Many real-world similarity measures are indefinite, violating the assumptions of kernel-based clustering methods.We propose a principled framework based on the polar decomposition of the similarity matrix, yielding a positive semi-definite component that preserves relational structure while enabling consistent out-of-sample extensions also for dissimilarities.The resulting polarized kernels support stable and interpretable clustering across synthetic and real datasets, demonstrating that polar decomposition provides a theoretically sound and practically effective bridge between indefinite similarity learning and kernel-based methods.

Federated learning enables privacy-preserving machine learning across distributed data sources, but real-world deployments face challenges that extend beyond standard protocols. This tutorial provides a structured overview of the field, addressing issues such as non-stationary data, client heterogeneity, resource constraints, and security threats. Beyond existing surveys, it incorporates hands-on insights and deployment experiences, including concrete war stories illustrating how federated learning methods perform under real-world conditions. The tutorial also outlines emerging directions, including federated graph learning, game-theoretic approaches, and sustainable AI concepts. It aims to provide both a conceptual framework and practical guidance for researchers and practitioners advancing federated learning in dynamic and evolving environments.

We present an extended formulation of our base framework FedT4T-Evo ; a Federated Learning approach that systematically evaluates utility-driven client strategies under resource limitations. To address challenges in distributed learning systems, including resource constraints and non- cooperative behaviors, we model client interactions through the Iterated Prisoner’s Dilemma. Our framework enables clients to adapt decision rules based on prior interactions and resource availability, optimizing both individual utility and contributions to the global optimization target. To further extend the natural perspective, we present a novel evolutionary selection algorithm that simulates ecological dynamics over populations of client strategies, providing a instinctive mechanism for the emergence and persistence of cooperation. Applied to benchmark tasks, our experimental results showed that the framework offers an effective approach for gaining insights into Federated Learning systems through the lens of cooperation theory. • A cooperation-theoretic FL framework is proposed to natively study and foster collaborative client behaviors. • Resource-aware mechanisms are introduced to adapt to heterogeneity and constraints in real-world FL environments. • Evolutionary dynamics are integrated to simulate ecological patterns of cooperation across FL clients.

In modern data analysis, there is an increasing trend towards the integration of information across diverse input formats and perspectives.If the available data is not given in large quantities deep learning is in general impractical.The recently introduced Adaptive Subspace Kernel Fusion (ASKF) technique provides an efficient solution for binary classification, facilitating the effective integration of diverse views throughout the learning process.In this paper, we extend ASKF by employing a vector-labeled multi-class model, eliminating the need for multiple individual models typically required in conventional one-vs-rest or one-vs-one approaches.We also evaluated the effect of using GPU-based numerical solvers, optimizing our problem formulation and the generated code for better efficiency.The approach is evaluated on various kernel functions, highlighting our methods ability of robustly dealing with multi-view data.

We present a novel Federated Learning framework, FedT4T, that systematically evaluates utility-driven client strategies under resource constraints.Recognizing the significant challenges in practical distributed learning environments, such as limited resources and non-cooperative behaviors, we model client interactions using the Iterated Prisoner's Dilemma.Our framework enables clients to adapt their decision rules based on prior interactions and available resources, optimizing both individual utility and collective contribution to solve a global learning task.We apply FedT4T to a Federated Learning benchmark classification task and explore the dynamics of cooperation between clients driven by common strategies from cooperation theory under the impact of varying resource availability.The code is publicly available at https://github.com/cairo-thws/FedT4T.

We introduce an enhanced formulation of FedT4T-Pro, a Federated Learning framework designed to systematically assess utility-driven client strategies within resource-constrained environments. To address key challenges in practical distributed learning systems, such as resource limitations and non-cooperative behaviors, we model client interactions using the Iterated Prisoner’s Dilemma. Our framework empowers clients to refine their decision rules based on past interactions and available resources, optimizing both individual utility and overall contributions to a global learning objective. In addition, a novel sampling algorithm for client selection, drawing inspiration from evolutionary biology, is proposed as a natural incentive mechanism to encourage consistent cooperation and resource contributions. We apply FedT4T-Pro to a Federated Learning benchmark classification task and explore the dynamics of cooperation between clients driven by common strategies from Cooperation theory under the impact of varying resource availability. Furthermore, we experimentally show that the proposed sampling algorithm fosters collaborative behavior in FL training.

This tutorial provides an overview of machine learning methodologies applied in distributed, federated, and non-stationary environments.We focus on recent advancements and novel research contributions of the field.Key topics include data analysis and pattern recognition for non-stationary environments, model compression, federated learning algorithms, and privacy preservation.This tutorial aims to equip researchers and practitioners with insights into current challenges and innovative solutions in this dynamic field. 47

We present a numerically robust, computationally efficient approach for non-I.I.D. data stream sampling in federated client systems, where resources are limited and labeled data for local model adaptation is sparse and expensive.The proposed method identifies relevant stream observations to optimize the underlying client model, given a local labeling budget, and performs instantaneous labeling decisions without relying on any memory buffering strategies.Our experiments show enhanced training batch diversity and an improved numerical robustness of the proposal compared to existing strategies over large-scale data streams, making our approach an effective and convenient solution in FL environments.* MR is supported through the Bavarian HighTech Agenda, specifically by the Würzburg Center for Artificial Intelligence and Robotics (CAIRO) and the ProPere THWS scholarship.57

Federated Learning has gained significant attention as a data protecting paradigm for decentralized, clientside learning in the era of interconnected, sensor-equipped edge devices. However, practical applications of Federated Learning face three major challenges: First, the expensive data labeling process required for target adaptation involves human participation. Second, the data collection process on client devices suffers from covariate shift due to environmental impact on attached sensors, leading to a discrepancy between source and target samples. Third, in resource-limited environments, both continuous or regular model updates are often infeasible due to limited data transmission capabilities or technical constraints on channel availability and energy efficiency. To address these challenges, we propose FedAcross, an efficient and scalable Federated Learning framework designed specifically for real-world client adaptation in industrial environments. It is based on a pre-trained source model that includes a deep backbone, an adaptation module, and a classifier running on a powerful server. By freezing the backbone and the classifier during client adaptation on resourceconstrained devices, we enable the domain adaptive linear layer to solely handle target domain adaptation and minimize the overall computational overhead. Our extensive experimental results validate the effectiveness of FedAcross in achieving competitive adaptation on low-end client devices with limited target samples, effectively addressing the challenge of domain shift. Our framework effectively handles sporadic model updates within resource-limited environments, ensuring practical and seamless deployment.

Kernel functions are a key element in many machine learning methods to capture the similarity between data points. However, a considerable number of these functions do not meet all mathematical requirements to be a valid positive semi-definite kernel, a crucial precondition for kernel-based classifiers such as Support Vector Machines or Kernel Fisher Discriminant classifiers. In this paper, we propose a novel strategy employing a polar decomposition to effectively transform invalid kernel matrices to positive semi-definite matrices, while preserving the topological structure inherent to the data points. Utilizing polar decomposition allows the effective transformation of indefinite kernel matrices from Krein space to positive semi-definite matrices in Hilbert space, thereby providing an efficient out-of-sample extension for new unseen data and enhancing kernel method applicability across diverse classification tasks. We evaluate our approach on a variety of benchmark datasets and demonstrate its superiority over competitive methods.

We introduce an efficient approach for supervised landmark selection in sparse Nyström approximation of kernel matrices.Our method converts structured non-vectorial input data such as graphs or text into a vectorial dissimilarity representation, enabling class-informed landmark identification through prototype-based learning.Experimental results show competitive approximation quality compared to existing strategies and demonstrate the positive effect of integrating class information into the selection process of Nyström landmarks making our approach an efficient and versatile solution for large-scale kernel learning.

Driving at night is a challenging task for humans due to low-light conditions and often low concentration caused by drowsiness. Here, advanced driver assistance systems can come to the rescue and support the driver to increase comfort as well as safety. For that, the vehicle needs a sound and complete understanding of its environment, especially other road participants. The earlier this information is available, the more proactive decisions can be made by the system. To detect on-coming vehicles as soon as possible even before they are actually directly visible, the light reflections caused by their headlamps can be leveraged. Previous work showed that algorithms can perform this task on rural land roads. However, for more complex urban scenarios no approach exists so far. Yet, before starting the dataset and algorithm development for a computer vision system able to solve the task, a sound understanding of the problem is required. In a recent study we already showed that humans can anticipate oncoming vehicles based on their light reflections also in urban scenarios. Still, it remains unclear whether spatial information alone is sufficient to perform the task, or if the temporal context is required. This understanding is essential when designing labeling pipelines for a dataset, as well as algorithm development. Therefore, in this paper we perform a large experiment to evaluate the importance of temporal context for the human ability to anticipate oncoming vehicles at night in urban scenarios. We present participants scenes with different numbers of frames and measure their anticipation performance. We show that providing temporal context significantly increases the human detection accuracy as well as decision confidence. With this we provide additional insights into the task of anticipatory vehicle detection at night which can be taken into consideration when designing a dataset as well as algorithms.

Heterogeneous data is common in many real-world machine learning applications, such as healthcare, market analysis, environmental sciences, and social media analysis. In these domains, data is often represented in different modalities and, most of the time, in non-vectorial formats, like text, images, and video. Traditional machine learning algorithms are often limited in their ability to effectively analyze and learn from such diverse data types. In this paper, we propose two approaches for such heterogeneous data analysis: static and adaptive subspace kernel fusion. The first approach is a kernel-based method extracting the essential parts of the subspace of each input modality and creating one single fused representation of the data. The second approach utilizes an adaptation step by integrating the weighting of spectral properties into the fusion process in order to improve the data’s representation with respect to a given classification task. Our proposed methods are evaluated on several multi-modal, heterogeneous data sets and demonstrate significant performance improvement compared to other methods in the field. Our results highlight the importance of fusing the underlying subspace information of heterogeneous data for achieving superior performance in machine learning tasks.

Data and information are nowadays frequently available in multiple modalities like different sensor signals, textual descriptions, graph structures, and other formats.The maximum information from these heterogeneous representations can be obtained by fusing the various modalities by specific embeddings or proximity measures.Current approaches are widely limited in the fusion model and the applied measures, especially when the given data is non-vectorial.We propose a model to learn the spectral properties of the different inner product representations in a joined optimization problem.The approach is evaluated on various multimodal data and compared to modern multiple-kernel learning and baseline techniques.* MM and MR are supported by the Bavarian HighTech agenda and the Würzburg Center for Artificial Intelligence and Robotics (CAIRO).Additionally, we thank Dr. Benjamin Paaßen for the invaluable discussions about this research topic during a fantastic boating trip.

Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently pro-posed method MEKA [1] effectively employs two common assumptions in Hilbert spaces: the low-rank property of an inner product matrix obtained from a shift-invariant kernel function and a data compactness hypothesis by means of an inherent block-cluster structure. In this work, we extend MEKA to be applicable not only for shift-invariant kernels but also for non-stationary kernels like polynomial kernels and an extreme learning kernel. We also address in detail how to handle non-positive semi-definite kernel functions within MEKA, either caused by the approximation itself or by the intentional use of general kernel functions. We present a Lanczos-based estimation of a spectrum shift to develop a stable positive semi-definite MEKA approximation, also usable in classical convex optimization frameworks. Furthermore, we support our findings with theoretical considerations and a variety of experiments on synthetic and real-world data.

Abstract Concept drift is a change of the underlying data distribution which occurs especially with streaming data. Besides other challenges in the field of streaming data classification, concept drift has to be addressed to obtain reliable predictions. Robust Soft Learning Vector Quantization as well as Generalized Learning Vector Quantization has already shown good performance in traditional settings and is modified in this work to handle streaming data. Further, momentum-based stochastic gradient descent techniques are applied to tackle concept drift passively due to increased learning capabilities. The proposed work is tested against common benchmark algorithms and streaming data in the field and achieved promising results.

In recent years the applications of machine learning models have increased rapidly, due to the large amount of available data and technological progress.While some domains like web analysis can benefit from this with only minor restrictions, other fields like medicine with patient data are stronger regulated.In particular data privacy plays an important role as recently highlighted by the trustworthy AI initiative of the EU or general privacy regulations in legislation.Another major challenge is, that the required training data is often distributed in terms of features or samples and unavailable for classical batch learning approaches.In 2016 Google came up with a framework, called Federated Learning to solve both of these problems.We provide a brief overview on existing Methods and Applications in the field of vertical and horizontal Federated Learning, as well as Federated Transfer Learning.

The interest in time series analysis is rapidly increasing, providing new challenges for machine learning.Over many decades, Dynamic Time Warping (DTW) is referred to as the de facto standard distance measure for time series and the tool of choice when analyzing such data.Nevertheless, DTW has two major drawbacks: (a) it is non-metric and therefore hard to handle by standard machine learning techniques, and (b) it is not well suited for multi-dimensional time series.For this purpose, we propose a multi-perspective embedding of the time series into a complex-valued vector space and the evaluation by a model that is able to handle complex-valued data.The approach is evaluated on various multi-dimensional time series data and with different classifier techniques.

Deep learning struggles to generalize well to an unseen target domain of interest.Current domain adaptation methods simultaneously learn a classifier and an adversarial game for invariant representations but inadequately align local structures, while the underlying process is hard to interpret.We propose a new interpretable adversarial domain architecture, matching local manifold approximations across domains.Evaluated against related networks, the approach is competitive, while the adaptation process can be visually verified.

Domain-specific proximity measures, like divergence measures in signal processing or alignment scores in bioinformatics, often lead to non-metric, indefinite similarities or dissimilarities. However, many classical learning algorithms like kernel machines assume metric properties and struggle with such metric violations. For example, the classical support vector machine is no longer able to converge to an optimum. One possible direction to solve the indefiniteness problem is to transform the non-metric (dis-)similarity data into positive (semi-)definite matrices. For this purpose, many approaches have been proposed that adapt the eigenspectrum of the given data such that positive definiteness is ensured. Unfortunately, most of these approaches modify the eigenspectrum in such a strong manner that valuable information is removed or noise is added to the data. In particular, the shift operation has attracted a lot of interest in the past few years despite its frequently reoccurring disadvantages. In this work, we propose a modified advanced shift correction method that enables the preservation of the eigenspectrum structure of the data by means of a low-rank approximated nullspace correction. We compare our advanced shift to classical eigenvalue corrections like eigenvalue clipping, flipping, squaring, and shifting on several benchmark data. The impact of a low-rank approximation on the data’s eigenspectrum is analyzed.

We present a theoretical analysis of Learning Vector Quantization (LVQ) with adaptive distance measures. Specifically, we consider generalized Euclidean distances which are parameterized in terms of a quadratic matrix of adaptive relevance parameters. Winner-takes-all prescriptions based on the heuristic LVQ1 are in the center of our interest. We derive and study stationarity conditions and show, among other results, that stationary prototypes can be written as linear combinations of the training data apart from irrelevant contributions in the null-space of the relevance matrix. The investigation of the metrics updates reveals that relevance matrices become singular with only one or very few non-zero eigenvalues. Implications of this property are discussed and, furthermore, the effect of preventing singularity by introducing an appropriate penalty term is studied. Theoretical findings are confirmed in terms of illustrative example data sets.

The probabilistic classification vector machine is a very effective and generic probabilistic and sparse classifier. A recently published incremental version improved the runtime complexity to quadratic costs. We derive the Nyström approximation for asymmetric matrices to obtain linear runtime and memory complexity for the incremental probabilistic classification vector machine while keeping similar prediction performance.

Transverse Flux Permanent Magnet Motor (TFPMM) has received extensive attention in the field of electric vehicles. The magnetic circuit of TFPMM is three-dimensional and non-linear, which leads to the high nonlinearity of electromagnetic torque. Although the three-dimensional finite element method (3DFEM) could be used to estimate torque, it is very time-consuming. Instead of it, this study adopts a kind of machine learning method—Gaussian process regression (GPR). For the hyper-parameters optimization of GPR, most previous studies used single-objective algorithms for improving the regression accuracy. However, GPR is an algorithm of probability prediction and it could not guarantee to have the satisfactory confidence interval characteristic simultaneously while the regression precision achieves optimal. Therefore this paper proposes a variable parameters fuzzy dominance genetic algorithm (VPFDGA) which is suitable for the multi-objective optimization, including the optimization of regression precision, confidence interval reliability, confidence interval width and skill score. By combining GPR with VPFDGA, the electromagnetic torque of a building-block transverse flux permanent magnet motor (B-TFPMM) is estimated by VPFDGA-GPR (GPR based on variable parameters fuzzy dominance genetic algorithm). Besides, two other GPRs based multi-objective optimization, three GPRs based on single-objective optimization and a GPR based on weighted sum method that is the classic multi-objective optimization algorithm are all implemented to compare with VPFDGA-GPR. The results of comparison show that VPFDGA-GPR has the better performances including the higher regression precision, more powerful ability of probability prediction, higher stability, less convergence time and so on.

Efficient learning of a data analysis task strongly depends on the data representation. Most methods rely on (symmetric) similarity or dissimilarity representations by means of metric inner products or distances, providing easy access to powerful mathematical formalisms like kernel or branch-and-bound approaches. Similarities and dissimilarities are, however, often naturally obtained by nonmetric proximity measures that cannot easily be handled by classical learning algorithms. Major efforts have been undertaken to provide approaches that can either directly be used for such data or to make standard methods available for these types of data. We provide a comprehensive survey for the field of learning with nonmetric proximities. First, we introduce the formalism used in nonmetric spaces and motivate specific treatments for nonmetric proximity data. Second, we provide a systematization of the various approaches. For each category of approaches, we provide a comparative discussion of the individual algorithms and address complexity issues and generalization properties. In a summarizing section, we provide a larger experimental study for the majority of the algorithms on standard data sets. We also address the problem of large-scale proximity learning, which is often overlooked in this context and of major importance to make the method relevant in practice. The algorithms we discuss are in general applicable for proximity-based clustering, one-class classification, classification, regression, and embedding approaches. In the experimental part, we focus on classification tasks.

We suggest and investigate the use of Generalized Matrix Relevance Learning (GMLVQ) in the context of discriminative visualization. This prototype-based, supervised learning scheme parameterizes an adaptive distance measure in terms of a matrix of relevance factors. By means of a few benchmark problems, we demonstrate that the training process yields low rank matrices which can be used efficiently for the discriminative visualization of labeled data. Comparison with well known standard methods illustrate the flexibility and discriminative power of the novel approach. The mathematical analysis of GMLVQ shows that the corresponding stationarity condition can be formulated as an eigenvalue problem with one or several strongly dominating eigenvectors. We also study the inclusion of a penalty term which enforces non-singularity of the relevance matrix and can be used to control the role of higher order eigenvalues, efficiently.

Digital data characterizing physiological processes over time are becoming increasingly important such as spectrometric data or gene expression profiles. Typical characteristics of such data are high dimensionality due to a fine grained measurement, but usually only few time points of the series. Due to the short length, classical time series models cannot be used. At the same time, due to the high dimensionality, data cannot be treated by means of time windows using simple vectorial techniques. Here, we consider the generative topographic mapping through time (GTM-TT) as a highly regularized model for time series inspection in the unsupervised setting, based on hidden Markov models enhanced with topographic mapping facilities. We extend the model such that supervised classification can be built on top of GTM-TT, resulting in supervised GTM-TT, and we extend the technique by supervised relevance learning. The latter adapts the metric according to given auxiliary information resulting in an interpretable form which can deal with high dimensional inputs. We demonstrate the technique in simulated data as well as an example from the biomedical domain, reaching state of the art classification accuracy in both cases.

Prototype based learning offers an intuitive interface to inspect large quantities of electronic data in supervised or unsupervised settings. Recently, many techniques have been extended to data described by general dissimilarities rather than Euclidean vectors, so-called relational data settings. Unlike the Euclidean counterparts, the techniques have quadratic time complexity due to the underlying quadratic dissimilarity matrix. Thus, they are infeasible already for medium sized data sets. The contribution of this article is twofold: On the one hand we propose a novel supervised prototype based classification technique for dissimilarity data based on popular learning vector quantization (LVQ), on the other hand we transfer a linear time approximation technique, the Nyström approximation, to this algorithm and an unsupervised counterpart, the relational generative topographic mapping (GTM). This way, linear time and space methods result. We evaluate the techniques on three examples from the biomedical domain.

The increasing size and complexity of modern data sets turns modern data mining techniques to indispensable tools when inspecting biomedical data sets. Thereby, dedicated data formats and detailed information often cause the need for problem specific similarities or dissimilarities instead of the standard Euclidean norm. Therefore, a number of clustering techniques which rely on similarities or dissimilarities only have recently been proposed. In this contribution, we review some of the most popular dissimilarity based clustering techniques and we discuss possibilities how to get around the usually squared complexity of the models due to their dependency on the full dissimilarity matrix. We evaluate the techniques on two benchmarks from the biomedical domain.

Clustering approaches are very important methods to analyze data sets in an initial unsupervised setting. Traditionally many clustering approaches assume data points to be independent. Here we present a method to make use of local dependencies to improve clustering under guaranteed distortions. Such local dependencies are very common for data generated by imaging technologies with an underlying topographic support of the measured data. We provide experimental results on artificial and real world data of clustering tasks.

MOTIVATION: The analysis of metabolic processes is becoming increasingly important to our understanding of complex biological systems and disease states. Nuclear magnetic resonance spectroscopy (NMR) is a particularly relevant technology in this respect, since the NMR signals provide a quantitative measure of the metabolite concentrations. However, due to the complexity of the spectra typical of biological samples, the demands of clinical and high-throughput analysis will only be fully met by a system capable of reliable, automatic processing of the spectra. An initial step in this direction has been taken by Targeted Profiling (TP), employing a set of known and predicted metabolite signatures fitted against the signal. However, an accurate fitting procedure for (1)H NMR data is complicated by shift uncertainties in the peak systems caused by measurement imperfections. These uncertainties have a large impact on the accuracy of identification and quantification and currently require compensation by very time consuming manual interactions. Here, we present an approach, termed Extended Targeted Profiling (ETP), that estimates shift uncertainties based on a genetic algorithm (GA) combined with a least squares optimization (LSQO). The estimated shifts are used to correct the known metabolite signatures leading to significantly improved identification and quantification. In this way, use of the automated system significantly reduces the effort normally associated with manual processing and paves the way for reliable, high-throughput analysis of complex NMR spectra. RESULTS: The results indicate that using simultaneous shift uncertainty correction and least squares fitting significantly improves the identification and quantification results for (1)H NMR data in comparison to the standard targeted profiling approach and compares favorably with the results obtained by manual expert analysis. Preservation of the functional structure of the NMR spectra makes this approach more realistic than simple binning strategies.

Prototype based classifiers are effective algorithms in modeling classification problems and have been applied in multiple domains. While many supervised learning algorithms have been successfully extended to kernels to improve the discrimination power by means of the kernel concept, prototype based classifiers are typically still used with Euclidean distance measures. Kernelized variants of prototype based classifiers are currently too complex to be applied for larger data sets. Here we propose an extension of Kernelized Generalized Learning Vector Quantization (KGLVQ) employing a sparsity and approximation technique to reduce the learning complexity. We provide generalization error bounds and experimental results on real world data, showing that the extended approach is comparable to SVM on different public data.

We discuss the use of divergences in dissimilarity-based classification. Divergences can be employed whenever vectorial data consists of non-negative, potentially normalized features. This is, for instance, the case in spectral data or histograms. In particular, we introduce and study divergence based learning vector quantization (DLVQ). We derive cost function based DLVQ schemes for the family of γ‐divergences which includes the well-known Kullback–Leibler divergence and the so-called Cauchy–Schwarz divergence as special cases. The corresponding training schemes are applied to two different real world data sets. The first one, a benchmark data set (Wisconsin Breast Cancer) is available in the public domain. In the second problem, color histograms of leaf images are used to detect the presence of cassava mosaic disease in cassava plants. We compare the use of standard Euclidean distances with DLVQ for different parameter settings. We show that DLVQ can yield superior classification accuracies and Receiver Operating Characteristics.

In this paper, we develop a Tanimoto metric variant of the evolving tree for the analysis of mass spectrometric data of animal fur. The evolving tree is an extension of self-organizing maps developed to analyze hierarchical clustering problems. Together with the Tanimoto similarity measure, which is intended to work with taxonomic structured data, the evolving tree is well suited for the identification of animal hair based on mass spectrometry fingerprints. Results show a suitable hierarchical clustering of the test data and also a good retrieval capability with a logarithmic number of comparisons.

Nuclear magnetic resonance spectroscopy is a technique for the analysis of complex biochemical materials. Thereby the identification of known sub-patterns is important. These measurements require an accurate preprocessing and analysis to meet clinical standards. Here we present a method for an appropriate sparse encoding of NMR spectral data combined with a fuzzy classification system allowing the identification of sub-patterns including mixtures thereof. The method is evaluated in contrast to an alternative approach using simulated metabolic spectra.

In the present contribution we propose two recently developed classification algorithms for the analysis of mass-spectrometric data-the supervised neural gas and the fuzzy-labeled self-organizing map. The algorithms are inherently regularizing, which is recommended, for these spectral data because of its high dimensionality and the sparseness for specific problems. The algorithms are both prototype-based such that the principle of characteristic representants is realized. This leads to an easy interpretation of the generated classifcation model. Further, the fuzzy-labeled self-organizing map is able to process uncertainty in data, and classification results can be obtained as fuzzy decisions. Moreover, this fuzzy classification together with the property of topographic mapping offers the possibility of class similarity detection, which can be used for class visualization. We demonstrate the power of both methods for two exemplary examples: the classification of bacteria (listeria types) and neoplastic and non-neoplastic cell populations in breast cancer tissue sections.

Proteomic profiling based on mass spectrometry (ms) is an important tool for studies at the protein and peptide level. Thereby, the identification of relevant masses for a specific kind of disease, discriminating classification models as well as a reliable visualization is complicated. For the analysis of tissue sections the new technique of MALDI-Imaging has been introduced, which results in new data analysis challenges. Here we present a method for the analysis and visualization of MALDI Imaging spectra applied on a clinical cancer data set.

We present a general framework for association learning in self-organizing maps (SOMs), which can be specified for the utilization for supervised fuzzy classification. In this way, we obtain a prototype based fuzzy classification model (FLSOM), which can be easily interpreted and visualized due to the fundamental properties of SOMs. Moreover, the provided extension gives the ability to detect class similarities. We apply this approch to classification and class similarity detection for mass spectrometric data in case of cancer disease and obtain comparable results. We demonstrate that the FLSOM-based class similarity detection leads to clinically expected class similarities. Finally, this approach can be taken a semi-supervised learning approach in a twofold sense: association learning is influenced by two terms an unsupervised and a supervised learning term. Further, if no association is given for a data point, only the unsupervised learning amount is applied.

K-means clustering combines a variety of striking properties because of which it is widely used in applications: training is intuitive and simple, the final classifier represents classes by geometrically meaningful prototypes, and the algorithm is quite powerful compared to more complex alternative clustering algorithms. In this contribution, we focus on extensions which incorporate additional information into the clustering algorithm to achieve a better accuracy: neighborhood cooperation from neural gas, (possibly fuzzy) label information of input data, and general problem-adapted distances instead of the standard Euclidean metric. These extensions can be formulated in a simple general framework by means of a cost function. We demonstrate the ability of these variants on several representative clustering problems from computational biology.

We extend the self-organizing map in the variant as proposed by Heskes to a supervised fuzzy classification method. This leads to a robust classifier where efficient learning with fuzzy labeled or partially contradictory data is possible. Further, the integration of labeling into the location of prototypes in a self-organizing map leads to a visualization of those parts of the data relevant for the classification. The method is incorporated in a clinical proteomics toolkit dedicated for biomarker search which allows the necessary preprocessing and further data analysis with additional visualizations.

We extend soft nearest neighbor classification to fuzzy classification with adaptive class labels. The adaptation follows a gradient descent on a cost function. Further, it is applicable for general distance measures, in particular task specific choices and relevance learning for metric adaptation can be done. The performance of the algorithm is shown on synthetic as well as on real life data taken from proteomic research.

The paper deals with the application of the novel generalized relevance learning vector quantization based classification algorithm in comparison to the unified maximum separability analysis as a special variant of support vector machine algorithms. The algorithms are compared and their performance on real life data, taken from clinical studies, is demonstrated. It is shown that the vector quantization classifier gives competitive results in comparison to the considered support vector machine algorithm and shows the recently theoretical proven equivalence in classification capability of both paradigms.