Table 1.

Glossary

Term	Definition
Variance	The variance of a random variable measures the spread (variability) of its realizations (values of the random variable). The variance is always a positive number. If the variance is small, the values of the random variable are close to the mean of the random variable (the spread of the data is low). A high variance is equivalent to widely spread values of the random variable. See [11].
Standard deviation	The standard deviation of a random variable measures the spread (variability) of its realizations (values of the random variable). It is defined as the square root of the variance. The standard deviation will have the same units as the random variable, in contrast to the variance. See [11].
Covariance	The covariance is an unstandardized measure about the tendency of two random variables to vary together. See [12].
Correlation	The correlation of two random variables is defined by the covariance of the two random variables normalized by the product between their standard deviations. It measures the linear relationship between the two random variables. The correlation coefficient ranges between −1 and +1. See [12].
Inertia	Inertia is a measure for the variability of the data. The inertia of a set of points relative to one point P is defined by the weighted sum of the squared distances between each considered point and the point P. Correspondingly, the inertia of a centered matrix (mean is equal to zero) is simply the sum of the squared matrix elements. The inertia of the matrix X defined by the metrics L and D is the weighted sum of its squared values. The inertia is equal the total variance of X when X is centered, L is the Euclidean metric and D is a diagonal matrix with diagonal elements equal to 1/n. See [13].
Co-inertia	The co-inertia is a global measure for the co-variability of two data sets (for example, two high-dimensional random variables). If the data sets are centered, the co-inertia is the sum of squared covariances. When coupling a pair of data sets, the co-inertia between two matrices, X and Y, is calculated as trace (XLXTDYRYTD). See [13].
Orthogonal	Two vectors are called orthogonal if they form an angle that measures 90 degrees. Generally, two vectors are orthogonal if their inner product is equal to zero. Two orthogonal vectors are always linearly independent. See [12].
Independent	In linear algebra, two vectors are called linearly independent if their liner combination is equal to zero only when all constants of the linear combination are equal to zero. See [14]. In statistics, two random variables are called statistically independent if the distribution of one of them does not affect the distribution of the other. If two independent random variables are added, then the mean of the sum is the sum of the two mean values. This is also true for the variance. The covariance of two independent variables is equal to zero. See [11].
Eigenvector, eigenvalue	An eigenvector of a matrix is a vector that does not change its direction after a linear transformation. The vector $v$ is an eigenvector of the matrix A if: $Av\hspace{0.17em}=\hspace{0.17em}\lambda v$. $\lambda$ is the eigenvalue associated with the eigenvector $v$ and it reflects the stretch of the eigenvector following the linear transformation. The most popular way to compute eigenvectors and eigenvalues is the SVD. See [14].
Linear combination	Mathematical expression calculated through the multiplication of variables with constants and adding the individual multiplication results. A linear combination of the variables x and y is $ax\hspace{0.17em}+\hspace{0.17em}by$ where a and b are the constants. See [15].
Omics	The study of biological molecules in a comprehensive fashion. Examples of omics data types include genomics, transcriptomics, proteomics, metabolomics and epigenomics [16].
Dimension reduction	Dimension reduction is the mapping of data to a lower dimensional space such that redundant variance in the data is reduced or discarded, enabling a lower-dimensional representation without significant loss of information. See [17].
Exploratory data analysis	EDA is the application of statistical techniques that summarize the main characteristics of data, often with visual methods. In contrast to statistical hypothesis testing (confirmatory data analysis), EDA can help to generate hypotheses. See [18].
Sparse vector	A sparse vector is a vector in which most elements are zero. A sparse loadings matrix in PCA or related methods reduce the number of features contributing to a PC. The variables with nonzero entries (features) are the ‘selected features'. See [19].