Principal Component Analysis - Table of Symbols and Abbreviations

Table of Symbols and Abbreviations

Symbol Meaning Dimensions Indices
data matrix, consisting of the set of all data vectors, one vector per column
the number of column vectors in the data set scalar
the number of elements in each column vector (dimension) scalar
the number of dimensions in the dimensionally reduced subspace, scalar
vector of empirical means, one mean for each row m of the data matrix
vector of empirical standard deviations, one standard deviation for each row m of the data matrix
vector of all 1's
deviations from the mean of each row m of the data matrix
z-scores, computed using the mean and standard deviation for each row m of the data matrix
covariance matrix
correlation matrix
matrix consisting of the set of all eigenvectors of C, one eigenvector per column
diagonal matrix consisting of the set of all eigenvalues of C along its principal diagonal, and 0 for all other elements
matrix of basis vectors, one vector per column, where each basis vector is one of the eigenvectors of C, and where the vectors in W are a sub-set of those in V
matrix consisting of N column vectors, where each vector is the projection of the corresponding data vector from matrix X onto the basis vectors contained in the columns of matrix W.

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