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New technologies to generate, store and retrieve medical and research data are inducing a rapid change in clinical and translational research and health care. Systems medicine is the interdisciplinary approach wherein physicians and clinical investigators team up with experts from biology, biostatistics, informatics, mathematics and computational modeling to develop methods to use new and stored data to the benefit of the patient. We here provide a critical assessment of the opportunities and challenges arising out of systems approaches in medicine and from this provide a definition of what systems medicine entails. Based on our analysis of current developments in medicine and healthcare and associated research needs, we emphasize the role of systems medicine as a multilevel and multidisciplinary methodological framework for informed data acquisition and interdisciplinary data analysis to extract previously inaccessible knowledge for the benefit of patients. Creating specialised computer systems to integrate big data from multiple sources may help provide tailored future healthcare. A healthcare system that meets the needs of every individual needs the ability to collect and mine data precisely and efficiently. Olaf Wolkenhauer at Rostock University, Germany and co-workers have explored the requirements for developing this ‘systems medicine’ approach. Interdisciplinary teams should be established specifically to develop software, computational models and integrated datasets for use in healthcare. Being able to harness information from huge medical datasets could dramatically improve our understanding of disease, and allow scientists to examine illnesses from the molecular scale to whole body responses. Systems medicine could also allow doctors to investigate an individual's specific needs, trial treatments through computer models, and analyze data captured on patients' smartphones, to provide safer, more personalised heathcare.

In Mixed Fuzzy Rule Formation [Int. J. Approx. Reason. 32 (2003) 67] a method to extract mixed fuzzy rules from data was introduced. The underlying algorithm’s performance is influenced by the choice of fuzzy t-norm and t-conorm, and a heuristic to avoid conflicts between patterns and rules of different classes throughout training. In the following addendum to [Int. J. Approx. Reason. 32 (2003) 67], we discuss in more depth how these parameters affect the generalization performance of the resulting fuzzy rule models.

Many fuzzy rule induction algorithms have been proposed during the past decade or so. Most of these algorithms tend to scale badly with large dimensions of the feature space and in addition have trouble dealing with different feature types or noisy data. In this paper, an algorithm is proposed that extracts a set of so called mixed fuzzy rules. These rules can be extracted from feature spaces with diverse types of attributes and handle the corresponding different types of constraints in parallel. The extracted rules depend on individual subsets of only few attributes, which is especially useful in high dimensional feature spaces. The algorithm along with results on several classification benchmarks is presented and how this method can be extended to handle outliers or noisy training instances as well is sketched briefly.

Classifying multivariate time series is often dealt with by transforming the numeric series into labelled intervals, because many pattern representations exist to deal with labelled intervals. Finding the right preprocessing is not only time consuming but also critical for the success of the learning algorithms. In this paper we show how pattern graphs, a powerful pattern language for temporal classification rules, can be extended in order to handle labelled intervals in combination with the raw time series. We thereby reduce dependence on the quality of the preprocessing and at the same time increase performance. These benefits are demonstrated experimentally on 10 different data sets.

This article proposes a new approach to extract existing (or detect missing) concepts from a loosely integrated collection of information units by means of concept graph detection. Thereby a concept graph defines a concept by a quasi bipartite sub-graph of a bigger network with the members of the concept as the first vertex partition and their shared aspects as the second vertex partition. Once the concepts have been extracted they can be used to create higher level representations of the data. Concept graphs further allow the discovery of missing concepts, which could lead to new insights by connecting seemingly unrelated information units.

Knowledge discovery generally focuses on finding patterns within a reasonably well connected domain of interest. In this article we outline a framework for the discovery of new connections between domains (so called bisociations), supporting the creative discovery process in a more powerful way. We motivate this approach, show the difference to classical data analysis and conclude by describing a number of different types of domain-crossing connections.

Diversity selection is a common task in early drug discovery. One drawback of current approaches is that usually only the structural diversity is taken into account, therefore, activity information is ignored. In this article, we present a modified version of diversity selection, which we term Maximum-Score Diversity Selection, that additionally takes the estimated or predicted activities of the molecules into account. We show that finding an optimal solution to this problem is computationally very expensive (it is NP-hard), and therefore, heuristic approaches are needed. After a discussion of existing approaches, we present our new method, which is computationally far more efficient but at the same time produces comparable results. We conclude by validating these theoretical differences on several data sets.

We present a supervised method for Learning in Parallel Universes, i.e. problems given in multiple descriptor spaces. The goal is the construction of local models in individual universes and their fusion to a superior global model that comprises all the available information from the given universes. We employ a predictive clustering approach using Neighborgrams, a one-dimensional data structure for the neighborhood of a single object in a universe. We also present an intuitive visualization, which allows for interactive model construction and visual comparison of cluster neighborhoods across universes.

In this paper we propose two methods to derive two different kinds of node similarities in a network based on their neighborhood. The first similarity measure focuses on the overlap of direct and indirect neighbors. The second similarity compares nodes based on the structure of their - possibly also very distant - neighborhoods. Instead of using standard node measures, both similarities are derived from spreading activation patterns over time. Whereas in the first method the activation patterns are directly compared, in the second method the relative change of activation over time is compared. We apply both methods to a real-world graph dataset and discuss the results.

We discuss Learning in parallel universes as a learning concept that encompasses the simultaneous analysis from multiple descriptor spaces. In contrast to existing approaches, this approach constructs a global model that is based on only partially applicable, local models in each descriptor space. We present some application scenarios and compare this learning strategy to other approaches on learning in multiple descriptor spaces. As a representative for learning in parallel universes we introduce different extensions to a family of unsupervised fuzzy clustering algorithms and evaluate their performance on an artificial data set and a benchmark of 3D objects.

Many real-world applications have very high dimensionality and require very complex decision borders. In this case, the number of fuzzy rules can proliferate, and the easy interpretability of fuzzy models can progressively disappear. An important part of the model interpretation lies on the evaluation of the effectiveness of the input features on the decision process. In this paper, we present a method that quantifies the discriminative power of the input features in a fuzzy model. The separability among all the rules of the fuzzy model produces a measure of the information available in the system. Such measure of information is calculated to characterize the system before and after each input feature is used for classification. The resulting information gain quantifies the discriminative power of that input feature. The comparison among the information gains of the different input features can yield better insights into the selected fuzzy classification strategy, even for very high dimensional cases, and can lead to a possible reduction of the input space dimension. Several artificial and real-world data analysis scenarios are reported as examples in order to illustrate the characteristics and potentialities of the proposed method.

We present an extension of the fuzzy c-Means algorithm, which operates simultaneously on different feature spaces—so-called parallel universes—and also incorporates noise detection. The method assigns membership values of patterns to different universes, which are then adopted throughout the training. This leads to better clustering results since patterns not contributing to clustering in a universe are (completely or partially) ignored. The method also uses an auxiliary universe to capture patterns that do not contribute to any of the clusters in the real universes and therefore are likely to represent noise. The outcome of the algorithm is clusters distributed over different parallel universes, each modeling a particular, potentially overlapping subset of the data and a set of patterns detected as noise. One potential target application of the proposed method is biological data analysis where different descriptors for molecules are available but none of them by itself shows global satisfactory prediction results.

In this chapter we describe methods that assist the user to visually explore fuzzy clusters. We focus on a supervised approach to generate clusters for classes of interest of a given data set. The algorithm constructs local, one-dimensional neighborhood models, so-called Neighborgrams, for objects of the classes of interest that serve as a set of potential cluster candidates. The presented algorithm automatically chooses the best subset of Neighborgrams, but, more importantly, the accompanying visualization allows the user to fine-tune the clustering process by visually selecting, discarding, or adjusting potential cluster candidates. We also show how the algorithm can be applied to problems where multiple descriptions of data are available. This type of data can be found in biological data analysis for example, where often several different descriptors for the same molecule exist but each individual descriptor is only able to model parts of the data.

The theory of gene assembly in ciliates has much in common with the theory of sorting by reversal. Both model processes that are based on splicing, and have a fixed begin and end product. The main difference is the type of splicing operations used to obtain the end product from the begin product. In this overview paper we show that the concept of breakpoint graph, known from the theory of sorting by reversal, has many uses in the theory of gene assembly. Our aim is to present the material in an intuitive and informal manner to allow for an efficient introduction into the subject.

Assuming that the dynamics of peptides and proteins can be described by Markov transitions between different configurational states, we present a method which can calculate the mean first passage time (MFPT) between sets of initial and final states. The method is described in detail and differences between this and a method commonly employed [1] are explained. It is shown that the proposed method is (i) more general in allowing sets of final states, (ii) significantly faster, (iii) more accurate since it does not involve the calculation of infinite summations. Particular attention is given to the biologically important case of multiple final states.

Minimal cut sets (MCSs) have been introduced to define perturbations in a metabolic network needed to repress the activity of a given target reaction. While this approach gives interesting insight into the structure of metabolic networks, it suffers from two major drawbacks that are limiting in practice. First, using MCSs becomes inadequate when we are interested in inhibiting only one direction of a reversible target reaction. Second, and more importantly, the computation of MCSs by currently available methods is limited by the combinatorial explosion of the number of elementary modes and hence is not practical for genomescale networks. To overcome these problems, we introduce the concept of minimal direction cuts. A minimal forward (resp. backward) direction cut (MFC) (resp. MBC) is a minimal set of reactions whose removal prevents the target reaction from carrying a flux in the forward (resp. backward) direction. Computing MFCs and MBCs does not require to determine beforehand the elementary modes of the network. Instead it can be based on the Farkas lemma for equality and inequality constraints. This leads to a new algorithm to identify minimal direction cuts, which can also be used for a direct computation of MCSs.

Most of the existing methods for the identification of biologically interesting genes in a temporal expression profiling dataset do not fully exploit the temporal ordering in the dataset and are based on normality assumptions for the gene expression.In this paper, we introduce a Bayesian median regression model to detect genes whose temporal profile is significantly different across a number of biological conditions. The regression model is defined by a polynomial function where both time and condition effects as well as interactions between the two are included. MCMC‐based inference returns the posterior distribution of the polynomial coefficients. From this a simple Bayes factor test is proposed to test for significance.The estimation of the median rather than the mean, and within a Bayesian framework, increases the robustness of the method compared to a Hotelling T2‐test previously suggested. This is shown on simulated data and on muscular dystrophy gene expression data.

In this paper, we show how an existing fuzzy rule induction algorithm can incorporate missing values in the training procedure in a very natural way. The underlying algorithm generates rules which restrict the feature space only along a few, important attributes. This property can be used to limit the algorithm's three major steps to the reduced feature space for each training instance, which allows the features for which no values are known to be ignored. Hence no replacement is necessary and the algorithm simply uses all available knowledge from each training instance. We demonstrate on data sets from the UCI repository that this method works well, generates rule sets that have comparable classification accuracy, and are, at times, even smaller than the rule sets generated by the original algorithm

Many fuzzy rule induction algorithms have been proposed in the past. Most of them tend to generate too many rides during the learning process. This is due to data sets obtained from real world systems containing distorted elements or noisy data. Most approaches try to completely ignore outliers, which can be potentially harmful since the example may describe a rare but still extremely interesting phenomena in the data. In order to avoid this conflict, we propose to build a hierarchy of fuzzy rule systems. The goal of this model-hierarchy are interpretable models with only few relevant rules on each level of the hierarchy. The resulting fuzzy model hierarchy forms a structure in which the top model covers all data explicitly and generates a significant smaller number of rules than the original fuzzy rule learner. The models on the bottom, on the other hand, consist of only a few rules in each level and explain pans with only weak relevance in the data. We demonstrate the proposed method's usefulness on several classification benchmark data sets. The results demonstrate how the rule hierarchy allows to build much smaller fuzzy rule systems and how the model-especially at higher levels of the hierarchy-remains interpretable.

We describe an interactive method to generate a set of fuzzy clusters for classes of interest of a given, labeled data set. The presented method is therefore best suited for applications where the focus of analysis lies on a model for the minority class or for small to medium-sized data sets. The clustering algorithm creates one-dimensional models of the neighborhood for a set of patterns by constructing cluster candidates for each pattern of interest and then chooses the best subset of clusters that form a global model of the data. The accompanying visualization of these neighborhoods allows the user to interact with the clustering process by selecting, discarding, or fine-tuning potential cluster candidates. Clusters can be crisp or fuzzy and the latter leads to a substantial improvement of the classification accuracy. We demonstrate the performance of the underlying algorithm on several data sets from the StatLog project and show its usefulness for visual cluster exploration on the Iris data and a large molecular dataset from the National Cancer Institute.

Most learning algorithms operate in a clearly defined feature space and assume that all relevant structure can he found in this one, single space. For many local learning methods, especially the ones working on distance metrics (e.g. clustering algorithms), this poses a serious limitation. We disucss an algorithm that directly finds a set of cluster centers based on an analysis of the distribution of patterns in the local neighborhood of each potential cluster center through the use of so-called Neighborgrams. This type of cluster construction makes it feasable to find clusters in several feature spaces in parallel, effectively finding the optimal feature space for each cluster independently. We demonstrate how the algorithm works on an artificial data set and show its usefulness using a well-known benchmark data set.

In this paper we present a variant of fuzzy c-means that allows to find similar shapes in time series data in a scale-invariant fashion. We use data from protein mass spectrography to show how this approach finds areas of interest without a need for ad-hoc normalizations.

Different learning algorithms based on learning from examples are described based on a set of graph rewrite rules. Starting from either a very general or a very special rule set which is modeled as graph, two to three basic rewrite rules are applied until a rule graph explaining all examples is reached. The rewrite rules can also be used to model the corresponding hypothesis space as they describe partial relations between different rule set graphs. The possible paths, algorithms can take through the hypothesis space can be described as application sequences. This schema is applied to general learning algorithms as well as to fuzzy rule learning algorithms.

Outliers or distorted attributes very often severely interfere with data analysis algorithms that try to extract few meaningful rules. Most methods to deal with outliers try to completely ignore them. This can be potentially harmful since the very outlier that was ignored might have described a rare but still extremely interesting phenomena. We describe an approach that tries to build an interpretable model while still maintaining all the information in the data. This is achieved through a two stage process. A first phase builds an outlier model for data points of low relevance, followed by a second stage which uses this model as filter and generates a simpler model, describing only examples with higher relevance, thus representing a more general concept. The outlier model on the other hand may point out potential areas of interest to the user. Preliminary experiments using an existing algorithm to construct fuzzy rule sets from data indicate that the two models in fact have lower complexity and sometimes even offer superior performance.

Function approximation based on example data has gained considerable interest in the past. The automatic extraction of a fuzzy rule base has proven to be a powerful tool to build approximators that allow an interpretation of the underlying model. In contrast to most known systems which find a set of rules based on a global grid that covers the whole input space, a different approach is presented in this paper. A constructive algorithm finds a set of local individual rules forming a fuzzy graph. The proposed algorithm builds the fuzzy graph from scratch, without the need to control additional parameters and shows promising performance and robustness against noise on an artificial dataset.

Many algorithms to train radial basis function (RBF) networks have already been proposed. Most of them, however, concentrate on building function approximators and only few specialized algorithms are known that concentrate on RBFs for classification. They are based on heuristics that focus on finding areas where relatively few (or no) conflicts occur, but do not try to approximate the underlying probability distribution function (PDF) of the data. In this paper an extension for an already existing constructive algorithm for RBF networks is introduced. The new method uses the dynamic decay adjustment (DDA) algorithm to find conflict free areas and builds more appropriate PDFs inside each such zone. On a dataset which was generated using Gaussian distributions it is demonstrated that this method builds almost optimal classifiers that compare very well with the theoretical Bayes classifier. It is shown, however, that the generalization capability of such networks does not compare favourable to the DDA itself.

Function approximation using example data has gained considerable interest in the past. The automatic extraction of a fuzzy rule base has proven to be a powerful tool to build approximators that allow an interpretation of the underlying model. In contrast to most known systems, which find a rule set based on a global grid that covers the whole input space, a different approach is presented in this paper. A constructive algorithm finds a locally independent rule set that forms a fuzzy graph. The proposed algorithm builds the fuzzy graph from scratch, without the need to control additional parameters. First results show promising performance and robustness against noise on an artificial dataset.

Graph transformations offer a unifying framework to formalize neural networks together with their corresponding training algorithms. It is straightforward to describe also topology changing training algorithms with the help of these transformations. One of the benefits using this formal framework is the support for proving properties of the training algorithms. A training algorithm for probabilistic neural networks is used as an example to prove its termination and correctness on the basis of the corresponding graph rewriting rules.

The paper investigates techniques for comparing two fuzzy graphs. Fuzzy graphs are attracting attention because they not only allow easy interpretation but in addition finding regions of interest or tolerating missing attributes can be done computationally in a very efficient manner. This is of great interest in numerous applications such as intelligent data analysis, meta-modeling and others. Two ways of comparing fuzzy graphs are presented.

The ability to visualize data often leads to new insights. Data that is more than three dimensional must be visualized as a series of projections or transformed into some other representation which usually causes a loss of detail. Parallel coordinates allow one to visualize data in two dimensions without a loss of information. In this paper, we discuss the use of parallel coordinates to visualize fuzzy data. Fuzzy data may consist of fuzzy rules, which can be viewed as cutting a swath through an n-dimensional space. Fuzzy clusters may also be considered as fuzzy data in a similar way. Examples are given from three domains. The examples show that parallel coordinates can be used to find extraneous fuzzy rules, separate fuzzy clusters as well as validate previous findings about data sets.

Many fuzzy rule induction algorithms have been proposed during the past decade or so. Most of these algorithms tend to scale badly with large dimensions of the feature space, because the underlying heuristics tend to constrain suboptimal features. Often, noisy training instances also influence the size of the resulting rule set. In this paper, an algorithm is discussed that extracts a set of so-called mixed fuzzy rules. These rules can be extracted from feature spaces with diverse types of attributes and handle the corresponding different types of constraints in parallel. The underlying heuristic minimizes the loss of coverage for each rule when a conflict occurs. We present the original algorithm, which avoids conflicts for each pattern individually, and demonstrate how a subsampling strategy improves the resulting rule set, both with respect to performance and the interpretability of the resulting rules.

It is often desirable to summarize a set of time series through typical shapes in order to analyze them. The algorithm presented here compares pieces of different time series in order to find similar shapes. The use of a fuzzy clustering technique based on fuzzy c-means allows us to consider such subsets as belonging to typical shapes with a degree of membership. Additionally, this matching is invariant with respect to a scaling of the time series. The algorithm is demonstrated on a widely known set of data taken from the ECG rhythm analysis experiments performed at MIT laboratories.

The Goodman-Nguyen relation generalises the implication (inclusion) relation to conditional events. As such, it induces inequality constraints relevant in extension problems with precise probabilities. We extend this framework to imprecise probability judgements, highlighting the role of this relation in determining the natural extension of lower/upper probabilities defined on certain sets of conditional events. Further, a generalisation of the Goodman–Nguyen relation to conditional random numbers is proposed.

International audience; This paper proposes a new integrated sequential data clustering framework based on an iterative process which alternates between the EM process and a modified b-coloring clustering algorithm. It exhibits two important features: Firstly, the proposed framework allows to give an assignment of clusters to the sequences where the b-coloring properties are maintained as long as the clustering process runs. Secondly, it gives each cluster a twofold representation by a generative model (Markov chains) as well as dominant members which ensure the global stability of the returned partition. The proposed framework is evaluated against benchmark datasets in UCI repository and its effectiveness is confirmed.