Waldemar Wołyński

New variants of pairwise classification

Pairwise classification is the technique that deals with multi-class problems by converting them into a series of binary problems, one for each pair of classes. Typically, K-class classification rules tend to be easier to learn for KÂ =Â 2 than for KÂ >Â 2 - only one decision boundary requires attention. This paper presents new methods for obtaining class membership probability estimates for multi-class classification problems by coupling the probability estimates created by binary classifiers. Classifiers used include linear Bayes normal classifier, Parzen density based classifier, naive Bayes classifier, binary decision tree classifier and random neural net classifier. The accuracy of new pairwise classifiers is examined on some real data sets. The classification errors were estimated by stratified version of 10-fold cross-validation technique, i.e. the training examples were partitioned into 10 equal-sized blocks with similar class distributions as in the original set. The validation technique was repeated 10 times for each data set.

A comparison of some tests for determining the number of nonzero canonical correlations

When considering the relationships between two sets of variates, the number of nonzero population canonical correlations may be called the dimensionality. In the literature, several tests for dimensionality in the canonical correlation analysis are known. A comparison of seven sequential test procedures is presented, using results from some simulation study. The tests are compared with regard to the relative frequencies of underestimation, correct estimation, and overestimation of the true dimensionality. Some conclusions from the simulation results are drawn.

Analysis of multivariate repeated measures data using a MANOVA model and principal components

Abstract In this paper we consider a set of T repeated measurements on p characteristics on each of n individuals. The n individuals themselves may be divided and randomly assigned to K groups. These data are analyzed using a mixed effect MANOVA model, assuming that the data on an individual have a covariance matrix which is a Kronecker product of two positive definite matrices. Results are illustrated on a data set obtained from experiments with varieties of winter rye.

Minimal Sample Size in the Group Classification Problem

AbstractBayes classification procedure for a group of independent vectors treated as a whole is considered. When the distributions are not specified, we obtain the bounds of the minimal sample size based on the Chernoff and the Bhattacharyya distances between the populations. The case of the normal distribution is also discussed.

Nonlinear Principal Component Analysis for Geographically Weighted Temporal‑spatial Data

Scholkopf, Smola and Muller (1998) have proposed a nonlinear principal component analysis (NPCA) for fixed vector data. In this paper, we propose an extension of the aforementioned analysis to temporal ‑ spatial data and weighted temporal ‑ spatial data. To illustrate the proposed theory, data describing the condition of state of higher education in 16 Polish voivodships in the years 2002–2016 are used.

Correlation Analysis for Multivariate Functional Data

The relationship between two sets of real variables defined for the same individuals can be evaluated by few different correlation coefficients. For the functional data we have only one important tool: the canonical correlations. It is not immediately straightforward to extend other similar measures to the context of functional data analysis. In this work we show how to use commonly known measures of correlation for two sets of variables: \(\mathop{\mathrm{rV}}\nolimits\) coefficient and distance correlation coefficient for multivariate functional case. Finally, these three different coefficients are compared and their use is demonstrated on two real examples.

Multivariate Functional Regression Analysis with Application to Classification Problems

Multivariate functional data analysis is an effective approach to dealing with multivariate and complex data. These data are treated as realizations of multivariate random processes; the objects are represented by functions. In this paper we discuss different types of regression model: linear and logistic. Various methods of representing functional data are also examined. The approaches discussed are illustrated with an application to two real data sets.

The mineralization effect of wheat straw on soil properties described by MFPC analysis and other methods

Abstract Recycling of crop residues is essential to sustain soil fertility and crop production. Despite the positive effect of straw incorporation, the slow decomposition of that organic substance is a serious issue. The aim of the study was to assess the influence of winter wheat straws with different degrees of stem solidness on the rate of decomposition and soil properties. An incubation experiment lasting 425 days was carried out in controlled conditions. To perform analyses, soil samples were collected after 7, 14, 21, 28, 35, 49, 63, 77, 91, 119, 147, 175, 203, 231, 259, 313, 341, 369, 397 and 425 days of incubation. The addition of two types of winter wheat straw with different degree of stem solidness into the sandy soil differentiated the experimental treatments. The results demonstrate that straw mineralization was a relatively slow process and did not depend on the degree of filling of the stem by pith. Multivariate functional principal component analysis (MFPC) gave proof of significant variation between the control soil and the soil incubated with the straws. The first functional principal component describes 48.53% and the second 18.55%, of the variability of soil properties. Organic carbon, mineral nitrogen and sum of bases impact on the first functional principal component, whereas, magnesium, sum of bases and total nitrogen impact on the second functional principal component.