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1

Generalized ordered linear regression with regularization

Łęski J., Henzel N.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2012

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Vol. 60, nr 3

481-489

EN

Linear regression analysis has become a fundamental tool in experimental sciences. We propose a new method for parameter estimation in linear models. The 'Generalized Ordered Linear Regression with Regularization' (GOLRR) uses various loss functions (including the o-insensitive ones), ordered weighted averaging of the residuals, and regularization. The algorithm consists in solving a sequence of weighted quadratic minimization problems where the weights used for the next iteration depend not only on the values but also on the order of the model residuals obtained for the current iteration. Such regression problem may be transformed into the iterative reweighted least squares scenario. The conjugate gradient algorithm is used to minimize the proposed criterion function. Finally, numerical examples are given to demonstrate the validity of the method proposed.

2

Określanie wielkości buforów czasu w odpornych harmonogramach budowlanych

Jaśkowski P., Biruk S.

Zeszyty Naukowe / Wyższa Szkoła Oficerska Wojsk Lądowych im. gen. T. Kościuszki

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2010

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Nr 3

366-377

PL

Podstawowym zadaniem harmonogramu budowlanego jest ustalenie terminów realizacji poszczególnych procesów w sposób zapewniający osiągnięcie założonych celów przedsięwzięcia. Istnieje wiele metod harmonogramowania przedsięwzięć budowlanych w warunkach deterministycznych, jednak realizacja przedsięwzięć jest podatna na oddziaływanie różnych czynników ryzyka, co może prowadzić do dezaktualizacji wcześniej opracowanych planów, sporządzanych tymi metodami. W artykule jest prezentowana metoda tworzenia harmonogramów budowlanych odpornych na zakłócenia realizacyjne, polegająca na alokacji zapasu czasu ciągów czynności w postaci buforów czasu. Wielkość buforów jest określana na podstawie badań symulacyjnych i z zastosowaniem programowania matematycznego. Stabilność harmonogramu opracowanego w przykładzie z wykorzystaniem proponowanej metody porównano z wynikami uzyskanymi przy zastosowaniu innej znanej metody heurystycznej.

EN

The assumption of static and deterministic conditions is common in the practice of construction project planning. However, at the construction phase, projects are subject to uncertainty. This may lead to serious schedule disruptions and, as a consequence, serious revisions of the schedule baseline. The paper focuses on the problem of constructing robust project schedules with a proactive procedure. Robust project scheduling aims at constructing schedules to cope with multiple disruptions during project execution. The method proposed by the authors, based on simulation technique and mathematical programming, was applied to scheduling a sample project. The results were compared, in terms of schedule stability, to those of the float factor heuristic procedure.

3

Modelowanie zakłóceń impulsowych w przetwarzaniu sygnałów biomedycznych

Pander T.

Pomiary Automatyka Kontrola

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2007

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R. 53, nr 9 bis

429--432

PL

Literatura cyfrowego przetwarzania sygnałów jest zdominowana przez założenie o gaussowskim charakterze zakłóceń. Jednak w rzeczywistych warunkach zakłócenia charakteryzują się rozkładami innymi niż gaussowskie. Często zakłócenia mają charakter impulsowy. Z uwagi na dużą liczbę sygnałów elektrofizjologicznych, do badań został wybrany sygnał EKG. Podczas przeprowadzania prób wysiłkowych zakłócenia mięśniowe wykazują charakter impulsowy. Celem pracy jest przedstawienie różnych modeli zakłóceń impulsowych stosowanych do zakłócania sygnałów biomedycznych. W pracy zostaną przedstawione następujące modele zakłóceń: Gaussa-Bernoulliego, Gaussa-Laplace'a, Gaussa-Cauchy'ego oraz model wykorzystujący symetryczne rozkłady alfa-stabilne. Symulowane zakłócenia są dodawane do sygnału o zadanej wartości SNR. Następnie wykorzystując filtrację liniową oraz nieliniową zostaną zmierzone zniekształcenia resztowe w sygnale po filtracji.

EN

A literature of digital signal processing is dominated by the assumption of Gaussian distribution of disturbances. But in a real world of signals such statement is too optimistic. Some noises distributions differ from the idealistic Gaussian model. Noises are often impulsive in their nature. There exists many different electrophysiological signals, but for the purpose of this work the electrocardiogram (ECG signal) was chosen. This signal is almost always disturbed by a noise. A noise that appears in ECG signals during the stress test (mainly a muscle noise) has an impulsive nature. The main aim of this work is to present different models of an impulsive noise. In this paper the following models of impulsive disturbances are introduced: a Gaussian-Bernoulli, a Gaussian-Laplace, a Gaussian-Cauchy and a symmetric alpha-stable model. Simulated noise is added to signal with known values of SNR. Then the linear and nonlinear filtering methods are applied and the rest distortions in a filtered signal are measured.

4

Kernel Ho-Kashyap classifier with generalization control

Łęski J.

International Journal of Applied Mathematics and Computer Science

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2004

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Vol. 14, no 1

53-61

EN

This paper introduces a new classifier design method based on a kernel extension of the classical Ho-Kashyap procedure. The proposed method uses an approximation of the absolute error rather than the squared error to design a classifier, which leads to robustness against outliers and a better approximation of the misclassification error. Additionally, easy control of the generalization ability is obtained using the structural risk minimization induction principle from statistical learning theory. Finally, examples are given to demonstrate the validity of the introduced method.

5

Improving the Generalization Ability of Neuro-Fuzzy Systems by e-Insensitive Learning

Łęski J.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 3

437-447

EN

A new learning method tolerant of imprecision is introduced and used in neuro-fuzzy modelling. The proposed method makes it possible to dispose of an intrinsic inconsistency of neuro-fuzzy modelling, where zero-tolerance learning is used to obtain a fuzzy model tolerant of imprecision. This new method can be called e-insensitive learning, where, in order to fit the fuzzy model to real data, the e-insensitive loss function is used. e-insensitive learning leads to a model with minimal Vapnik-Chervonenkis dimension, which results in an improved generalization ability of this system. Another advantage of the proposed method is its robustness against outliers. This paper introduces two approaches to solving e-insensitive learning problem. The first approach leads to a quadratic programming problem with bound constraints and one linear equality constraint. The second approach leads to a problem of solving a system of linear inequalities. Two computationally efficient numerical methods for e-insensitive learning are proposed. Finally, examples are given to demonstrate the validity of the introduced methods.

6

Epsilon-Insensitive Fuzzy c-Medians Clustering

Łęski J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2002

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Vol. 50, Nr 4

361--374

EN

Fuzzy clustering helps to find natural vague boundaries in data. The fuzzy C-Means (FCM) method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensivity to presence of noise and outliers in data. This paper introduces a new ε-insensitive Fuzzy C-Medians (εFCMed) clustering algorithm. As a special case, this algorithm includes the well-known Fuzzy C-Medians method (FCMed). Performance of the new clustering algorithm is experimentally compared with the Fuzzy C-Means (FCM) and the FCMed methods using synthetic heavy-tailed and overlapped groups in background noise, and the Iris database.

7

Minimum absolute error classifier design with generalization control

Łęski J.

Archives of Control Sciences

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2002

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Vol. 12, no. 3

289-299

EN

This paper introduces a new classifier design method, that is based on an extension of the classical Ho-Kashyap procedure. The proposed method uses absolute error rather than square errorto design a linear classifier. Additionally, easy control of generalization ability and outliers robustness is obtained. Finally, examples are giver to demonstrate the validity of the introduced method.

8

An varepsilon-Insensitive Approach to Fuzzy Clustering

Łęski J.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 4

993-1007

EN

Fuzzy clustering can be helpful in finding natural vague boundaries in data. The fuzzy c-means method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in the data. The present paper introduces a new varepsilon-insensitive Fuzzy C-Means (varepsilonFCM) clustering algorithm. As a special case, this algorithm includes the well-known Fuzzy C-Medians method (FCMED). The performance of the new clustering algorithm is experimentally compared with the Fuzzy C-Means (FCM) method using synthetic data with outliers and heavy-tailed, overlapped groups of the data.

9

Robust possibilistic clustering

Łęski J.

Archives of Control Sciences

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2000

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Vol. 10, no. 3/4

141-155

EN

Fuzzy and possibilistic clustering helps to find natural vague boundaries in data and has long been a popular unsupervised learning method. The Fuzzy C-Means (FCM) method is one of the most popular clustering methods based on minimization of a criterion function. However, one of the greatest disadvantages of this method is its sensitivity to the presence of noise and outliers in data. The FCM applies the constraint that the memberships of each datum across groups sum to 1. Due to this constraint and L/sub 2/ norm as the dissimilarity measure, the FCM has considerable trouble in a noisy environment. In possibilistic C-means (PCM) the above constraint is not used. In this case membership values may be interpreted as degrees of possibility that the datum belongs to the groups. In the possibilistic approach still L/sub 2/ norm is usually used and the second reason of sensitivity for outliers and noise remains. This paper introduces a new epsilon -insensitive Possibilistic C-Means ( epsilon PCM) clustering algorithm. The performance of the new clustering algorithm is experimentally compared with the PCM method using simple two-dimensional synthetic data with outliers and the real-world Iris database.