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Klasifikátor založený na inverzních hodnotách indexů II. teorie a příloha
Jiřina, Marcel ; Jiřina jr., M.
A theory of a new method for the classification of data into classes is presented. The method is based on the sum of reciprocals of neighbors' indexes. We show that neighbors' indexes are in close relation to the approximate polynomial transform of the neighbors' distances. The sum of the reciprocals of indexes for all neighbors forms truncated harmonic series due to a finite number of its elements. For the neighbors of one class there is a sum of the selected elements of this truncated series. It is proved that the ratio of these sums gives just the probability that the point to be classified - the query point - is of that class.
Fulltext: content.csg -  PDF
Plný tet: v1041-08 - PDF
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Klasifikátor založený na inverzních hodnotách indexů
Jiřina, Marcel ; Jiřina jr., M.
A new method for the classification of data into classes is presented. The method is based on the sum of reciprocals of neighbors' indexes. We show that neighbors' indexes are in close relation to the polynomial transform of the neighbors' distances. The sum of the reciprocals of indexes for all neighbors forms truncated harmonic series due to a finite number of its elements. For the neighbors of one class there is a sum of the selected elements of this truncated series. It is proved that the ratio of these sums gives just the probability that the point to be classified -- the query point -- is of that class. The classification ability is demonstrated on real-life data from the Machine Learning Repository and the results are compared with published results obtained through other methods.
Fulltext: content.csg - PDF
Plný tet: v1034-08 - PDF
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Robustnost testu iid založeného na principu korelačního integrálu
Briatka, Ľuboš
Kočenda (2001) introduced the test for nonlinear dependencies in time series data based on the correlation integral. The idea of the test is to estimate the correlation dimension by integrating over a range of proximity parameter. However, there is an unexplored avenue if one wants to use the test to identify nonlinear structure in non-normal data. Using Monte Carlo studies we show that non-normality leads to over-rejection of the null hypothesis due to two reasons: first, the data are not iid; and second, the data are nonnormal. It is shown that even very small deviation from normality could lead to a rejection of the null hypothesis and hence wrong conclusion. The bootstrap method is revisited and it is shown that it helps to avoid the over-rejection problem, moreover the power of the test increases by a significant amount.
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Chaotic time-series prediction
Dědič, Martin ; Tichý, Vladimír (advisor) ; Smrčka, Pavel (referee)
This thesis focuses on possibility of chaotic (specially economic) time-series prediction. Chaotic time-series are unpredictable in long-term due to their high sensitivity on initial conditions. Nevertheless, their behavior should be more or less predictable in short-term. Goal of this thesis is to show, how much and if any prediction, is possible by non-linear prediction method, and try to reveal or to reject presence of chaotic behavior in them. Work is split into three chapters. Chapter One briefly introduces chosen important concepts and methods from this area. In addition, to describe some prediction methods, there are outlined which indicators and methods are possible to use in order to find possibilities and boundaries of this prediction. Chapter Two is focused on modifications of FracLab software, which is used for create this prediction. Last chapter is experimental. Besides the description of examined time-series and methods, it includes discussion of results.
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