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Expert in Empirical Law: Extracting Knowledge from Multi-Dimensional Data

Expert ID: 727388 Russian Federation

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As the “black box” data we mean the results of observations on the “input” and “output” “black box”. Data the "black box" can be obtained as a result of active or passive experiment. In the active experiment, the object is fully manageable, and the researcher can establish the values of the input parameters that he requires, in particular, forming a ordered multi-dimensional table (type matrix). In the passive experiment, the input factors are observable, measurable, but out of control and represent a multi-dimensional “cloud” of random points. The task analysis is to construct a model describing the dependence of the output parameters from the input. As a visibility models for the "black boxes" should be considered as analytical (e.g., formulas) and graph-analytical (e.g., nomogram) models. Note that the computational methods and means allow almost always to solve problem of approximation for almost of any set of initial data if we have the model of a certain species with a certain number of unknown coefficients, which are to be found. But for the “black box” the kind of the model is unknown by definition!
If we study the dependence of one variable factor, the type of model can "spy" on a planar point graphs. It is available for both active and passive experiments. For two variables it need "peep" to the three-dimensional point graph, or to a set of planar point graphs, obtained from the three-dimensional by fixing the values of one of the variables. It is difficult, but feasible. For the passive experiment "peep" is harder, because, as a rule, you can not get the set of the planar graphs. For the three variables, this approach is useless for any experiments. We live in the three-dimensional world!
What to do?
If we could somehow separate the variables in the data into separate groups so that their point graphs could be examined separately by using visualization! A method of visual representation of multivariate relationships with the known separation of variables has been known for half a century - a nomogram.
Method of separation of variables exists!
It is called by the author, nonlinear multifactor analysis (NLMFA).
The initial data for the NLMFA is a multidimensional table (the type of matrix).
As the result is? nonlinear transformation (new scale of measurement) of the original table, which by the best way (in the sense of minimum least squares) is approached by the sum of the tables which depended on fewer variables (groups of variables). The number of all possible approximations is finite. Of these, you can choose the one that will satisfy the researcher as adequate, for example, the most simple and yet satisfying for deviations from the original data. If the group of the variables contains no more than two variables, then the table depending on them can be visualized as the point graph. For these it can espy and create analytical descriptions (or suitable types of charts). And in conjunction with the new scale of measurement can be constructed the graph-analytical or analytical model of the "black box". The NLMFA requires data in a table (type matrices), i.e. applied only to data of the active experiment. At the same time, most research active experiment is not possible; available are data only the passive experiments, which usually are the disordered massive, the "cloud data". The way out is obvious. It should be by interpolation and extrapolation or by using neural networks out from the “cloud data” get the “quasi-truthful” table like the active experiment (the model "black box" as a "black box"); afterward using the NLMFA find the kind of the visual model; and, finally, to make the model by means of the original ”cloud data”.

He helped to identify new thermal patterns that are important for the safety of nuclear power stations.


Year Degree Subject Institution
Year: 1956 Degree: BS Subject: Nuclear Engineering Institution: MEPhI

Work History

Years Employer Title Department Responsibilities
Years: 1956 to Present Employer: Undisclosed Title: Senior Researcher Department: Responsibilities:

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