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Stacked regression with restrictions

100%
Górecki T.
Discussiones Mathematicae Probability and Statistics
|
2005
|
tom 25
|
nr 1
103-113
EN
When we apply stacked regression to classification we need only discriminant indices which can be negative. In many situations, we want these indices to be positive, e.g., if we want to use them to count posterior probabilities, when we want to use stacked regression to combining classification. In such situation, we have to use leastsquares regression under the constraint βₖ ≥ 0, k = 1,2,...,K. In their earlier work [5], LeBlanc and Tibshirani used an algorithm given in [4]. However, in this paper we use a more general algorithm given in [6].
2
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Effect of choice of dissimilarity measure on classification efficiency with nearest neighbor method

100%
Górecki T.
Discussiones Mathematicae Probability and Statistics
|
2005
|
tom 25
|
nr 2
217-239
EN
In this paper we will precisely analyze the nearest neighbor method for different dissimilarity measures, classical and weighed, for which methods of distinguishing were worked out. We will propose looking for weights in the space of discriminant coordinates. Experimental results based on a number of real data sets are presented and analyzed to illustrate the benefits of the proposed methods. As classical dissimilarity measures we will use the Euclidean metric, Manhattan and post office metric. We gave the first two metrics weights and now these measures are not metrics because the triangle inequality does not hold. Howeover, it does not make them useless for the nearest neighbor classification method. Additionally, we will analyze different methods of tie-breaking.
3
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A learning algorithm combining functional discriminant coordinates and functional principal components

64%
Górecki T., Krzyśko M.
Discussiones Mathematicae Probability and Statistics
|
2014
|
tom 34
|
nr 1-2
127-141
EN
A new type of discriminant space for functional data is presented, combining the advantages of a functional discriminant coordinate space and a functional principal component space. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on 35 functional data sets (time series). Experiments show that constructed combined space provides a higher quality of classification of LDA method compared with component spaces.
4
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Some methods of constructing kernels in statistical learning

64%
Górecki T., Łuczak M.
Discussiones Mathematicae Probability and Statistics
|
2010
|
tom 30
|
nr 2
179-201
EN
This paper is a collection of numerous methods and results concerning a design of kernel functions. It gives a short overview of methods of building kernels in metric spaces, especially $R^n$ and $S^n$. However we also present a new theory. Introducing kernels was motivated by searching for non-linear patterns by using linear functions in a feature space created using a non-linear feature map.
5
Content available remote

Linear discriminant analysis with a generalization of the Moore-Penrose pseudoinverse

64%
Górecki T., Łuczak M.
International Journal of Applied Mathematics and Computer Science
|
2013
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tom 23
|
nr 2
463-471
EN
The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this area, and we present a new approach which uses a generalization of the Moore-Penrose pseudoinverse to remove this weakness. Our new approach, in addition to managing the problem of inverting the covariance matrix, significantly improves the quality of classification, also on data sets where we can invert the covariance matrix. Experimental results on various data sets demonstrate that our improvements to LDA are efficient and our approach outperforms LDA.
6
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A variant of gravitational classification

64%
Górecki T., Luczak M.
Biometrical Letters
|
2014
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tom 51
|
nr 1
1-12
EN
In this article there is proposed a new two-parametrical variant of the gravitational classification method. We use the general idea of objects' behavior in a gravity field. Classification depends on a test object's motion in a gravity field of training points. To solve this motion problem, we use a simulation method. This classifier is compared to the 1NN method, because our method tends towards it for some parameter values. Experimental results on different data sets demonstrate an improvement in efficiency and that this approach outperforms the 1NN method by providing a significant reduction in the mean classification error rate.
7
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Principal component analysis for functional data on grain yield of winter wheat cultivars

51%
Krzyśko M., Derejko A., Górecki T., Gacek E.
Biometrical Letters
|
2013
|
tom 50
|
nr 2
81-94
EN
The aim of this paper is to present a statistical methodology to assess patterns of cultivars' adaptive response to agricultural environments (agroecosystems) on the basis of complete Genotype x Crop Management x Location x Year (GxMxLxY) data obtained from 3-year multi-location twofactor trials conducted within the framework of the Polish post-registration trials (PDOiR), with an illustration of the application and usefulness of this methodology in analyzing winter wheat grain yield. Producing specific varieties for each subregion of a target region, from widely adapted varieties, may exploit positive genotype x location (GL) interactions to increase crop yields. Experiments designed to examine combinations of environment (E), management practices (M) and cultivars (G) also provide evidence of the relative importance of each of these factors for yield improvement. The evidence shows that variation due to E far outweighs the variation of grain yield that can be attributed to M or G, or the interactions between these factors, and between these factors and E (Anderson, 2010). This statistical method involves the use of functional PCA and cluster analysis. A total of 24 cultivars were evaluated over 3 years in 20 environments using randomized incomplete split-block designs with two replications per trial. The methodology proved an efficient tool for the reliable classification of 24 winter wheat cultivars, distinguishing cultivar groups that exhibited homogeneous adaptive response to environments. It enables the identification of cultivars displaying wide or specific adaptation. The remaining cultivars were locally adapted to some testing environments, or some of them were not relatively adapted to the environments because they always yielded substantially below the environmental means. Performing earlier specific selection, or adopting distinct genetic bases for each agro-ecosystem, may further increase the advantage of specific breeding.
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