Parzen window

The K-PLS method can be reformulated to resemble support vector machines, but it can also be interpreted as a kernel and centering transformation of the descriptor data followed by a regular PLS method [99]. K-PLS was first introduced by Lindgren, Geladi, and Wold [143] in the context of working with linear kernels on data sets with more descriptor fields than data, in order to make the PLS modeling more efficient. Early applications of K-PLS were done mainly in this context [144-146]. The Parzen window, o, in the formula above is a free parameter that is determined by hyper-tuning on a validation set. For each dataset c is then held constant, independent of the various bootstrap splits. 

N. Kwak, C.H. Choi, Input feature selection by mutual information based on Parzen window. IEEE Trans. Pattern Anal. Mach. Intell. 24(12), 1667-1671 (2002)... 

The probability distribution for the evaluation of MI and NMI can be estimated with Parzen windows, histograms or other probability density estimators. The most common method uses images histograms. Q and K are images with M pixels that can assume N gray levels gi>g2y-gN The MI between Q and K can be defined as ... 

Other window functions, such as triangular windows of variable widths, can also be used. In fact, there is a whole bevy of window functions available, often named after their originators or proponents, such as Bartlett, Hamming, Hanning, Parzen (for the triangular window), andWelch. Some of these are discussed in Section 12.7 of the book Numerical Recipes (W. H. Press etal., Cambridge University Press 1986). 

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