Dengyong Zhou

Semi-Supervised Graph-Based Hyperspectral Image Classification

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.

Learning from labeled and unlabeled data on a directed graph

We propose a general framework for learning from labeled and unlabeled data on a directed graph in which the structure of the graph including the directionality of the edges is considered. The time complexity of the algorithm derived from this framework is nearly linear due to recently developed numerical techniques. In the absence of labeled instances, this framework can be utilized as a spectral clustering method for directed graphs, which generalizes the spectral clustering approach for undirected graphs. We have applied our framework to real-world web classification problems and obtained encouraging results.

Semi-supervised protein classification using cluster kernels

MOTIVATION Building an accurate protein classification system depends critically upon choosing a good representation of the input sequences of amino acids. Recent work using string kernels for protein data has achieved state-of-the-art classification performance. However, such representations are based only on labeled data--examples with known 3D structures, organized into structural classes--whereas in practice, unlabeled data are far more plentiful. RESULTS In this work, we develop simple and scalable cluster kernel techniques for incorporating unlabeled data into the representation of protein sequences. We show that our methods greatly improve the classification performance of string kernels and outperform standard approaches for using unlabeled data, such as adding close homologs of the positive examples to the training data. We achieve equal or superior performance to previously presented cluster kernel methods and at the same time achieving far greater computational efficiency. AVAILABILITY Source code is available at www.kyb.tuebingen.mpg.de/bs/people/weston/semiprot. The Spider matlab package is available at www.kyb.tuebingen.mpg.de/bs/people/spider. SUPPLEMENTARY INFORMATION www.kyb.tuebingen.mpg.de/bs/people/weston/semiprot.

Regularization on discrete spaces

We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is well-known that many meaningful inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as discrete analogue of classical regularization theory. A family of transductive inference schemes is then systemically derived from the framework, including our earlier algorithm for transductive inference, with which we obtained encouraging results on many practical classification problems. The discrete regularization framework is built on discrete analysis and geometry developed by ourselves, in which a number of discrete differential operators of various orders are constructed, which can be thought of as discrete analogues of their counterparts in the continuous case.

Learning from Labeled and Unlabeled Data Using Random Walks

We consider the general problem of learning from labeled and unlabeled data. Given a set of points, some of them are labeled, and the remaining points are unlabeled. The goal is to predict the labels of the unlabeled points. Any supervised learning algorithm can be applied to this problem, for instance, Support Vector Machines (SVMs). The problem of our interest is if we can implement a classifier which uses the unlabeled data information in some way and has higher accuracy than the classifiers which use the labeled data only. Recently we proposed a simple algorithm, which can substantially benefit from large amounts of unlabeled data and demonstrates clear superiority to supervised learning methods. Here we further investigate the algorithm using random walks and spectral graph theory, which shed light on the key steps in this algorithm.

Semi-supervised Hyperspectral Image Classification with Graphs

This paper presents a semi-supervised graph-based method for the classification of hyperspectral images. The method is designed to exploit the spatial/contextual information in the im- ages through composite kernels. The proposed method produces smoother classifications with respect to the intrinsic structure collectively revealed by known labeled and unlabeled points. Good accuracy in high dimensional spaces and low number of labeled samples (ill-posed situations) are produced as compared to standard inductive support vector machines.