## A unified development of several techniques for the representation of random vectors and data sets |

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APPENDIX autocorrelation function coefficient vectors combinations of orthonormal constant vector j£q coordinate vectors correlation function data vectors eigenfunctions eigenvalues empirical orthogonal functions entropy equa equation 31 error vector Euclidean space Example A2 expectation operator expected value familiar Karhunen-Loeve expansion feature extraction finite dimensional follows Hilbert space infinite inner product integral operator k=l x kernel R(t,s largest eigenvalues linear combinations Linear vector space matrix of row maximized in turn mean norm squared mean square integrable mean squared error minimum mean squared mx(t norm squared values normalized eigenvectors orthonormal vectors principal component analysis problem process x(t random process random vectors reduce the dimensionality representation is minimized representation of equation row vectors sample covariance matrix sample function self-adjoint transformation set of orthonormal set of vectors subspace theorem theoretical development tion unitary space vector in representation vector space theory vectors by linear Xk ln Xk xn(t zero