Outlier detection is a classic task having many different ways to solve. However, in a number of tasks, it is important to find less pronounced deviations from the natural flow of a certain process. This article propo...
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ISBN:
(纸本)9781665426053
Outlier detection is a classic task having many different ways to solve. However, in a number of tasks, it is important to find less pronounced deviations from the natural flow of a certain process. This article proposes to search for such deviations using Stepanets approach for classification of functions describing the corresponding process. It is shown that in some cases this approach allows to reveal better the deviation from standard behavior than a direct comparison of it with current behavior. The proposed approach is illustrated by the example of the analysis of data on the results of football matches in the 2013/14 season in the French Ligue 2.
We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, this is an invariant of this function with respect to a certain group of transformations of va...
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We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, this is an invariant of this function with respect to a certain group of transformations of variables;on the other hand, this is a special probability measure in the space of matrices (tensors) that is invariant under actions of natural infinite permutation groups. The intricate interplay of both interpretations of matrix (tensor) distributions makes them an important subject of modern functional analysis. We formulate and prove a theorem that, under certain conditions on a measurable function of two variables, its matrix distribution is a complete invariant.
classification of ternary logic functions by NPC group of operations is investigated using ternary parametron logic. Based on multiplexor (MUX) realization of a function, a self-dual function is constructed by introdu...
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classification of ternary logic functions by NPC group of operations is investigated using ternary parametron logic. Based on multiplexor (MUX) realization of a function, a self-dual function is constructed by introducing Goto's self-dualizing variable which feeds constant signals to MUX circuit. Self-dualizing operation is an operation to transform from one function to another among functions realized by different values of self-dualizing variable. It is an element of NPC group which is a combination of permutation operation on values and positions of variables (Negation and Permutation), and that on values of function (Cyclic permutation). These operations can be formulated as an exponentiation group and the equivalence class count is obtained from the cycle index of the group.
The classification of measurable functions of several variables is reduced to the problem of describing some special measures on the matrix (tensor) space, namely, the so-called matrix (tensor) distributions, that are...
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The classification of measurable functions of several variables is reduced to the problem of describing some special measures on the matrix (tensor) space, namely, the so-called matrix (tensor) distributions, that are invariant with respect to the permutations of indices. In the case of functions with additional symmetries (symmetric, unitarily or orthogonally invariant, etc.), these measures also have additional symmetries. This relationship between measurable functions and measures on the tensor space as well as our method in itself are used in both directions, namely, on one hand, to investigate invariance properties of functions and characterizations of matrix distributions, and, on the other hand, to classify the set of all invariant measures. We also give a canonical model of a measurable function with a given matrix distribution.
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