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New Interpretation of Principal Components Analysis

Gniazdowski Z.

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

2017

nr 16

43--65

A new look on the principal component analysis has been presented. Firstly,ageometric interpretation of determination coefﬁcient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of easy-tounderstand basic geometric structures was shown. As a result of the analysis of these structures it was proposed to enrich the classical PCA. In particular, it was proposed a new criterion for the selection of important principal components and a new algorithm for clustering primary variables by their level of similarity to the principal components. Virtual and real data spaces, as well as tensor operations on data, have also been identiﬁed.The anisotropy of the data was identiﬁed too.

Reach of river channel filling forecasting by means of autoregression integrated moving a verage method (ARIMA-models)

Baranenko F.F.

Ecological Chemistry and Engineering. A

2008

Vol. 15, nr 12

1419-1423

This review considers the application of statistical methods and ARIMA (autoregression integrated moving average) models to rainfall-runoff modeling and flood forecasting have been discussed. This is a relatively emerging field of research, characterized by a wide variety of techniques, an amenity of hulk source data, a possibility of intermodel comparisons, determina-tion its adequacy to observable data and also inconsistent reporting of model skin. The paper outlines the basic principles of ARIMA modeling and algorithms used. Literature survey underlines the need for clear guidance in current ARIMA modeling practice, as well as the comparison of ARIMA models with already existing models of rainfall-runoff. Accordingly, a template is proposed in order to assist the construction of future ARIMA rainfall-runoff models.

Przedstawiono zastosowanie metod statystycznych, w tym zwłaszcza modelu ARIMA (autoregresji całkowanej zmiennej średniej), do prognozowania przebiegu sytuacji powodziowych. Omówiono zastosowanie modelu ARIMA do opisu powsta-wania wód powodziowych spowodowanych ulewnymi deszczami oraz spływu tych wód.