduce a new class of cost functions (containing Ncut and AverageCut) for graph partitioning whose corresponding suboptimal solution can be efficiently computed by solving a generalized eigenvalue problem. Then, among these cost functions, we propose one that considers the size of regions in the partitioning procedure. By simulation, the performance of the proposed cost function is quantitatively compared with that of the Ncut and AverageCut.

A game-theoretic approach to hypergraph clustering

Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using high-order (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a predetermined number of classes, thereby obtaining the clusters as a by-product of the partitioning process. In this paper, we offer a radically different view of the problem. In contrast to the classical approach, we attempt to provide a meaningful formalization of the very notion of a cluster and we show that game theory offers an attractive and unexplored perspective that serves our purpose well. To this end, we formulate the hypergraph clustering problem in terms of a noncooperative multiplayer "clustering game," and show that a natural notion of a cluster turns out to be equivalent to a classical (evolutionary) game-theoretic equilibrium concept. We prove that the problem of finding the equilibria of our clustering game is equivalent to locally optimizing a polynomial function over the standard simplex, and we provide a discrete-time high-order replicator dynamics to perform this optimization, based on the Baum-Eagon inequality. Experiments over synthetic as well as real-world data are presented which show the superiority of our approach over the state of the art.

Adaptive hypergraph learning and its application in image classification

Recent years have witnessed a surge of interest in graph-based transductive image classification. Existing simple graph-based transductive learning methods only model the pairwise relationship of images, however, and they are sensitive to the radius parameter used in similarity calculation. Hypergraph learning has been investigated to solve both difficulties. It models the high-order relationship of samples by using a hyperedge to link multiple samples. Nevertheless, the existing hypergraph learning methods face two problems, i.e., how to generate hyperedges and how to handle a large set of hyperedges. This paper proposes an adaptive hypergraph learning method for transductive image classification. In our method, we generate hyperedges by linking images and their nearest neighbors. By varying the size of the neighborhood, we are able to generate a set of hyperedges for each image and its visual neighbors. Our method simultaneously learns the labels of unlabeled images and the weights of hyperedges. In this way, we can automatically modulate the effects of different hyperedges. Thorough empirical studies show the effectiveness of our approach when compared with representative baselines.