Multi-organ segmentation is a critical problem in medical image analysis due to its great value for computer-aided diagnosis, computer-aided surgery, and radiation therapy. Although fully-supervised segmentation methods can achieve good performance, they usually require a large amount of 3D data, such as CT scans, with voxel-wised annotations which are usually difficult, expensive, and slow to obtain. By contrast, large unannotated datasets of CT images are available. Inspired by the well-known semi-supervised learning framework co-training, we propose multi-planar co-training (MPCT), to generate more reliable pseudo-labels by enforcing consistency among multiple planes, i.e., saggital, coronal, and axial planes, of 3D unlabeled medical data, which play a vital role in our framework. Empirical results show that generating pseudo-labels by the multi-planar fusion rather than a single plane leads to a significant performance gain. We evaluate our approach on a new collected dataset and show that MPCT boosts the performance of a typical segmentation model, fully convolutional networks, by a large margin, when only a small set of labeled 3D data is available, i.e., 77.49 vs. 73.14 .
Graph-based semi-supervised methods define a graph where the nodes are labeled and unlabeled examples in the dataset, and edges reflect the similarity of examples. These methods have been widely adopted in non-deep-learning based semi-supervised learning algorithms in the biomedical imaging domain @cite_26 @cite_46 @cite_42 .
@cite_46 @cite_26 @cite_42
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In the literature, most existing graph-based semi-supervised learning methods only use the label information of observed samples in the label propagation stage, while ignoring such valuable information when learning the graph. In this paper, we argue that it is beneficial to consider the label information in the graph learning stage. Specifically, by enforcing the weight of edges between labeled samples of different classes to be zero, we explicitly incorporate the label information into the state-of-the-art graph learning methods, such as the low-rank representation (LRR), and propose a novel semi-supervised graph learning method called semi-supervised low-rank representation. This results in a convex optimization problem with linear constraints, which can be solved by the linearized alternating direction method. Though we take LRR as an example, our proposed method is in fact very general and can be applied to any self-representation graph learning methods. Experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data, and therefore is more effective for semi-supervised learning tasks. Graph-based semi-supervised learning is one of the most popular methods in machine learning. Some of its theoretical properties such as bounds for the generalization error and the convergence of the graph Laplacian regularizer have been studied in computer science and statistics literatures. However, a fundamental statistical property, the consistency of the estimator from this method has not been proved. In this article, we study the consistency problem under a non-parametric framework. We prove the consistency of graph-based learning in the case that the estimated scores are enforced to be equal to the observed responses for the labeled data. The sample sizes of both labeled and unlabeled data are allowed to grow in this result. When the estimated scores are not required to be equal to the observed responses, a tuning parameter is used to balance the loss function and the graph Laplacian regularizer. We give a counterexample demonstrating that the estimator for this case can be inconsistent. The theoretical findings are supported by numerical studies. An approach to semi-supervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning problem is then formulated in terms of a Gaussian random field on this graph, where the mean of the field is characterized in terms of harmonic functions, and is efficiently obtained using matrix methods or belief propagation. The resulting learning algorithms have intimate connections with random walks, electric networks, and spectral graph theory. We discuss methods to incorporate class priors and the predictions of classifiers obtained by supervised learning. We also propose a method of parameter learning by entropy minimization, and show the algorithm's ability to perform feature selection. Promising experimental results are presented for synthetic data, digit classification, and text classification tasks. This paper presents a semi-supervised graph-based method for the classification of hyperspectral images. The method is designed to handle the special characteristics of hyperspectral images, namely, high-input dimension of pixels, low number of labeled samples, and spatial variability of the spectral signature. To alleviate these problems, the method incorporates three ingredients, respectively. First, being a kernel-based method, it combats the curse of dimensionality efficiently. Second, following a semi-supervised approach, it exploits the wealth of unlabeled samples in the image, and naturally gives relative importance to the labeled ones through a graph-based methodology. Finally, it incorporates contextual information through a full family of composite kernels. Noting that the graph method relies on inverting a huge kernel matrix formed by both labeled and unlabeled samples, we originally introduce the Nystro umlm method in the formulation to speed up the classification process. The presented semi-supervised-graph-based method is compared to state-of-the-art support vector machines in the classification of hyperspectral data. The proposed method produces better classification maps, which capture the intrinsic structure collectively revealed by labeled and unlabeled points. Good and stable accuracy is produced in ill-posed classification problems (high dimensional spaces and low number of labeled samples). In addition, the introduction of the composite-kernel framework drastically improves results, and the new fast formulation ranks almost linearly in the computational cost, rather than cubic as in the original method, thus allowing the use of this method in remote-sensing applications. Graph based semi-supervised learning (SSL) methods play an increasingly important role in practical machine learning systems. A crucial step in graph based SSL methods is the conversion of data into a weighted graph. However, most of the SSL literature focuses on developing label inference algorithms without extensively studying the graph building method and its effect on performance. This article provides an empirical study of leading semi-supervised methods under a wide range of graph construction algorithms. These SSL inference algorithms include the Local and Global Consistency (LGC) method, the Gaussian Random Field (GRF) method, the Graph Transduction via Alternating Minimization (GTAM) method as well as other techniques. Several approaches for graph construction, sparsification and weighting are explored including the popular k-nearest neighbors method (kNN) and the b-matching method. As opposed to the greedily constructed kNN graph, the b-matched graph ensures each node in the graph has the same number of edges and produces a balanced or regular graph. Experimental results on both artificial data and real benchmark datasets indicate that b-matching produces more robust graphs and therefore provides significantly better prediction accuracy without any significant change in computation time. In many practical data mining applications such as text classification, unlabeled training examples are readily available, but labeled ones are fairly expensive to obtain. Therefore, semi supervised learning algorithms have aroused considerable interests from the data mining and machine learning fields. In recent years, graph-based semi supervised learning has been becoming one of the most active research areas in the semi supervised learning community. In this paper, a novel graph-based semi supervised learning approach is proposed based on a linear neighborhood model, which assumes that each data point can be linearly reconstructed from its neighborhood. Our algorithm, named linear neighborhood propagation (LNP), can propagate the labels from the labeled points to the whole data set using these linear neighborhoods with sufficient smoothness. A theoretical analysis of the properties of LNP is presented in this paper. Furthermore, we also derive an easy way to extend LNP to out-of-sample data. Promising experimental results are presented for synthetic data, digit, and text classification tasks. Active and semi-supervised learning are important techniques when labeled data are scarce. We combine the two under a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The semi-supervised learning problem is then formulated in terms of a Gaussian random field on this graph, the mean of which is characterized in terms of harmonic functions. Active learning is performed on top of the semisupervised learning scheme by greedily selecting queries from the unlabeled data to minimize the estimated expected classification error (risk); in the case of Gaussian fields the risk is efficiently computed using matrix methods. We present experimental results on synthetic data, handwritten digit recognition, and text classification tasks. The active learning scheme requires a much smaller number of queries to achieve high accuracy compared with random query selection. Abstract In this paper, we propose a novel graph-based approach for semi-supervised learning problems, which considers an adaptive adjacency of the examples throughout the unsupervised portion of the training. Adjacency of the examples is inferred using the predictions of a neural network model which is first initialized by a supervised pretraining. These predictions are then updated according to a novel unsupervised objective which regularizes another adjacency, now linking the output nodes. Regularizing the adjacency of the output nodes, inferred from the predictions of the network, creates an easier optimization problem and ultimately provides that the predictions of the network turn into the optimal embedding. Ultimately, the proposed framework provides an effective and scalable graph-based solution which is natural to the operational mechanism of deep neural networks. Our results show comparable performance with state-of-the-art generative approaches for semi-supervised learning on an easier-to-train, low-cost framework. Graph-based approaches have been successful in unsupervised and semi-supervised learning. In this paper, we focus on the real-world applications where the same instance can be represented by multiple heterogeneous features. The key point of utilizing the graph-based knowledge to deal with this kind of data is to reasonably integrate the different representations and obtain the most consistent manifold with the real data distributions. In this paper, we propose a novel framework via the reformulation of the standard spectral learning model, which can be used for multiview clustering and semisupervised tasks. Unlike other methods in the literature, the proposed methods can learn an optimal weight for each graph automatically without introducing an additive parameter as previous methods do. Furthermore, our objective under semisupervised learning is convex and the global optimal result will be obtained. Extensive empirical results on different real-world data sets demonstrate that the proposed methods achieve comparable performance with the state-of-the-art approaches and can be used more practically. Deep learning algorithms require large amounts of labeled data which is difficult to attain for medical imaging. Even if a particular dataset is accessible, a learned classifier struggles to maintain the same level of performance on a different medical imaging dataset from a new or never-seen data source domain. Utilizing generative adversarial networks in a semi-supervised learning architecture, we address both problems of labeled data scarcity and data domain overfitting. For cardiac abnormality classification in chest X-rays, we demonstrate that an order of magnitude less data is required with semi-supervised learning generative adversarial networks than with conventional supervised learning convolutional neural networks. In addition, we demonstrate its robustness across different datasets for similar classification tasks. Semi-supervised learning is one of the important topics in machine learning, concerning with pattern classification where only a small subset of data is labeled. In this paper, a new network-based (or graph-based) semi-supervised classification model is proposed. It employs a combined random-greedy walk of particles, with competition and cooperation mechanisms, to propagate class labels to the whole network. Due to the competition mechanism, the proposed model has a local label spreading fashion, i.e., each particle only visits a portion of nodes potentially belonging to it, while it is not allowed to visit those nodes definitely occupied by particles of other classes. In this way, a &#x201C;divide-and-conquer&#x201D; effect is naturally embedded in the model. As a result, the proposed model can achieve a good classification rate while exhibiting low computational complexity order in comparison to other network-based semi-supervised algorithms. Computer simulations carried out for synthetic and real-world data sets provide a numeric quantification of the performance of the method. The lack of labeled data always poses challenges for tasks where machine learning is involved. Semi-supervised and cross-domain approaches represent the most common ways to overcome this difficulty. Graph-based algorithms have been widely studied during the last decade and have proved to be very effective at solving the data limitation problem. This paper explores one of the most popular stateof-the-art graph-based algorithms - label propagation, together with its modifications previously applied to sentiment classification. We study the impact of modified graph structure and parameter variations and compare the performance of graph-based algorithms in cross-domain and semi-supervised settings. The results provide a strategy for selecting the most favourable algorithm and learning paradigm on the basis of the available labeled and unlabeled data. Recent studies have shown that graph-based approaches are effective for semi-supervised learning. The key idea behind many graph-based approaches is to enforce the consistency between the class assignment of unlabeled examples and the pairwise similarity between examples. One major limitation with most graph-based approaches is that they are unable to explore dissimilarity or negative similarity. This is because the dissimilar relation is not transitive, and therefore is difficult to be propagated. Furthermore, negative similarity could result in unbounded energy functions, which makes most graph-based algorithms unapplicable. In this paper, we propose a new graph-based approach, termed as "mixed label propagation" which is able to effectively explore both similarity and dissimilarity simultaneously. In particular, the new framework determines the assignment of class labels by (1) minimizing the energy function associated with positive similarity, and (2) maximizing the energy function associated with negative similarity. Our empirical study with collaborative filtering shows promising performance of the proposed approach. Traditional graph-based semi-supervised learning (SSL) approaches, even though widely applied, are not suited for massive data and large label scenarios since they scale linearly with the number of edges @math and distinct labels @math . To deal with the large label size problem, recent works propose sketch-based methods to approximate the distribution on labels per node thereby achieving a space reduction from @math to @math , under certain conditions. In this paper, we present a novel streaming graph-based SSL approximation that captures the sparsity of the label distribution and ensures the algorithm propagates labels accurately, and further reduces the space complexity per node to @math . We also provide a distributed version of the algorithm that scales well to large data sizes. Experiments on real-world datasets demonstrate that the new method achieves better performance than existing state-of-the-art algorithms with significant reduction in memory footprint. We also study different graph construction mechanisms for natural language applications and propose a robust graph augmentation strategy trained using state-of-the-art unsupervised deep learning architectures that yields further significant quality gains. Semi-supervised learning is becoming increasingly important because it can combine data carefully labeled by humans with abundant unlabeled data to train deep neural networks. Classic methods on semi-supervised learning that have focused on transductive learning have not been fully exploited in the inductive framework followed by modern deep learning. The same holds for the manifold assumption---that similar examples should get the same prediction. In this work, we employ a transductive label propagation method that is based on the manifold assumption to make predictions on the entire dataset and use these predictions to generate pseudo-labels for the unlabeled data and train a deep neural network. At the core of the transductive method lies a nearest neighbor graph of the dataset that we create based on the embeddings of the same network.Therefore our learning process iterates between these two steps. We improve performance on several datasets especially in the few labels regime and show that our work is complementary to current state of the art. We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin. We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin. In traditional machine learning approaches to classification, one uses only a labeled set to train the classifier. Labeled instances however are often difficult, expensive, or time consuming to obtain, as they require the efforts of experienced human annotators. Meanwhile unlabeled data may be relatively easy to collect, but there has been few ways to use them. Semi-supervised learning addresses this problem by using large amount of unlabeled data, together with the labeled data, to build better classifiers. Because semi-supervised learning requires less human effort and gives higher accuracy, it is of great interest both in theory and in practice. We present a series of novel semi-supervised learning approaches arising from a graph representation, where labeled and unlabeled instances are represented as vertices, and edges encode the similarity between instances. They address the following questions: How to use unlabeled data? (label propagation); What is the probabilistic interpretation? (Gaussian fields and harmonic functions); What if we can choose labeled data? (active learning); How to construct good graphs? (hyperparameter learning); How to work with kernel machines like SVM? (graph kernels); How to handle complex data like sequences? (kernel conditional random fields); How to handle scalability and induction? (harmonic mixtures). An extensive literature review is included at the end. Semi-supervised learning, which uses unlabeled data to help learn a discriminative model, is especially important for structured output problems, as considerably more effort is needed to label its multi-dimensional outputs versus standard single output problems. We propose a new max-margin framework for semi-supervised structured output learning, that allows the use of powerful discrete optimization algorithms and high order regularizers defined directly on model predictions for the unlabeled examples. We show that our framework is closely related to Posterior Regularization, and the two frameworks optimize special cases of the same objective. The new framework is instantiated on two image segmentation tasks, using both a graph regularizer and a cardinality regularizer. Experiments also demonstrate that this framework can utilize unlabeled data from a different source than the labeled data to significantly improve performance while saving labeling effort. Typical graph-theoretic approaches for semi-supervised classification infer labels of unlabeled instances with the help of graph Laplacians. Founded on the spectral decomposition of the graph Laplacian, this paper learns a kernel matrix via minimizing the leave-one-out classification error on the labeled instances. To this end, an efficient algorithm is presented based on linear programming, resulting in a transductive spectral kernel. The idea of our algorithm stems from regularization methodology and also has a nice interpretation in terms of spectral clustering. A simple classifier can be readily built upon the learned kernel, which suffices to give prediction for any data point aside from those in the available dataset. Besides this usage, the spectral kernel can be effectively used in tandem with conventional kernel machines such as SVMs. We demonstrate the efficacy of the proposed algorithm through experiments carried out on challenging classification tasks.