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

100%
Górecki T., Łuczak M.
International Journal of Applied Mathematics and Computer Science
|
2013
|
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.
2
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Application of multivariate statistical methods in the assessment of mountain organic soil transformation in the central Sudetes

88%
Zawieja B., Glina B.
Biometrical Letters
|
2017
|
tom 54
|
nr 1
43-59
EN
In studies of organic soil degradation and transformation, alongside the conventional methods used in soil science, an increase in the importance of advanced statistical methods can be observed. In this study some multivariate statistical methods were applied in an investigation of organic soil transformation in the central Sudetes. Andrews curves, linear and kernel discriminant variable analysis and cluster analysis were used. The similarities among peatland soils and their layers were determined. It can be stated that the application of statistical methods in soil science research related to organic soil transformation is a valuable tool. The use of various statistical methods (such as Andrews curves, linear and kernel discriminant variables and cluster analysis) can with high probability confirm earlier laboratory or field observations. This is particularly justified in the case of organic soils derived from varied geobotanical peat materials, different types of peatlands and water supply types, which impact the primary properties of the soil.
3
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Analysis of correlation based dimension reduction methods

88%
Shin Y., Park C.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 3
549-558
EN
Dimension reduction is an important topic in data mining and machine learning. Especially dimension reduction combined with feature fusion is an effective preprocessing step when the data are described by multiple feature sets. Canonical Correlation Analysis (CCA) and Discriminative Canonical Correlation Analysis (DCCA) are feature fusion methods based on correlation. However, they are different in that DCCA is a supervised method utilizing class label information, while CCA is an unsupervised method. It has been shown that the classification performance of DCCA is superior to that of CCA due to the discriminative power using class label information. On the other hand, Linear Discriminant Analysis (LDA) is a supervised dimension reduction method and it is known as a special case of CCA. In this paper, we analyze the relationship between DCCA and LDA, showing that the projective directions by DCCA are equal to the ones obtained from LDA with respect to an orthogonal transformation. Using the relation with LDA, we propose a new method that can enhance the performance of DCCA. The experimental results show that the proposed method exhibits better classification performance than the original DCCA.
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