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Šioje santraukoje trumpai aprašoma V. Kurausko disertacija. Pristatomos abi disertacijos dalys, įvedami atsitiktinių sankirtų grafų ir digrafų modeliai, apibrėžiamos minorinės grafų klasės, suformuluojami sprendžiami uždaviniai bei pateikiami pagrindiniai rezultatai., This paper summarizes (in Lithuanian) the doctoral dissertation "On two models of random graphs" (in English) by V. Kurauskas. We introduce the random graph models (random intersection graphs, graphs with disjoint excluded minors) studied in the thesis, overview the problems and state the main results.

Daugelis praktiškai reikšmingu sistemu mokymo uždaviniu reikalauja gebeti panaudoti didelio matavimo, strukturizuotus, netiesinius duomenis. Vaizdu, teksto, socialiniu bei verslo ryšiu analize, ivairus bioinformatikos uždaviniai galetu buti tokiu uždaviniu pavyzdžiais. Todel požymiu išskyrimas dažnai yra pirmasis žingsnis, kuriuo pradedama duomenu analize ir nuo kurio priklauso galutinio rezultato sekme. Šio disertacinio darbo tyrimo objektas yra požymiu išskyrimo algoritmai, besiremiantys priklausomumo savoka. Darbe nagrinejamas priklausomumas, nusakytas kovariacinio operatoriaus Hilberto-Šmidto normos (HSIC mato) branduoliniu ivertiniu. Pasiulyti šiuo ivertiniu besiremiantys HBFE ir HSCA algoritmai leidžia dirbti su bet kokios strukturos duomenimis, bei yra formuluojami tikriniu vektoriu terminais (tai leidžia optimizavimui naudoti standartinius paketus), bei taikytini ne tik prižiurimo, bet ir dalinai prižiurimo mokymo imtims. Pastaruoju atveju HBFE ir HSCA modifikacijos remiasi Laplaso reguliarizacija. Eksperimentais su klasifikavimo bei daugiažymio klasifikavimo duomenimis parodyta, jog pasiulyti algoritmai leidžia pagerinti klasifikavimo efektyvuma lyginant su PCA ar LDA., In many important real world applications the initial representation of the data is inconvenient, or even prohibitive for further analysis. For example, in image analysis, text analysis and computational genetics high-dimensional, massive, structural, incomplete, and noisy data sets are common. Therefore, feature extraction, or revelation of informative features from the raw data is one of fundamental machine learning problems. Efficient feature extraction helps to understand data and the process that generates it, reduce costs for future measurements and data analysis. The representation of the structured data as a compact set of informative numeric features allows applying well studied machine learning techniques instead of developing new ones.. The dissertation focuses on supervised and semi-supervised feature extraction methods, which optimize the dependence structure of features. The dependence is measured using the kernel estimator of Hilbert-Schmidt norm of covariance operator (HSIC measure). Two dependence structures are investigated: in the first case we seek features which maximize the dependence on the dependent variable, and in the second one, we additionally minimize the mutual dependence of features. Linear and kernel formulations of HBFE and HSCA are provided. Using Laplacian regularization framework we construct semi-supervised variants of HBFE and HSCA. Suggested algorithms were investigated experimentally using conventional and multilabel classification data... [to full text]

Daugelis praktiškai reikšmingu sistemu mokymo uždaviniu reikalauja gebeti panaudoti didelio matavimo, strukturizuotus, netiesinius duomenis. Vaizdu, teksto, socialiniu bei verslo ryšiu analize, ivairus bioinformatikos uždaviniai galetu buti tokiu uždaviniu pavyzdžiais. Todel požymiu išskyrimas dažnai yra pirmasis žingsnis, kuriuo pradedama duomenu analize ir nuo kurio priklauso galutinio rezultato sekme. Šio disertacinio darbo tyrimo objektas yra požymiu išskyrimo algoritmai, besiremiantys priklausomumo savoka. Darbe nagrinejamas priklausomumas, nusakytas kovariacinio operatoriaus Hilberto-Šmidto normos (HSIC mato) branduoliniu ivertiniu. Pasiulyti šiuo ivertiniu besiremiantys HBFE ir HSCA algoritmai leidžia dirbti su bet kokios strukturos duomenimis, bei yra formuluojami tikriniu vektoriu terminais (tai leidžia optimizavimui naudoti standartinius paketus), bei taikytini ne tik prižiurimo, bet ir dalinai prižiurimo mokymo imtims. Pastaruoju atveju HBFE ir HSCA modifikacijos remiasi Laplaso reguliarizacija. Eksperimentais su klasifikavimo bei daugiažymio klasifikavimo duomenimis parodyta, jog pasiulyti algoritmai leidžia pagerinti klasifikavimo efektyvuma lyginant su PCA ar LDA., In many important real world applications the initial representation of the data is inconvenient, or even prohibitive for further analysis. For example, in image analysis, text analysis and computational genetics high-dimensional, massive, structural, incomplete, and noisy data sets are common. Therefore, feature extraction, or revelation of informative features from the raw data is one of fundamental machine learning problems. Efficient feature extraction helps to understand data and the process that generates it, reduce costs for future measurements and data analysis. The representation of the structured data as a compact set of informative numeric features allows applying well studied machine learning techniques instead of developing new ones.. The dissertation focuses on supervised and semi-supervised feature extraction methods, which optimize the dependence structure of features. The dependence is measured using the kernel estimator of Hilbert-Schmidt norm of covariance operator (HSIC measure). Two dependence structures are investigated: in the first case we seek features which maximize the dependence on the dependent variable, and in the second one, we additionally minimize the mutual dependence of features. Linear and kernel formulations of HBFE and HSCA are provided. Using Laplacian regularization framework we construct semi-supervised variants of HBFE and HSCA. Suggested algorithms were investigated experimentally using conventional and multilabel classification data... [to full text]

In many important real world applications the initial representation of the data is inconvenient, or even prohibitive for further analysis. For example, in image analysis, text analysis and computational genetics high-dimensional, massive, structural, incomplete, and noisy data sets are common. Therefore, feature extraction, or revelation of informative features from the raw data is one of fundamental machine learning problems. Efficient feature extraction helps to understand data and the process that generates it, reduce costs for future measurements and data analysis. The representation of the structured data as a compact set of informative numeric features allows applying well studied machine learning techniques instead of developing new ones.. The dissertation focuses on supervised and semi-supervised feature extraction methods, which optimize the dependence structure of features. The dependence is measured using the kernel estimator of Hilbert-Schmidt norm of covariance operator (HSIC measure). Two dependence structures are investigated: in the first case we seek features which maximize the dependence on the dependent variable, and in the second one, we additionally minimize the mutual dependence of features. Linear and kernel formulations of HBFE and HSCA are provided. Using Laplacian regularization framework we construct semi-supervised variants of HBFE and HSCA. Suggested algorithms were investigated experimentally using conventional and multilabel classification data... [to full text], Daugelis praktiškai reikšmingu sistemu mokymo uždaviniu reikalauja gebeti panaudoti didelio matavimo, strukturizuotus, netiesinius duomenis. Vaizdu, teksto, socialiniu bei verslo ryšiu analize, ivairus bioinformatikos uždaviniai galetu buti tokiu uždaviniu pavyzdžiais. Todel požymiu išskyrimas dažnai yra pirmasis žingsnis, kuriuo pradedama duomenu analize ir nuo kurio priklauso galutinio rezultato sekme. Šio disertacinio darbo tyrimo objektas yra požymiu išskyrimo algoritmai, besiremiantys priklausomumo savoka. Darbe nagrinejamas priklausomumas, nusakytas kovariacinio operatoriaus Hilberto-Šmidto normos (HSIC mato) branduoliniu ivertiniu. Pasiulyti šiuo ivertiniu besiremiantys HBFE ir HSCA algoritmai leidžia dirbti su bet kokios strukturos duomenimis, bei yra formuluojami tikriniu vektoriu terminais (tai leidžia optimizavimui naudoti standartinius paketus), bei taikytini ne tik prižiurimo, bet ir dalinai prižiurimo mokymo imtims. Pastaruoju atveju HBFE ir HSCA modifikacijos remiasi Laplaso reguliarizacija. Eksperimentais su klasifikavimo bei daugiažymio klasifikavimo duomenimis parodyta, jog pasiulyti algoritmai leidžia pagerinti klasifikavimo efektyvuma lyginant su PCA ar LDA.