on essential data points and their relative importance for efficient data reduction

The term data reduction methods are defined as different mathematical algorithms that can be used to decrease big data dimensionality and/or data size by maintaining information. the extreme observations in a multidimensional data set for unraveling its underlying structure can be considered for efficient data reduction. these extreme observations are corresponding to actual signal vectors (data points) which are the most linearly dissimilar and they are representative of the most independent observed patterns in data set. detection of these essential data points allows reproducing all the measured information and removing redundancies in data points which brings simplicity and computational speed. the new term data point importance (dpi) defines an easily calculable value corresponding to each row or column of data matrix to reflect its impact for keeping the pattern of the data structure. usually a lot of data points have dpis equal or very close to zero that they do not carry on useful information about keeping the data pattern. dpi values for some of the data points are significant and they have been sorted regarding to their importances [1-3]. the basic idea for definition of essential points (ep) and also the concept behind the new term data point importance (dpi) will be explained. application of both strategy in effiecient data reduction in several simulated and real experimental data will be discussed.