Viacheslav Kovtun

Measurement is a typical way of gathering information about an investigated object, generalized by a finite set of characteristic parameters. The result of each iteration of the measurement is an instance of the class of the investigated object in the form of a set of values of characteristic parameters. An ordered set of instances forms a collection whose dimensionality for a real object is a factor that cannot be ignored. Managing the dimensionality of data collections, as well as classification, regression, and clustering, are fundamental problems for machine learning. Compactification is the approximation of the original data collection by an equivalent collection (with a reduced dimension of characteristic parameters) with the control of accompanying information capacity losses. Related to compactification is the data completeness verifying procedure, which is characteristic of the data reliability assessment. If there are stochastic parameters among the initial data collection characteristic parameters, the compactification procedure becomes more complicated. To take this into account, this study proposes a model of a structured collection of stochastic data defined in terms of relative entropy. The compactification of such a data model is formalized by an iterative procedure aimed at maximizing the relative entropy of sequential implementation of direct and reverse projections of data collections, taking into account the estimates of the probability distribution densities of their attributes. The procedure for approximating the relative entropy function of compactification to reduce the computational complexity of the latter is proposed. To qualitatively assess compactification this study undertakes a formal analysis that uses data collection information capacity and the absolute and relative share of information losses due to compaction as its metrics. Taking into account the semantic connection of compactification and completeness, the proposed metric is also relevant for the task of assessing data reliability. Testing the proposed compactification procedure proved both its stability and efficiency in comparison with previously used analogues, such as the principal component analysis method and the random projection method.

The article is devoted to the research of the peripheral server energy consumption managing process defined based on the threshold policy by manipulating the values of the characteristic parameters of the arithmetic-logical complex of the latter. The research object is formalized by a Markov queue model with a single-threshold control scheme for the intensity of accepted requests service. A characteristic feature of the life cycle of a peripheral server is the non-stationary mode of operation in terms of energy consumption, due to the need to periodically poll the controlled sensor network and process the received data in real-time. To take into account this circumstance, the intensities of transitions in the heterogeneous birth-and-death Markov process of the created model are interpreted as non-random periodic functions of time. The resulting mathematical apparatus is summarized in the metric that allows us to estimate the target peripheral server’s energy consumption both at a specific moment and for a censored time interval (this distinguishes the obtained result from existing analogs).