Claus Weihs

klaR Analyzing German Business Cycles

Decision making often asks for classification. We will present a new R package klaR including functions to build, check, tune, visualize, and compare classification rules. The software is illustrated by means of a case study of prediction of the German economy’s business cycle phases.

Exploratory landscape analysis

Exploratory Landscape Analysis subsumes a number of techniques employed to obtain knowledge about the properties of an unknown optimization problem, especially insofar as these properties are important for the performance of optimization algorithms. Where in a first attempt, one could rely on high-level features designed by experts, we approach the problem from a different angle here, namely by using relatively cheap low-level computer generated features. Interestingly, very few features are needed to separate the BBOB problem groups and also for relating a problem to high-level, expert designed features, paving the way for automatic algorithm selection.

Variable window adaptive Kernel Principal Component Analysis for nonlinear nonstationary process monitoring

On-line control of nonlinear nonstationary processes using multivariate statistical methods has recently prompt a lot of interest due to its industrial practical importance. Indeed basic process control methods do not allow monitoring of such processes. For this purpose this study proposes a variable window real-time monitoring system based on a fast block adaptive Kernel Principal Component Analysis scheme. While previous adaptive KPCA models allow only handling of one observation at a time, in this study we propose a way to fast update or downdate the KPCA model when a block of data is provided and not only one observation. Using a variable window size procedure to determine the model size and adaptive chart parameters, this model is applied to monitor two simulated benchmark processes. A comparison of performances of the adopted control strategy with various Principal Component Analysis (PCA) control models shows that the derived strategy is robust and yields better detection abilities of disturbances.

Resampling methods for meta-model validation with recommendations for evolutionary computation

Meta-modeling has become a crucial tool in solving expensive optimization problems. Much of the work in the past has focused on finding a good regression method to model the fitness function. Examples include classical linear regression, splines, neural networks, Kriging and support vector regression. This paper specifically draws attention to the fact that assessing model accuracy is a crucial aspect in the meta-modeling framework. Resampling strategies such as cross-validation, subsampling, bootstrapping, and nested resampling are prominent methods for model validation and are systematically discussed with respect to possible pitfalls, shortcomings, and specific features. A survey of meta-modeling techniques within evolutionary optimization is provided. In addition, practical examples illustrating some of the pitfalls associated with model selection and performance assessment are presented. Finally, recommendations are given for choosing a model validation technique for a particular setting.

Classification of high and low achievers in a music sight-reading task

The unrehearsed performance of music, called ‘sight-reading’ (SR), is a basic skill for all musicians. It is of particular interest for musical occupations such as the piano accompanist, the conductor, or the correpetiteur. However, up until now, there is no theory of SR which considers all relevant factors such as practice-related variables (e.g. expertise), speed of information processing (e.g. mental speed), or psychomotor speed (e.g. speed of trills). Despite the merits of expertise theory, there is no comprehensive model that can classify subjects into high- and low-performance groups. In contrast to previous studies, this study uses a data mining approach instead of regression analysis and tries to classify subjects into predetermined achievement classes. It is based on an extensive experiment in which the total SR performance of 52 piano students at a German music department was measured by use of an accompanying task. Additionally, subjects completed a set of psychological tests, such as tests of mental speed, reaction time, working memory, inner hearing, etc., which were found in earlier studies to be useful predictors of SR achievement. For the first time, classification methods (cluster analysis, regression trees, classification trees, linear discriminant analysis) were applied to determine combinations of variables for classification. Results of a linear discriminant analysis revealed a two-class solution with four predictors (cross-validated error: 15%) and a three-class solution with five predictors (cross-validated error: 33%).

Classification in music research

Since a few years, classification in music research is a very broad and quickly growing field. Most important for adequate classification is the knowledge of adequate observable or deduced features on the basis of which meaningful groups or classes can be distinguished. Unsupervised classification additionally needs an adequate similarity or distance measure grouping is to be based upon. Evaluation of supervised learning is typically based on the error rates of the classification rules. In this paper we first discuss typical problems and possible influential features derived from signal analysis, mental mechanisms or concepts, and compositional structure. Then, we present typical solutions of such tasks related to music research, namely for organization of music collections, transcription of music signals, cognitive psychology of music, and compositional structure analysis.

Tuning and evolution of support vector kernels

Kernel-based methods like Support Vector Machines (SVM) have been established as powerful techniques in machine learning. The idea of SVM is to perform a mapping from the input space to a higher-dimensional feature space using a kernel function, so that a linear learning algorithm can be employed. However, the burden of choosing the appropriate kernel function is usually left to the user. It can easily be shown that the accuracy of the learned model highly depends on the chosen kernel function and its parameters, especially for complex tasks. In order to obtain a good classification or regression model, an appropriate kernel function in combination with optimized pre- and post-processed data must be used. To circumvent these obstacles, we present two solutions for optimizing kernel functions: (a) automated hyperparameter tuning of kernel functions combined with an optimization of pre- and post-processing options by Sequential Parameter Optimization (SPO) and (b) evolving new kernel functions by Genetic Programming (GP). We review modern techniques for both approaches, comparing their different strengths and weaknesses. We apply tuning to SVM kernels for both regression and classification. Automatic hyperparameter tuning of standard kernels and pre- and post-processing options always yielded to systems with excellent prediction accuracy on the considered problems. Especially SPO-tuned kernels lead to much better results than all other tested tuning approaches. Regarding GP-based kernel evolution, our method rediscovered multiple standard kernels, but no significant improvements over standard kernels were obtained.

A Note on the Behavior of Cpmk With Asymmetric Specification Limits

The properties of Cpmk in the presence of asymmetric specification limits are discussed. It is shown that Cpmk tends to zero as the process variation increases and vice versa. Furthermore, if the process variation is small, Cpmk has its maximum near the target value but the maximum moves towards the specification midpoint as the variation increases. This may be a desirable property because for large variation the percentage of items inside the specification limits is larger if the process mean is equal to the specification midpoint than if it is equal to the target value. Considering Cpmk as a mixture of Cpk and Cpm, Cpmk behaves more like Cpm if the process variation is small, whereas Cpmk behaves more like Cpk if the process variation is large. Attention is drawn to the fact that for small process variations there is a shoulder in the graph of Cpmk when the process mean is equal to the specification midpoint.

Kernel k-means clustering based local support vector domain description fault detection of multimodal processes

The multimodal and nonlinear structure of a system makes process modeling and control quite complex. To monitor processes that have these characteristics, this paper presents a procedure based on kernel techniques for unsupervised learning that are able to separate different nonlinear process modes and to effectively detect faults. These techniques are named Kernel k-means (KK-means) clustering and support vector domain description (SVDD). In order to assess this monitoring strategy two different simulation studies as well as a real case study of an Etch Metal process are performed. Results show that the proposed control chart provides efficient fault detection performance with reduced false alarm rates.

Detection of chatter vibration in a drilling process using multivariate control charts

Time series analysis and multivariate control charts are used to devise a real-time monitoring strategy in a drilling process. The process is used to produce holes with high length-to-diameter ratio, good surface finish and straightness. It is subject to dynamic disturbances that are classified as either chatter vibration or spiralling. A new nonparametric control chart for multivariate processes is proposed. It is used to detect chatter vibration which is dominated by single frequencies. The results showed that the proposed monitoring strategy can detect chatter vibration and that some alarm signals are related to changing physical conditions of the process.