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K-LKarhunen-Loeve (mathematical expansion)
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The method we use is a natural extension of the classical Karhunen-Loeve method (Karhunen, 1946; Loeve, 1945) and it is based on the orthogonal transformation which is a popular choice for geoscience analysis to reduce data dimensionality.
Depending on the field of application, it is also named the discrete Karhunen-Loeve transform, the Hotelling transform or proper orthogonal decomposition (POD).
The forward and inverse discrete sine transforms are important functions used in digital signal processing applications especially in image compression due to the fact that they behave very much like the statistically optimal transform known to be Karhunen-Loeve transform (KLT).
Karhunen-loeve eigenvalue problems in cosmology: how should we tackle large data sets?
3] Alon Amar, Amir Leshem, and Michael Gastpar, "Recursive implementation of the distributed karhunen-loeve transform," Signal Processing, IEEE Transactions on, 58(10):5320-5330, 2010.
Here we will extend Sequential Karhunen-Loeve [25] algorithm to make it suitable for updating SVD efficiently with mean update simultaneously.
Phoon, "Convergence study of the truncated Karhunen-Loeve expansion for simulation of stochastic processes," International Journal for Numerical Methods in Engineering, vol.
But scientists at Kodak in Rochester, at the National Research Council of Canada and at the National Physical Laboratory in the UK took spectro-radiometric readings of the north sky at varying times and dates and the data were averaged and then fitted by NIST using a relatively new technology we now call Karhunen-Loeve decomposition or proper orthogonal components or even principal components.
PCA is based on the Karhunen-Loeve transform (the transformation).
the Karhunen-Loeve (KL) expansion [10] of the multipath field to yield uncorrelated coefficients.
2009b) also proposed to compress the SIFT descriptor with Karhunen-Loeve transform, yielding approximate 2 bits per SIFT dimension.