Semi-supervised learning, i.e. learning from both labeled and unlabeled data has received significant attention in the machine learning literature in recent years.

One of the intuitions underlying many graph-based methods for clustering and semi-supervised learning, is that class or cluster boundaries pass through areas of low probability density. In this paper we provide some formal analysis of that notion for a probability distribution. We introduce a notion of weighted boundary volume, which measures the length of the class/cluster boundary weighted by the density of the underlying probability distribution. We show that sizes of the cuts of certain commonly used data adjacency graphs converge to this continuous weighted volume of the boundary.

Correspondence algorithms typically struggle with shapes that display part-based variation. We present a probabilistic approach that matches shapes using independent parttransformations, where the parts themselves are learnt during matching. Ideas from semi-supervised learning are used to bias the algorithm towards finding'perceptuallyvalid' part structures. Shapes are represented by unlabeled point sets of arbitrary size and a background component is used to handle occlusion, local dissimilarity and clutter. Thus, unlike many shape matching techniques, our approach can be applied to shapes extracted from real images. Model parameters areestimated using an EM algorithm that alternates between finding a soft correspondence and computing the optimal part transformations using Procrustes analysis.

Semi-supervised learning is more powerful than supervised learning by using both labeled and unlabeled data. In particular, the manifold regularization framework, together with kernel methods, leads to the Laplacian SVM (LapSVM) that has demonstrated state-of-the-art performance. However, the LapSVM solution typically involveskernel expansions of all the labeled and unlabeled examples, and is slow on testing. Moreover, existing semi-supervised learning methods, including theLapSVM, can only handle a small number of unlabeled examples. In this paper, we integrate manifold regularization with the core vector machine, which has been used for large-scale supervised and unsupervised learning. By using a sparsified manifold regularizer and formulating as a center-constrained minimum enclosing ball problem, the proposed method produces sparse solutions with low time and space complexities. Experimental results show that it is much faster than the LapSVM, and can handle a million unlabeled examples on a standard PC; while the LapSVM can only handle several thousand patterns.

Semi-supervised learning algorithms have been successfully applied in many applications withscarce labeled data, by utilizing the unlabeled data. One important category is graph based semi-supervised learning algorithms, for which the performance dependsconsiderably on the quality of the graph, or its hyperparameters. In this paper, we deal with the less explored problem of learning the graphs. We propose agraph learning method for the harmonic energy minimization method; this is done by minimizing the leave-one-out prediction error on labeled data points. We use a gradient based method and designed an efficient algorithm which significantly acceleratesthe calculation of the gradient by applying the matrix inversion lemma and using careful pre-computation. Experimental results show that the graph learning method is effective in improving the performance of the classification algorithm.

Data mining allows the exploration of sequences of phenomena, whereas one usually tends to focus on isolated phenomena or on the relation between two phenomena. It offers invaluable tools for theoretical analyses and exploration of the structure of sentences, texts, dialogues, and speech. We report here the results of an attempt at using it for inspecting sequences of verbs from French accounts of road accidents. This analysis comes from an original approach of unsupervised training allowing the discovery of the structure of sequential data. The entries of the analyzer were only made of the verbs appearing in the sentences. It provided a classification of the links between two successive verbs into four distinct clusters, allowing thus text segmentation. We give here an interpretation of these clusters by applying a statistical analysis to independent semantic annotations.

We consider a framework for semi-supervised learning using spectral decomposition based unsupervised kernel design. This approach subsumes a class of previously proposed semi-supervised learning methods on data graphs. We examine various theoretical properties of such methods. In particular, we derive a generalization performance bound, and obtain the optimal kernel design by minimizing the bound. Based on the theoretical analysis, we are able to demonstrate why spectral kernel design based methods can often improve the predictive performance. Experiments are used to illustrate the main consequences of our analysis.

A foundational problem in semi-supervised learning is the construction of a graph underlying the data. We propose to use a method which optimally combinesa number of differently constructed graphs.

We examine various theoretical properties of such methods.

Many real-world classification problems involve the prediction of multiple interdependent variables forming some structural dependency. Recentprogress in machine learning has mainly focused on supervised classification of such structured variables. In this paper, we investigate structured classification in a semi-supervised setting. We present a discriminative approach that utilizes the intrinsic geometry ofinput patterns revealed by unlabeled data points and we derive a maximum-margin formulation of semi-supervised learning for structured variables.