In contrast, the JK-Biplot seeks to best represent rows or individuals, being useful in customer segmentation, student performance analysis,and user behavior analysis. Both methods share the common goal of providing a clear and comprehensible visual representation of the data, but they differ in their main focus [1]. While the GH-Biplot is applied in contexts where the precise representation of variables is critical, the JK-Biplot is better suited for analyzing and comparing individuals or observations. Despite these differences, both methods are widely applicable in multivariate data analysis, providing valuable tools for the visualization and understanding of complex data. For matrices \(\mathbf{Y}\) of observations of \(n\) units in \(m\) variables, it is essential to subtract the mean of each variable to center the data before proceeding with the analysis. [PERSON] uses the estimated _variance-covariance_ matrix \(\mathbf{S}\) to capture the variability and the linear relationships between the variables. This matrix is defined as  
Figure 1:0  
where \(\mathbf{Y}\) is the centered data matrix, \(\mathbf{Y}^{\mathrm{T}}\) is the transpose of \(\mathbf{Y}\), and \(n\) is the number of observations. The matrix \(\mathbf{S}\) provides a measure of how the variables co-vary, which is essential for multivariate analysis. The standardized distances between units \(i\) and \(e\) are calculated to understand the relative differences between observations in multivariate space. This _distance_ is defined as  
Figure 1:1  
where \(y_{i}\) and \(y_{e}\) are row vectors corresponding to units \(i\) and \(e\), and \(\mathbf{S}^{-1}\) is the inverse of the variance-covariance matrix. This formula allows measuring the similarity between observations, adjusting for the variance and correlations among variables. In a Biplot, standardized distances can be approximated to simplify the graphical representation. [PERSON] proposes the following approximation:  
Figure 1:2  
where \(g_{i}\) and \(g_{e}\) are vectors that represent the observations in the reduced space of the Biplot. This approximation facilitates visual interpretation, allowing for a direct comparison of the distances between points in the Biplot. The Biplot also allows for the visual representation of the variances and covariances of the variables. These equations enable the Biplot to visually represent the statistical relationships between variables, facilitating the interpretation of variance, covariance, and correlation in the data [11]. The vectors \(h\) in the Biplot indicate how the variables co-vary and provide an intuitive way to visualize associations between them. This is especially useful in identifying patterns and relationships in complex data, making the Biplot a valuable tool for multivariate analysis. Despite the fact that [PERSON]'s Biplots are powerful tools for the visualization of multivariate data, they have a crucial limitation: they only allow for the maximum quality of representation for either variables or individuals _but not both simultaneously_. This detail was identified by [PERSON] in 1986 [12], who developed the HJ-Biplot technique. This technique addresses this limitation by maximizing the quality of representation for both variables and individuals in the same plane or low-dimensional space. This innovation allows for a more complete and balanced interpretation of the data, facilitating a more robust and detailed analysis of multivariate structures. The HJ-Biplot technique shares similar principles with [PERSON]'s _correspondence analysis_ (CA) [13] and _multiple correspondence analysis_ (MCA) but with extended versatility that allows its application to any type of data, not just frequencies [12]. As shown in Figure 2, the HJ-Biplot is based on singular value decomposition (SVD) and allows projecting both individuals and variables in the same space, providing a graphical representation that facilitates the interpretation of multivariate relationships.