A Note on the Dimension of the Projection Space in a Latent Factor Regression Model with Application to Business Cycle Classification

In this paper it is shown that the number of latent factors in a multiple multivariate regression model need not be larger than the number of the response variables in order to achieve an optimal prediction. The practical importance of this lemma is outlined and an application of such a projection on latent factors in a classification example is given. --Latent Factor Models,Projection Matrix,Regression,Classification

Uncertainty of the optimum influence factor levels in multicriteria optimization using the concept of desirability

The Desirability Index (DI) is a widely used method for multicriteria optimization in industrial quality control, by which optimal levels of the process influencing factors are determined in order to archieve maximum process quality. In practice however situations may occur in which slight changes of these factor levels lead to lower production costs or to facilitation of the production process and therefore would be preferred. In this paper an innovative approach for measuring the effect of these changes on the DI based on its distribution is introduced. --

Improving Feature Extraction by Replacing the Fisher Criterion by an Upper Error Bound

A lot of alternatives and constraints have been proposed in order to improve the Fisher criterion. But most of them are not linked to the error rate, the primary interest in many applications of classification. By introducing an upper bound for the error rate a criterion is developed which can improve the classification performance. --Fisher criterion,Linear discriminant analysis,Feature extraction

D-optimal plans for variable selection in data bases

This paper is based on an article of Pumplün et al. (2005a) that investigates the use of Design of Experiments in data bases in order to select variables that are relevant for classification in situations where a sufficient number of measurements of the explanatory variables is available, but measuring the class label is hard, e. g. expensive or time-consuming. Pumplün et al. searched for D-optimal designs in existing data sets by means of a genetic algorithm and assessed variable importance based on the found plans. If the design matrix is standardized these D-optimal plans are almost orthogonal and the explanatory variables are nearly uncorrelated. Thus Pumplün et al. expected that their importance for discrimination can be judged independently of each other. In a simulation study Pumplün et al. applied this approach in combination with five classification methods to eight data sets and the obtained error rates were compared with those resulting from variable selection on the basis of the complete data sets. Based on the D-optimal plans in some cases considerably lower error rates were achieved. Although Pumplün et al. (2005a) obtained some promising results, it was not clear for different reasons if D-optimality actually is beneficial for variable selection. For example, D-efficiency and orthogonality of the resulting plans were not investigated and a comparison with variable selection based on random samples of observations of the same size as the D-optimal plans was missing. In this paper we extend the simulation study of Pumplün et al. (2005a) in order to verify their results and as basis for further research in this field. Moreover, in Pumplün et al. D-optimal plans are only used for data preprocessing, that is variable selection. The classification models are estimated on the whole data set in order to assess the effects of D-optimality on variable selection separately. Since the number of measurements of the class label in fact is limited one would normally employ the same observations that were used for variable selection for learning, too. For this reason in our simulation study the appropriateness of D-optimal plans for training classification methods is additionally investigated. It turned out that in general in terms of the error rate there is no difference between variable selection on the basis of D-optimal plans and variable selection on random samples. However, for training of linear classification methods D-optimal plans seem to be beneficial. --

Kernelized design of experiments

This paper describes an approach for selecting instances in regression problems in the cases where observations x are readily available, but obtaining labels y is hard. Given a database of observations, an algorithm inspired by statistical design of experiments and kernel methods is presented that selects a set of k instances to be chosen in order to maximize the prediction performance of a support vector machine. It is shown that the algorithm significantly outperforms related approaches on a number of real-world datasets. --

Parameter Optimization in Automatic Transcription of Music

Based on former work on automatic transcription of musical time series into sheet music (Ligges et al. (2002), Weihs and Ligges (2003, 2005)) in this paper parameters of the transcription algorithm are optimized for various real singers. Moreover, the parameters of various artificial singer models derived from the models of Rossignol et al. (1999) and Davy and Godsill (2002) are estimated. In both cases, optimization is carried out by the Nelder-Mead (1965) search algorithm. In the modelling case a hierarchical Bayes extension is estimated by WinBUGS (Spiegelhalter et al. (2004)) as well. In all cases, optimal parameters are compared to heuristic estimates from our former standard method. --

From Local to Global Analysis of Music Time Series

Local and more and more global musical structure is analyzed from audio time series by time-series-event analysis with the aim of automatic sheet music production and comparison of singers. Note events are determined and classified based on local spectra, and rules of bar events are identified based on accentuation events related to local energy. In order to compare the performances of different singers global summary measures are defined characterizing the overall performance. --

Pareto-Optimality and Desirability Indices

Pareto-Optimality and the Desirability Index are methods for multicriteria optimization in quality management. In this paper the pareto-optimality of the optimal influence factor settings of a process resulting from maximizing the DI is analyzed and is shown to be valid in most cases. --

Prediction Optimal Classification of Business Phases

Linear Discriminant Analysis (LDA) performs well for classifica- tion of business phases – even though the premises of an LDA are not met. As the variables are highly correlated there are numerical as well as interpretational shortcomings. By transforming the classification problem to a regression setting both problems can be addressed by a computer-intensive prediction oriented method which also improves the classification performance. --

Desirability to characterize process capability

Over the past few years continuously new process capability indices have been developed, most of them with the aim to add some feature missed in former process capability indices. Thus, for nearly any thinkable situation now a special index exists which makes choosing a certain index as difficult as interpreting and comparing index values correctly. In this paper we propose the use of the expected value of a certain type of function, the so-called desirability function, to assess the capability of a process. The resulting index may be used analogously to the classical indices related to Cp, but can be adapted to nearly any process and any specification. It even allows a comparison between different processes regardless of their distribution and may be extended straightforwardly to multivariate scenarios. Furthermore, its properties compare favorably to the properties of the ?classical? indices. --