Viggo Kann

Bio: Viggo Kann is an academic researcher from Royal Institute of Technology. The author has contributed to research in topics: Approximation algorithm & Time complexity. The author has an hindex of 25, co-authored 77 publications receiving 5390 citations.

Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties

Abstract: This book documents the state of the art in combinatorial optimization, presenting approximate solutions of virtually all relevant classes of NP-hard optimization problems. The wealth of problems, algorithms, results, and techniques make it an indispensible source of reference for professionals. The text smoothly integrates numerous illustrations, examples, and exercises.

An introduction to variable and feature selection

Abstract: Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available. These areas include text processing of internet documents, gene expression array analysis, and combinatorial chemistry. The objective of variable selection is three-fold: improving the prediction performance of the predictors, providing faster and more cost-effective predictors, and providing a better understanding of the underlying process that generated the data. The contributions of this special issue cover a wide range of aspects of such problems: providing a better definition of the objective function, feature construction, feature ranking, multivariate feature selection, efficient search methods, and feature validity assessment methods.

Robust Face Recognition via Sparse Representation

Abstract: We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

Efficient Graph-Based Image Segmentation

Abstract: This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm runs in time nearly linear in the number of graph edges and is also fast in practice. An important characteristic of the method is its ability to preserve detail in low-variability image regions while ignoring detail in high-variability regions.

Advances in kernel methods: support vector learning

Abstract: Introduction to support vector learning roadmap. Part 1 Theory: three remarks on the support vector method of function estimation, Vladimir Vapnik generalization performance of support vector machines and other pattern classifiers, Peter Bartlett and John Shawe-Taylor Bayesian voting schemes and large margin classifiers, Nello Cristianini and John Shawe-Taylor support vector machines, reproducing kernel Hilbert spaces, and randomized GACV, Grace Wahba geometry and invariance in kernel based methods, Christopher J.C. Burges on the annealed VC entropy for margin classifiers - a statistical mechanics study, Manfred Opper entropy numbers, operators and support vector kernels, Robert C. Williamson et al. Part 2 Implementations: solving the quadratic programming problem arising in support vector classification, Linda Kaufman making large-scale support vector machine learning practical, Thorsten Joachims fast training of support vector machines using sequential minimal optimization, John C. Platt. Part 3 Applications: support vector machines for dynamic reconstruction of a chaotic system, Davide Mattera and Simon Haykin using support vector machines for time series prediction, Klaus-Robert Muller et al pairwise classification and support vector machines, Ulrich Kressel. Part 4 Extensions of the algorithm: reducing the run-time complexity in support vector machines, Edgar E. Osuna and Federico Girosi support vector regression with ANOVA decomposition kernels, Mark O. Stitson et al support vector density estimation, Jason Weston et al combining support vector and mathematical programming methods for classification, Bernhard Scholkopf et al.

Sparse Subspace Clustering: Algorithm, Theory, and Applications

Abstract: Many real-world problems deal with collections of high-dimensional data, such as images, videos, text, and web documents, DNA microarray data, and more. Often, such high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories to which the data belong. In this paper, we propose and study an algorithm, called sparse subspace clustering, to cluster data points that lie in a union of low-dimensional subspaces. The key idea is that, among the infinitely many possible representations of a data point in terms of other points, a sparse representation corresponds to selecting a few points from the same subspace. This motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces. Since solving the sparse optimization program is in general NP-hard, we consider a convex relaxation and show that, under appropriate conditions on the arrangement of the subspaces and the distribution of the data, the proposed minimization program succeeds in recovering the desired sparse representations. The proposed algorithm is efficient and can handle data points near the intersections of subspaces. Another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances, such as noise, sparse outlying entries, and missing entries, by incorporating the model of the data into the sparse optimization program. We demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real-world problems of motion segmentation and face clustering.