The method of discretization signals to minimize the fallibility of information recovery

The paper proposes a fundamentally new approach to the formulation of the problem of optimizing the discretization interval (frequency). The well-known traditional methods of restoring an analog signal from its discrete implementations consist of sequentially solving two problems: restoring the output signal from a discrete signal at the output of a digital block and restoring the input signal of an analog block from its output signal. However, this approach leads to methodical fallibility caused by interpolation when solving the first problem and by regularizing the equation when solving the second problem. The aim of the work is to develop a method for the signal discretization to minimize the fallibility of information recovery to determine the optimal discretization frequency.The proposed method for determining the optimal discretization rate makes it possible to exclude both components of the methodological fallibility in recovering information about the input signal. This was achieved due to the fact that to solve the reconstruction problem, instead of the known equation, a relation is used that connects the input signal of the analog block with the output discrete signal of the digital block.The proposed relation is devoid of instabilities inherent in the well-known equation. Therefore, when solving it, neither interpolation nor regularization is required, which means that there are no components of the methodological fallibility caused by the indicated operations. In addition, the proposed ratio provides a joint consideration of the properties of the interference in the output signal of the digital block and the frequency properties of the transforming operator, which allows minimizing the fallibility in restoring the input signal of the analog block and determining the optimal discretization frequency.A widespread contradiction in the field of signal information recovery from its discrete values has been investigated. A decrease in the discretization frequency below the optimal one leads to an increase in the approximation fallibility and the loss of some information about the input signal of the analog-to-digital signal processing device. At the same time, unjustified overestimation of the discretization rate, complicating the technical implementation of the device, is not useful, since not only does it not increase the information about the input signal, but, if necessary, its restoration leads to its decrease due to the increase in the effect of noise in the output signal on the recovery accuracy. input signal. The proposed method for signal discretization based on the minimum information recovery fallibility to determine the optimal discretization rate allows us to solve this contradiction.

A nonparametric algorithm for automatic classification of large multivariate statistical data sets and its application

A nonparametric algorithm for automatic classification of large statistical data sets is proposed. The algorithm is based on a procedure for optimal discretization of the range of values of a random variable. A class is a compact group of observations of a random variable corresponding to a unimodal fragment of the probability density. The considered algorithm of automatic classification is based on the «compression» of the initial information based on the decomposition of a multidimensional space of attributes. As a result, a large statistical sample is transformed into a data array composed of the centers of multidimensional sampling intervals and the corresponding frequencies of random variables. To substantiate the optimal discretization procedure, we use the results of a study of the asymptotic properties of a kernel-type regression estimate of the probability density. An optimal number of sampling intervals for the range of values of one- and two-dimensional random variables is determined from the condition of the minimum root-mean square deviation of the regression probability density estimate. The results obtained are generalized to the discretization of the range of values of a multidimensional random variable. The optimal discretization formula contains a component that is characterized by a nonlinear functional of the probability density. An analytical dependence of the detected component on the antikurtosis coefficient of a one-dimensional random variable is established. For independent components of a multidimensional random variable, a methodology is developed for calculating estimates of the optimal number of sampling intervals for random variables and their lengths. On this basis, a nonparametric algorithm for the automatic classification is developed. It is based on a sequential procedure for checking the proximity of the centers of multidimensional sampling intervals and relationships between frequencies of the membership of the random variables from the original sample of these intervals. To further increase the computational efficiency of the proposed automatic classification algorithm, a multithreaded method of its software implementation is used. The practical significance of the developed algorithms is confirmed by the results of their application in processing remote sensing data.

NOVEL EVALUATION INDEX OF CROSS-SCALE DISCRETIZATION UNCERTAINTY BASED ON LOCAL STANDARD SCORE

Optimal discretization of continuously valued attributes is an uncertainty problem. The uncertainty of discretization is propagated and accumulated in the process of data mining, which has a direct influence on the usability and operation of the output results for mining. To address the limitations of existing discretization evaluation indices in describing accuracy and operation efficiency, this work suggests a discretization uncertainty index based on individuals. This method takes the local standard score as the general similarity measure in and between the intervals and evaluates discretization reliability according to the relative position of individuals in each interval. The experiment shows the new evaluation index is consistent with commonly used metrics. Under the premise of guaranteeing the validity of discrete evaluation, the proposed method has greater description accuracy and operation efficiency than extant approaches; it also has more advantages for massive data processing and special distribution detection.

A fast algorithm for the adaptive discretization of 3D parametric curves

Purpose The purpose of this paper is to present a fast algorithm for the adaptive discretization of three-dimensional parametric curves. Design/methodology/approach The proposed algorithm computes the parametric increments of all segments to obtain the parametric coordinates of all discrete nodes. This process is recursively applied until the optimal discretization of curves is obtained. The parametric increment of a segment is inversely proportional to the number of sub-segments, which can be subdivided, and the sum of parametric increments of all segments is constant. Thus, a new expression for parametric increment of a segment can be obtained. In addition, the number of sub-segments, which a segment can be subdivided is calculated approximately, thus avoiding Gaussian integration. Findings The proposed method can use less CPU time to perform the optimal discretization of three-dimensional curves. The results of curves discretization can also meet requirements for mesh generation used in the preprocessing of numerical simulation. Originality/value Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the algorithm saves in the process of curve discretization.