Computer Science and Information Technology Vol. 14(3), pp. 55 - 75
DOI: 10.13189/csit.2026.140301
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PCA Mathematics for Practitioners and the Use of a Zoning Biplot

Alfredo Piero Mateos-Papis ^*, Christian Sánchez-Sánchez
Department of Information Technology, Universidad Autónoma Metropolitana, Unidad Cuajimalpa, México

ABSTRACT

With respect to a normalized numerical dataset (its variables –attributes- with mean 0 and variance 1), visualized as points in a Euclidean space with Cartesian coordinates (one dimension per attribute), Principal Component Analysis (PCA) is a dimensionality reduction method that simplifies the visualization, which in this work helps to determine the relationships between the attributes. For this reduction, PCA is used to find a new set of perpendicular axes, ordered according to the amount of "information" that each one has in relation to the points, from which the two axes containing the first and second largest amount of "information" are usually selected, which are called PC1 and PC2. The "information" is related to the variance of the projection distances of the points along each axis. The simplified visualization consists of projecting the points onto the PC1-PC2 plane. Some literature suggests that the "information" from PC1 and PC2 should be at least 75% of the total to draw reliable results. This work has two objectives. First, it aims to present the mathematics of PCA in a detailed, comprehensive, and geometrically oriented manner, suitable for an initial learning step. The contribution lies in offering a presentation less mathematically compact compared to some existing literature, less extensive compared to other existing literature, and more geometrically oriented, facilitating the assimilation of PCA in a first learning step. The second objective is to propose a criterion for drawing results when the "information" from PC1 and PC2 is less than 75%, using a Zoning Biplot, where the shapes of the projected points depend on the value of the main attribute. If zoning exists based on the shapes of the point projections, conclusions can be drawn. This criterion constitutes another contribution of this work, with the limitation that it has not yet been fully validated. The practical implication of this work is that PCA can be applied to a larger amount of available data. This work provides an example with housing data using specialized Python PCA tools.

KEYWORDS
Principal Component Analysis (PCA), Biplot, Public Housing Data Analysis

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Alfredo Piero Mateos-Papis , Christian Sánchez-Sánchez , "PCA Mathematics for Practitioners and the Use of a Zoning Biplot," Computer Science and Information Technology, Vol. 14, No. 3, pp. 55 - 75, 2026. DOI: 10.13189/csit.2026.140301.

(b). APA Format:
Alfredo Piero Mateos-Papis , Christian Sánchez-Sánchez (2026). PCA Mathematics for Practitioners and the Use of a Zoning Biplot. Computer Science and Information Technology, 14(3), 55 - 75. DOI: 10.13189/csit.2026.140301.