New Interpretation of Principal Components Analysis

• Autorzy: Gniazdowski Z.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

determination coefficient; geometric interpretation of PCA; selection of principal components; clustering of variables; tensor data mining; anisotropy of data

PL

współczynnik determinacji; interpretacja geometryczna; PCA; wybór głównych składników; klastrowanie zmiennych; dane tensorowe; anizotropia danych

• Wydawca: Warszawska Wyższa Szkoła Informatyki
• Czasopismo: Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
• Rocznik: 2017
• Tom: nr 16
• Strony: 43--65
• Opis fizyczny: Bibliogr. 11 poz., rys., tab.

Twórcy

autor

Gniazdowski Z.

• Warsaw School of Computer Science

Bibliografia

• [1] David J. Hand, Heikki Mannila, and Padhraic Smyth. Principles of data mining. MIT press, 2001.
• [2] Daniel T. Larose. Data mining methods and models. John Wiley & Sons, 2006.
• [3] Taha Sochi. Introduction to tensor calculus. arXiv preprint arXiv:1603.01660, 2016.
• [4] John F. Nye. Physical properties of crystals. Clarendon Press, Oxford, 1957.
• [5] Zenon Gniazdowski. Geometric interpretation of a correlation. Zeszyty Naukowe WWSI, 7(9): 27-35, 2013.
• [6] Richard Taylor. Interpretation of the correlation coefficient: a basic review. Journal of diagnostic medical sonography, 6(1):35-39, 1990.
• [7] Athanasios Papoulis. Probability, random variables and stochastic processes. McGraw-Hill, 1965.
• [8] Ronald A. Fisher. The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2):179-188, 1936.
• [9] Michel Marie Deza and Elena Deza. Encyclopedia of Distances. Springer, 2009.
• [10] Daniel T Larose. Discovering knowledge in data: an introduction to data mining. John Wiley & Sons, 2005.
• [11] Ulrike Von Luxburg. A tutorial on spectral clustering. Statistics and computing, 17(4): 395-416, 2007.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).