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Conference Papers Year : 2020

Topological Principal Component Analysis

Abstract

Topological Principal Component Analysis (TPCA) is a multidimensional descriptive method witch studies a homogeneous set of continuous variables defined on the same set of individuals. Its a topological method of data analysis that consists of comparing and classifying proximity measures from among some of the most widely used measures for continuous data. Its proposes an adjacency matrix associated to a proximity measure according to the data under consideration, then analyzes and visualizes, with graphic representations, the relationship structure of the variables relating to, the known problem of Principal Component Analysis (PCA). Based on the notion of neighborhood graphs, some of these proximity measures are more-or-less equivalent. A topological equivalence index between two measures is defined and statistically tested according to the topological correlation between the variables. The principle of the proposed TPCA is illustrated using a real data set
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Dates and versions

hal-04636911 , version 1 (05-07-2024)

Identifiers

  • HAL Id : hal-04636911 , version 1

Cite

Rafik Abdesselam. Topological Principal Component Analysis. 6th Stochastic Modeling Techniques and Data Analysis International Conference, SMTDA-2020, 2-5 June 2020, Barcelona, Spain., SMTDA 2020, Jun 2020, Barcelona (SPAIN), Spain. ⟨hal-04636911⟩
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