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Visual Images Segmentation based on Uniform Textures Extraction
Goltsev, A.; Gritsenko, V.; Húsek, Dušan
2020 - English
A new effective procedure for partial texture segmentation of visual images is proposed. The procedure segments any input image into a number of non-overlapping homogeneous ne-grained texture areas. The main advantages of the proposed procedure are as follows. It is completely unsupervised, that is, it processes the input image without any prior knowledge of either the type of textures or the number of texture segments in the image. In addition, the procedure segments arbitrary images of all types. This means that no changes to the procedure parameters are required to switch from one image type to another. Another major advantage of the procedure is that in most cases it extracts the uniform ne-grained texture segments present in the image, just as humans do. This result is supported by series of experiments that demonstrate the ability of the procedure to delineate uniform ne-grained texture segments over a wide range of images. At a minimum, image processing according to the proposed technique leads to a signficant reduction in the uncertainty of the internal structure of the analyzed image.
Keywords:
Texture feature; Texture window; Homogeneous ne-grained texture segment; Texture segment extraction; Texture segmentation
Available at various institutes of the ASCR
Visual Images Segmentation based on Uniform Textures Extraction
A new effective procedure for partial texture segmentation of visual images is proposed. The procedure segments any input image into a number of non-overlapping homogeneous ne-grained texture areas. ...
Least Weighted Absolute Value Estimator with an Application to Investment Data
Vidnerová, Petra; Kalina, Jan
2020 - English
While linear regression represents the most fundamental model in current econometrics, the least squares (LS) estimator of its parameters is notoriously known to be vulnerable to the presence of outlying measurements (outliers) in the data. The class of M-estimators, thoroughly investigated since the groundbreaking work by Huber in 1960s, belongs to the classical robust estimation methodology (Jurečková et al., 2019). M-estimators are nevertheless not robust with respect to leverage points, which are defined as values outlying on the horizontal axis (i.e. outlying in one or more regressors). The least trimmed squares estimator seems therefore a more suitable highly robust method, i.e. with a high breakdown point (Rousseeuw & Leroy, 1987). Its version with weights implicitly assigned to individual observations, denoted as the least weighted squares estimator, was proposed and investigated in Víšek (2011). A trimmed estimator based on the 𝐿1-norm is available as the least trimmed absolute value estimator (Hawkins & Olive, 1999), which has not however acquired attention of practical econometricians. Moreover, to the best of our knowledge, its version with weights implicitly assigned to individual observations seems to be still lacking.
Keywords:
robust regression; regression median; implicit weighting; computational aspects; nonparametric bootstrap
Fulltext is available at external website.
Least Weighted Absolute Value Estimator with an Application to Investment Data
While linear regression represents the most fundamental model in current econometrics, the least squares (LS) estimator of its parameters is notoriously known to be vulnerable to the presence of ...
On the Effect of Human Resources on Tourist Infrastructure: New Ideas on Heteroscedastic Modeling Using Regression Quantiles
Kalina, Jan; Janáček, Patrik
2020 - English
Tourism represents an important sector of the economy in many countries around the world. In this work, we are interested in the effect of the Human Resources and Labor Market pillar of the Travel and Tourism Competitiveness Index on tourist service infrastructure across 141 countries of the world. A regression analysis requires to handle heteroscedasticity in these data, which is not an uncommon situation in various available human capital studies. Our first task is focused on testing significance of individual variables in the model. It is illustrated here that significance tests are influenced by heteroscedasticity, which remains true also for tests for regression quantiles or robust regression estimators, resistant to a possible contamination of data by outliers. Only if a suitable model is considered, which takes heteroscedasticity into account, the effect of the Human Resources and Labor Market pillar turns out to be significant. Further, we propose and present a new diagnostic tool denoted as aquintile plot, allowing to interpret immediately the heteroscedastic structure of the linear regression model for possibly contaminated data.
Keywords:
tourism infrastructure; human resources; regression; robustness; regression quantiles
Fulltext is available at external website.
On the Effect of Human Resources on Tourist Infrastructure: New Ideas on Heteroscedastic Modeling Using Regression Quantiles
Tourism represents an important sector of the economy in many countries around the world. In this work, we are interested in the effect of the Human Resources and Labor Market pillar of the Travel and ...
Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations
Vlček, Jan; Lukšan, Ladislav
2020 - English
Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey (1991) and Vlček and Lukšan (2019), satisfies the quasi-Newton equations with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the quasi-Newton equations as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously combined with methods based on vector corrections for conjugacy (Vlček and Lukšan, 2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods.
Keywords:
unconstrained minimization; variable metric methods; limited-memory methods; variationally derived methods; global convergence; numerical results
Available in a digital repository NRGL
Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations
Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey ...
Linear-time Algorithms for Largest Inscribed Quadrilateral
Keikha, Vahideh
2020 - English
Let P be a convex polygon of n vertices. We present a linear-time algorithm for the problem of computing the largest-area inscribed quadrilateral of P. We also design the parallel version of the algorithm with O(log n) time and O(n) work in CREW PRAM model, which is quite work optimal. Our parallel algorithm also computes all the antipodal pairs of a convex polygon with O(log n) time and O(log2n+s) work, where s is the number of antipodal pairs, that we hope is of independent interest. We also discuss several approximation algorithms (both constant factor and approximation scheme) for computing the largest-inscribed k-gons for constant values of k, in both area and perimeter measures.
Keywords:
Maximum-area quadrilateral; extreme area k-gon
Available in a digital repository NRGL
Linear-time Algorithms for Largest Inscribed Quadrilateral
Let P be a convex polygon of n vertices. We present a linear-time algorithm for the problem of computing the largest-area inscribed quadrilateral of P. We also design the parallel version of the ...
Globální implicitní funkce
Rohn, Jiří
2020 - Czech
Tento text pochází z roku 1973 a nebyl dosud zveřejněn. Jeho hlavním výsledkem je věta o existenci a jednoznačnosti globální implicitní funkce v Rn. Tomuto výsledku předchází řada pomocných tvrzení.
Keywords:
silně lokální souvislé množiny; iredundantní pokrytí; pokračování implicitní funkce; existence a jednoznačnost; globální implicitní funkce; inverzní zobrazení
Available in a digital repository NRGL
Globální implicitní funkce
Tento text pochází z roku 1973 a nebyl dosud zveřejněn. Jeho hlavním výsledkem je věta o existenci a jednoznačnosti globální implicitní funkce v Rn. Tomuto výsledku předchází řada pomocných tvrzení.
Regression for High-Dimensional Data: From Regularization to Deep Learning
Kalina, Jan; Vidnerová, Petra
2020 - English
Regression modeling is well known as a fundamental task in current econometrics. However, classical estimation tools for the linear regression model are not applicable to highdimensional data. Although there is not an agreement about a formal definition of high dimensional data, usually these are understood either as data with the number of variables p exceeding (possibly largely) the number of observations n, or as data with a large p in the order of (at least) thousands. In both situations, which appear in various field including econometrics, the analysis of the data is difficult due to the so-called curse of dimensionality (cf. Kalina (2013) for discussion). Compared to linear regression, nonlinear regression modeling with an unknown shape of the relationship of the response on the regressors requires even more intricate methods.
Keywords:
regression; neural networks; robustness; high-dimensional data; regularization
Fulltext is available at external website.
Regression for High-Dimensional Data: From Regularization to Deep Learning
Regression modeling is well known as a fundamental task in current econometrics. However, classical estimation tools for the linear regression model are not applicable to highdimensional data. ...
The Equation |x| - |Ax| = b
Rohn, Jiří
2020 - English
We formulate conditions on A and b under which the double absolute value equation |x| - |Ax| = b possesses in each orthant a unique solution which, moreover, belongs to the interior of that orthant.
Keywords:
absolute value equation; double absolute value equation; orthantwise solvability; theorem of the alternatives
Available in a digital repository NRGL
The Equation |x| - |Ax| = b
We formulate conditions on A and b under which the double absolute value equation |x| - |Ax| = b possesses in each orthant a unique solution which, moreover, belongs to the interior of that orthant.
The scalar-valued score functions of continuous probability distribution
Fabián, Zdeněk
2019 - English
In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not the observed value, which is to be used in probabilistic and statistical considerations, but its 'treated form', the value of the scalar-valued score function of distribution of the assumed model. Actually, the opinion that an observed value of random variable should be 'treated' with respect to underlying model is one of main ideas of the inference based on likelihood in classical statistics. However, a vector nature of Fisher score functions of classical statistics does not enable a consistent use of this point of view. Instead, various inference functions are suggested and used in solutions of various statistical problems. Inference function of this report is the scalar-valued score function of distribution.
Keywords:
Shortcomings of probability theory; Scalar-valued score functions; Characteristics of continous random variables; Parametric estimation; Transformed distributions; Skew-symmetric distributions
Available at various institutes of the ASCR
The scalar-valued score functions of continuous probability distribution
In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not ...
Lexicalized Syntactic Analysis by Restarting Automata
Mráz, F.; Otto, F.; Pardubská, D.; Plátek, Martin
2019 - English
We study h-lexicalized two-way restarting automata that can rewrite at most i times per cycle for some i ≥ 1 (hRLWW(i)-automata). This model is considered useful for the study of lexical (syntactic) disambiguation, which is a concept from linguistics. It is based on certain reduction patterns. We study lexical disambiguation through the formal notion of h-lexicalized syntactic analysis (hLSA). The hLSA is composed of a basic language and the corresponding h-proper language, which is obtained from the basic language by mapping all basic symbols to input symbols. We stress the sensitivity of hLSA by hRLWW(i)-automata to the size of their windows, the number of possible rewrites per cycle, and the degree of (non-)monotonicity. We introduce the concepts of contextually transparent languages (CTL) and contextually transparent lexicalized analyses based on very special reduction patterns, and we present two-dimensional hierarchies of their subclasses based on the size of windows and on the degree of synchronization. The bottoms of these hierarchies correspond to the context-free languages. CTL creates a proper subclass of context-sensitive languages with syntactically natural properties.
Keywords:
Restarting automaton; h-lexicalization; lexical disambiguation
Fulltext is available at external website.
Lexicalized Syntactic Analysis by Restarting Automata
We study h-lexicalized two-way restarting automata that can rewrite at most i times per cycle for some i ≥ 1 (hRLWW(i)-automata). This model is considered useful for the study of lexical (syntactic) ...
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