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- Michael R Berthold, Klaus{peter Huber, +4 authors De
- 1997

In this paper a technique is proposed to tolerate missing values based on a system of fuzzy rules for classiication. The presented method is mathematically solid but nevertheless easy and eecient to implement. Three possible applications of this methodology are outlined: the classiication of patterns with an incomplete feature vector, the completion of the… (More)

- A. Dress, K. T. Huber
- 2001

1 Introduction In a highly original, but not yet sufficiently appreciated contribution entitled " Six theorems about metric spaces " [32], John Isbell presented and discussed the following intriguing observations: from X into X with α • α = Id X and with d(α (x), α (y)) ≤ d (x , y) for all x , y ∈ X. (ii) Every metric space (X, d) can be embedded… (More)

- A. Dress, K. T. Huber
- 2007

In 1970, Farris introduced a procedure that can be used to transform a tree metric into an ultra metric. Since its discovery, Farris' procedure has been used extensively within phylogenetics where it has become commonly known as the Farris transform. Remarkably, the Farris transform has not only been rediscovered several times within phylogenetics, but also… (More)

- A. Dress, K. T. Huber, V. Moulton, Ulf Rehmann
- 2001

The close relationship between the theory of quadratic forms and distance analysis has been known for centuries, and the theory of metric spaces that formalizes distance analysis and was developed over the last century, has obvious strong relations to quadratic-form theory. In contrast, the first paper that studied metric spaces as such – without trying to… (More)

- A. Dress, K. T. Huber
- 2008

The combinatorial dimension of a metric space (X, d), denoted by dim combin (d), arises naturally in the subject of T-theory, and, in case X is finite, corresponds with the (topological) dimension of the tight span associated to d. Metric spaces of combinatorial dimension at most one are well understood; they are precisely the metric spaces that can be… (More)

| Function approximation using example data has gained considerable interest in the past. One interesting application is the approximation of the behaviour of simulation models , called metamodelling. The goal is to approximate the behaviour as well as to extract some understandable knowledge about the simulation model. In this paper a combination of a… (More)

- K. T. Huber, G. E. Scholz
- Algorithmica
- 2016

Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple relations on a set of sequences called orthology relations may be employed. In addition to being interesting from a practical point of view they are also attractive from a theoretical perspective in that e. g. a… (More)

- D. Cieslik, A. Dress, K. T. Huber, V. Moulton
- 2008

In this note, we continue our work devoted to investigating the concept of embedding complexity (cf. Cieslik et al. [3]) and present a new Divide and Conquer algorithm for solving the Steiner-tree problem for graphs that relies on dynamic-programming schemes. In this way, we show how the rather general conceptual framework developed in our previous paper… (More)

- Michael R Berthold, Klaus{peter Huber, +4 authors De
- 2007

Numerous learning tasks involve incomplete or connicting attributes. Most algorithms that automatically nd a set of fuzzy rules are not well suited to tolerate missing values in the input vector, and the usual technique to substitute missing values by their mean or another constant value can be quite harmful. In this paper a technique is proposed to… (More)

In this note, we describe a new and quite natural way of analyzing instances of discrete optimization problems in terms of what we call the embedding complexity of an associated (more or less) canonical embedding of the (in general, vast) solution space of a given problem into a product of (in general, small) sets. This concept arises naturally within the… (More)

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