Artificial Intelligence and Quantum Computing for Advanced Wireless Networks. Savo G. Glisic
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matrix), then the feature vectors are constructed as
Univariate variance is a second‐order statistical measure of the departure of the input observations with respect to the sample mean. A generalization of the univariate variance to multivariate variables is the trace of the input covariance matrix. By choosing the m largest eigenvalues of the covariance matrix Cx, we guarantee that we are making a representation in the feature space explaining as much variance of the input space as possible with only m variables. As already indicated in Section 2.1, in fact, w1 is the direction in which the data exhibit the largest variability, w2 is the direction with largest variability once the variability along w1 has been removed, w3 is the direction with largest variability once the variability along w1 and w2 has been removed, and so on. Thanks to the orthogonality of the wi vectors, and the subsequent decorrelation of the feature vectors, the total variance explained by PCA decomposition can be conveniently measured as the sum of the variances of each feature,
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