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EN
Fluctuation of groundwater levels around the world is an important theme in hydrological research. Rising water demand, faulty irrigation practices, mismanagement of soil and uncontrolled exploitation of aquifers are some of the reasons why groundwater levels are fluctuating. In order to effectively manage groundwater resources, it is important to have accurate readings and forecasts of groundwater levels. Due to the uncertain and complex nature of groundwater systems, the development of soft computing techniques (data-driven models) in the field of hydrology has significant potential. This study employs two soft computing techniques, namely, extreme learning machine (ELM) and support vector machine (SVM) to forecast groundwater levels at two observation wells located in Canada. A monthly data set of eight years from 2006 to 2014 consisting of both hydrological and meteorological parameters (rainfall, temperature, evapotranspiration and groundwater level) was used for the comparative study of the models. These variables were used in various combinations for univariate and multivariate analysis of the models. The study demonstrates that the proposed ELM model has better forecasting ability compared to the SVM model for monthly groundwater level forecasting.
PL
Na całym świecie fluktuacje poziomów wód gruntowych stanowią ważny temat badań hydrologicznych. Rosnące potrzeby wodne, błędne praktyki irygacyjne, niewłaściwa gospodarka glebowa i niekontrolowana eksploatacja poziomów wodonośnych są powodami, dla których poziom wód gruntowych podlega fluktuacjom. Dla skutecznego zarządzania zasobami wód gruntowych istotne jest dysponowanie dokładnymi zapiskami i zdolność prognozowania poziomu tych wód. Rozwój technik komputerowych (modele wykorzystujące dane) w dziedzinie hydrologii ma istotny potencjał z powodu niepewnego i złożonego charakteru systemów wód gruntowych. W prezentowanych badaniach wykorzystano dwie techniki komputerowe: maszynę uczenia ekstremalnego (ELM) i maszynę wektorów nośnych (SVM – ang. support vector machine) do przewidywania poziomów wód gruntowych w dwóch studzienkach obserwacyjnych w Kanadzie. Do porównawczych badań modeli wykorzystano zestaw danych miesięcznych z ośmiu lat (2006–2014), składający się z danych hydrologicznych i meteorologicznych (opady, temperatura, ewapotranspiracja, poziom wody). Wymienione zmienne zastosowano w rozmaitych kombinacjach do jedno- i wieloparametrycznej analizy modeli. Wyniki dowodzą, że model ELM ma lepsze zdolności przewidywania miesięcznych poziomów wód gruntowych w porównaniu z modelem SVM.
2
Content available remote Volcanic ash cloud detection from MODIS image based on CPIWS method
EN
Volcanic ash cloud detection has been a difficult problem in moderate-resolution imaging spectroradiometer (MODIS) multispectral remote sensing application. Principal component analysis (PCA) and independent component analysis (ICA) are effective feature extraction methods based on second-order and higher order statistical analysis, and the support vector machine (SVM) can realize the nonlinear classification in low-dimensional space. Based on the characteristics of MODIS multispectral remote sensing image, via presenting a new volcanic ash cloud detection method, named combined PCA-ICA-weighted and SVM (CPIWS), the current study tested the real volcanic ash cloud detection cases, i.e., Sangeang Api volcanic ash cloud of 30 May 2014. Our experiments suggest that the overall accuracy and Kappa coefficient of the proposed CPIWS method reach 87.20 and 0.7958%, respectively, under certain conditions with the suitable weighted values; this has certain feasibility and practical significance.
EN
Operation of a sewage treatment plant is a complex task because it requires maintaining the parameters of its activities at the appropriate level in order to achieve the desired effect of reducing pollution and reduce the flow of sediment discharged from the biological reactor. The basis for predicting the amount of excess sludge and operational parameters WWTP can provide physical models describing the biochemical changes occurring in the reactor, in which the input parameters, ie. Indicators of effluent quality and quantity of wastewater are modeled in advance. However, due to numerous interactions and uncertainty of the data in the physical models and forecast errors parameters of the inlet to the treatment plant Simulation results may be affected by significant errors. Therefore, to minimize the prediction error parameters of operation of the technological objects deliberate use of a black box model. In these models at the stage of learning is generated model structure underlying the projections analyzed the operating parameters of the plant. This publication presents the possibility of the use of methods: support vector, k – nearest neighbour and trees reinforced to predict the amount of the resulting excess sludge during wastewater treatment in the WWTP located in Sitkówka – News with a capacity of 72,000 3/d with a load of 275,000 PE . Due to the fact that did not have the quality parameters of wastewater at the inlet to the activated sludge chambers it was not possible to verify the empirical relationships commonly used in engineering practice to determine the size of the daily flow of excess sludge. Due to the significant differences in the amount of excess sludge generated in the period (t = 1-7 days) the simulation of the amount of sludge into the time were performed. To assessment the compatibility of measurement results and simulations quantities of sludge the mean absolute error and relative error of prediction for the considered parameter of technology was used. The analyzes carried out revealed that the amount of generated excess sludge can be predicted on the basis of parameters describing the quantity and quality of influent waste water (slurry concentration of total nitrogen and total phosphorus, BOD5) and the operating parameters of the biological reactor (recirculation rate, concentration and temperature of the sludge, the dosed amount of methanol and PIX). On the basis of computations, it can be concluded that the most accurate forecasting results amounts of sediment were obtained by using a reinforced trees (t = 2 to 5 days) and Support Vector Machines methods (t = 1, 6, 7 days). While the highest values of forecast errors sediments was obtained using a k – nearest neighbor (t = 2 to 5 days) and reinforced trees (t = 1, 6, 7 days).
EN
The simplest classification task is to divide a set of objects into two classes, but most of the problems we find in real life applications are multi-class. There are many methods of decomposing such a task into a set of smaller classification problems involving two classes only. Among the methods, pairwise coupling proposed by Hastie and Tibshirani (1998) is one of the best known. Its principle is to separate each pair of classes ignoring the remaining ones. Then all objects are tested against these classifiers and a voting scheme is applied using pairwise class probability estimates in a joint probability estimate for all classes. A closer look at the pairwise strategy shows the problem which impacts the final result. Each binary classifier votes for each object even if it does not belong to one of the two classes which it is trained on. This problem is addressed in our strategy. We propose to use additional classifiers to select the objects which will be considered by the pairwise classifiers. A similar solution was proposed by Moreira and Mayoraz (1998), but they use classifiers which are biased according to imbalance in the number of samples representing classes.
EN
The aim of this paper is to introduce a strategy to find a minimal set of test nodes for diagnostics of complex analog systems with single parametric faults using the support vector machine (SVM) classifier as a fault locator. The results of diagnostics of a video amplifier and a low-pass filter using tabu search along with genetic algorithms (GAs) as node selectors in conjunction with the SVM fault classifier are presented. General principles of the diagnostic procedure are first introduced, and then the proposed approach is discussed in detail. Diagnostic results confirm the usefulness of the method and its computational requirements. Conclusions on its wider applicability are provided as well.
PL
W elektrofizjologicznym badaniu wzroku najczęściej wykorzystuje się wzrokowe potencjały wywołane, które charakteryzują się kolejno ułożonymi w funkcji czasu ekstremami, zwanymi falami lub załamkami. Morfologia przebiegu, a w szczególności zależności czasowe i amplitudowe poszczególnych fal, umożliwiają neurologowi postawienie diagnozy, co nie jest zadaniem prostym. Wymaga od neurologa doświadczenia, skupienia uwagi i bardzo dobrej percepcji. W celu wsparcia procesu diagnostycznego autor opracował algorytm realizujący zautomatyzowaną klasyfikację słuchowych potencjałów wywołanych do grupy przypadków patologicznych lub prawidłowych. Czułość metody w 100 osobowym zbiorze przypadków określono na 94%, przy 16% prawdopodobieństwie fałszywego alarmu, co z medycznego punktu widzenia jest wynikiem satysfakcjonującym.
EN
In electrophysiological examination of sight are most often used visual evoked potentials which are characterized by extremes, called waves, successively arranged on timeline. Morphology of the waveforms, in particular, the timing and amplitude of each wave, allow neurologist diagnosis, which is not an easy task. Neurologist requires experience, attention and very good perception. In order to support the diagnostic process, the author have developed an algorithm implementing the automated classification of visual evoked potentials to the group of pathological or physiological cases. For a set of cases numbering 100 people, the sensitivity of the method is 94%, with 16% probability of false alarm. The obtained result is satisfactory from a medical point of view.
7
Content available remote DIFFRACT: DIaphyseal Femur FRActure Classifier SysTem
EN
Determining the types of fractured bones is the most important step of fracture treatment. Different fracture cases may be observed in daily life and each of them may require a specific treatment. It is not possible for a physician to know all fracture types and treatment methods by heart. Therefore, it is needed an effective solution to facilitate such a tedious process. Based on this need, we propose an auxiliary tool called a DIaphyseal Femur FRActure Classifier SysTem (DIFFRACT). The DIFFRACT can automatically classify diaphyseal femur fractures according to the Müller AO Classification system on X-ray images. In DIFFRACT, we have used the Niblack thresholding method to segment X-ray images. We have observed that Niblack is the most effective method for the segmentation of fractured bones since it does not lose information related to the fracture region. Moreover, we have developed a novel pre-processing method called a support vector machine (SVM) based sensitive noise remover to remove the noises occurring in the segmentation step. In addition, we have innovatively proposed two combined feature extraction methods, the bone completeness indicator (BCI) and fractured region mapping (FRM), to classify different types of fractures. We have used a multi-class SVM to determine the type of bone fractures. Based on the detailed experiments, 196 X-ray images were classified into nine classes according to AO-32 with 89.87% success rate. The DIFFRACT may be used as supplementary tool for the determination of fractured femur bones by physicians. It may facilitate decision making process of the physicians.
EN
In this paper we showed the method of resistive gas sensors data processing. The UV irradiation and temperature modulation was applied to improve gas sensors’ selectivity and sensitivity. Noise voltage across the sensor’s terminals (proportional to its resistance fluctuations) was recorded to estimate power spectral density. This function was an input data vector for LS-SVM (least squares – support vector machine) algorithm, which predicted a concentration of gas present in sensor’s ambient atmosphere. The algorithm creates a non-linear regression model at learning stage. This model can be used to predict gas concentration by recording resistance noise only. We have proposed a fast method of selecting LS-SVM parameters to determine high quality model. The method utilizes a behavior of immune system to determine optimal parameters of the LS-SVM algorithm. High accuracy of the applied method was proved for the recorded experimental data.
PL
W artykule pokazano metodę przetwarzania danych z rezystancyjnych czujników gazów, stosowaną do wykrywania gazów. W celu zwiększenia czułości i selektywności czujników zastosowano modulację temperaturową oraz oświetlenie diodą LED UV aby zebrać więcej danych. Szumy napięciowe rejestrowane na zaciskach czujnika (proporcjonalne do fluktuacji jego rezystancji) zostały wykorzystane do wyznaczenia gęstości widmowej mocy. Ta funkcja stanowiła wektor danych wejściowych dla algorytmu maszyny wektorów nośnych według kryterium najmniejszych kwadratów (LS-SVM), umożliwiając określenie stężenia gazu występującego w atmosferze otaczającej czujnik. Nieliniowy charakter algorytmu pozwala na tworzenie w fazie uczenia modelu na podstawie danych uzyskanych z pomiarów za pomocą metody odniesienia. Pokazano szybki sposób doboru optymalnych parametrów algorytmu LS-SVM, gwarantujących skuteczność szacowania stężenia gazu. W badaniach wykorzystano metodę symulującą działanie systemu odpornościowego. Analiza danych eksperymentalnych potwierdziła skuteczność prezentowanej metody.
EN
The present study aims to apply a least squares support vector model (LS–SVM) for predicting cleaning efficiency of an electromagnetic filtration process, also called quality factor, in order to remove corrosion particles (rust) of low concentrations from water media. For this purpose, three statistical parameters: correlation coefficient, root mean squared error and mean absolute percentage error were calculated for evaluating the performance of the LS–SVM model. It was found that the developed LS–SVM can be used to predict the effectiveness of electromagnetic filtration process.
EN
This paper proposes a soft sensing method of least squares support vector machine (LS-SVM) using temperature time series for gas flow measurements. A heater unit has been installed on the external wall of a pipeline to generate heat pulses. Dynamic temperature signals have been collected upstream of the heater unit. The temperature time series are the main secondary variables of soft sensing technique for estimating the flow rate. A LS-SVM model is proposed to construct a non-linear relation between the flow rate and temperature time series. To select its inputs, parameters of the measurement system are divided into three categories: blind, invalid and secondary variables. Then the kernel function parameters are optimized to improve estimation accuracy. The experiments have been conducted both in the single-pulse and multiple-pulse heating modes. The results show that estimations are acceptable.
EN
Power electronic circuits (PECs) are prone to various failures, whose classification is of paramount importance. This paper presents a data-driven based fault diagnosis technique, which employs a support vector data description (SVDD) method to perform fault classification of PECs. In the presented method, fault signals (e.g. currents, voltages, etc.) are collected from accessible nodes of circuits, and then signal processing techniques (e.g. Fourier analysis, wavelet transform, etc.) are adopted to extract feature samples, which are subsequently used to perform offline machine learning. Finally, the SVDD classifier is used to implement fault classification task. However, in some cases, the conventional SVDD cannot achieve good classification performance, because this classifier may generate some so-called refusal areas (RAs), and in our design these RAs are resolved with the one-against-one support vector machine (SVM) classifier. The obtained experiment results from simulated and actual circuits demonstrate that the improved SVDD has a classification performance close to the conventional one-against-one SVM, and can be applied to fault classification of PECs in practice.
EN
This paper presents the design process and the results of a novel fall detector designed and constructed at the Faculty of Electronics, Military University of Technology. High sensitivity and low false alarm rates were achieved by using four independent sensors of varying physical quantities and sophisticated methods of signal processing and data mining. The manuscript discusses the study background, hardware development, alternative algorithms used for the sensor data processing and fusion for identification of the most efficient solution and the final results from testing the Android application on smartphone. The test was performed in four 6-h sessions (two sessions with female participants at the age of 28 years, one session with male participants aged 28 years and one involving a man at the age of 49 years) and showed correct detection of all 40 simulated falls with only three false alarms. Our results confirmed the sensitivity of the proposed algorithm to be 100% with a nominal false alarm rate (one false alarm per 8 h).
EN
: The aim of this study was to create a two-class brain-computer interface. As in the case of research on SSVEP stimuli flashing at different frequencies were presented to four subjects. Optimal SSVEP recognition results can be obtained from electrodes: O1, O2 and Oz. In this work SVM classifier with Bilinear Separation algorithm have been compared. The best result in the offline tests using Bilinear Separation was: average accuracy of stimuli recognition 93% and ITR 33.1 bit/min, SVM: 90% and 32.8 bit/min.
EN
Groundwater contamination due to leakage of gasoline is one of the several causes which affect the groundwater environment by polluting it. In the past few years, In-situ bioremediation has attracted researchers because of its ability to remediate the contaminant at its site with low cost of remediation. This paper proposed the use of a new hybrid algorithm to optimize a multi-objective function which includes the cost of remediation as the first objective and residual contaminant at the end of the remediation period as the second objective. The hybrid algorithm was formed by combining the methods of Differential Evolution, Genetic Algorithms and Simulated Annealing. Support Vector Machines (SVM) was used as a virtual simulator for biodegradation of contaminants in the groundwater flow. The results obtained from the hybrid algorithm were compared with Differential Evolution (DE), Non Dominated Sorting Genetic Algorithm (NSGA II) and Simulated Annealing (SA). It was found that the proposed hybrid algorithm was capable of providing the best solution. Fuzzy logic was used to find the best compromising solution and finally a pumping rate strategy for groundwater remediation was presented for the best compromising solution. The results show that the cost incurred for the best compromising solution is intermediate between the highest and lowest cost incurred for other non-dominated solutions.
PL
Zanieczyszczenie wód gruntowych wyciekami benzyny jest jedną z kilku przyczyn wpływających na środowisko wód podziemnych. W ostatnich latach bioremediacja in situ przyciągała uwagę badaczy z powodu jej zdolności do usuwania zanieczyszczeń w ich siedlisku i niskich kosztów procesu. Przedstawiona praca proponuje użycie nowego algorytmu hybrydowego do optymalizacji wielozadaniowej funkcji, która obejmuje koszty remediacji jako pierwsze zadanie i resztową zawartość zanieczyszczeń po zakończeniu procesu jako drugie z zadań. Algorytm hybrydowy powstał z połączenia metod różnicowej ewolucji, algorytmu genetycznego i symulowanego wyżarzania. Maszyna wektorów nośnych (SVM) została użyta jako wirtualny symulator biologicznej degradacji zanieczyszczeń w wodach gruntowych. Wyniki uzyskane z algorytmy hybrydowego porównano z wynikami zróżnicowanej ewolucji (DE), algorytmu genetycznego (NSGA II) i symulowanego wyżarzania (SA). Stwierdzono, że proponowany algorytm był w stanie zapewnić najlepsze rozwiązanie. Użyto metody z zakresu logiki rozmytej dla znalezienia najlepszego rozwiązania kompromisowego i na końcu przedstawiono dla tego rozwiązania strategię szybkości pompowania celem remediacji wód gruntowych. Wyniki pokazały, że koszty ponoszone na rozwiązanie kompromisowe są pośrednie między najwyższymi i najniższymi kosztami innych rozwiązań.
EN
Bound-constrained Support Vector Machine(SVM) is one of the stateof- art model for binary classification. The decomposition method is currently one of the major methods for training SVMs, especially when the nonlinear kernel is used. In this paper, we proposed two new decomposition algorithms for training bound-constrained SVMs. Projected gradient algorithm and interior point method are combined together to solve the quadratic subproblem effciently. The main difference between the two algorithms is the way of choosing working set. The first one only uses first order derivative information of the model for simplicity. The second one incorporate part of second order information into the process of working set selection, besides the gradient. Both algorithms are proved to be global convergent in theory. New algorithms is compared with the famous package BSVM. Numerical experiments on several public data sets validate the effciency of the proposed methods.
PL
W elektrofizjologicznej ocenie słuchu oraz diagnozowaniu uszkodzeń pnia mózgu najczęściej wykorzystuje się słuchowe potencjały wywołane pnia mózgu o krótkiej latencji. Charakteryzują się one kolejno ułożonymi w funkcji czasu maksimami, zwanymi załamkami lub falami. Morfologia przebiegu, a w szczególności zależności czasowe i amplitudowe poszczególnych załamków, umożliwiają neurologowi postawienie diagnozy, co nie jest zadaniem prostym. Wymaga od neurologa doświadczenia, skupienia uwagi i bardzo dobrej percepcji. W celu wsparcia procesu diagnostycznego autorzy opracowali algorytm realizujący zautomatyzowaną klasyfikację słuchowych potencjałów wywołanych do grupy przypadków patologicznych i fizjologicznych, z czułością i specyficznością określoną na niezależnej grupie testowej liczącej 50 przypadków, wynoszącą odpowiednio 84% i 88%.
EN
For electrophysiological hearing assessment and diagnosis of brain stem lesions, the most often used are auditory brainstem evoked potentials of short latency. They are characterized by successively arranged maxima as a function of time, called waves. Morphology of the course, in particular, the timing and amplitude of each wave, allow a neurologist to make diagnose, what is not an easy task. A neurologist should be experienced, concentrated, and should have very good perception. In order to support his diagnostic process, the authors have developed an algorithm implementing the automated classification of auditory evoked potentials to the group of pathological and physiological cases, the sensitivity and specificity determined for an independent test group (of 50 cases) of respectively 84% and 88%.
PL
Zaprezentowane w niniejszym artykule badania stanowią kontynuację dotychczasowych prac mających na celu opracowanie mobilnego detektora upadków. Przedstawiony algorytm opiera się na dyskretnej transformacji falkowej sygnałów z dostępnych w detektorze sensorów oraz pojedynczym klasyfikatorze w postaci sieci wektorów nośnych - SVM (ang. Support Vector Machine). Do procesu redukcji cech zastosowano miarę istotności Fishera. W wyniku zmniejszenia liczby cech zmniejszeniu uległa również liczba wektorów nośnych sieci SVM, mająca bezpośredni wpływ na górne oszacowanie błędu klasyfikacji. Na podstawie otrzymanych wyników wyznaczono parametry klasyfikatora pozwalające na zaprezentowanie opracowanej koncepcji w polu krzywych ROC (ang. Receiver Operating Characteristics) oraz porównanie ich z wynikami otrzymanymi dla pojedynczych sensorów detektora. Opracowana koncepcja daje zdecydowanie lepsze rezultaty niż każdy z sensorów działający niezależnie. Rezultaty przeprowadzonych badań dały bardzo dobre wyniki w porównaniu z dotychczasowymi wynikami, przy znacznej redukcji liczby wymaganych deskryptorów. Z uwagi na ścisłą zależność pomiędzy liczbą danych uczących oraz liczbą wektorów nośnych, które bezpośrednio wpływają na górne oszacowanie błędu klasyfikacji, dokonano redukcji deskryptorów. W rezultacie uzyskano zadowalające efekty przy redukcji liczby deskryptorów z 38 do zaledwie 6, zapewniając, że górne oszacowanie błędu klasyfikacji, w zbiorze nowych danych testowych nie przekracza 5,3%.
EN
The studies presented in this article are the continuation of previous work to develop a mobile fall detector. The algorithm is based on a discrete wavelet transform of the signals from the sensors available at the detector and a linear support vector machine as a classifier. Fisher score method is used for feature selection in the proposed algorithm. As a result of reducing the number of features, the number of support vectors has been also reduced - it has a direct impact on the upper estimate of the classification error. On the basis of the obtained results, the classifier parameters have been calculated. This allows presenting the developed concept in the field of ROC curves (Receiver Operating Characteristics) and their comparison with the results obtained for individual sensors. The developed concept gives much better results than each of the sensors acting independently. The findings of this study have given very good results in comparison with the previous findings, with a significant reduction in the number of required features. Due to the close relationship between the number of training data and the number of support vectors which directly affect the upper estimate of the classification error, the number of features has been reduced. Finally, satisfactory results have been obtained with the reduction of the number of features from 38 to just six, ensuring that the upper estimation of the classification error in the set of the new test data does not exceed 5.3%.
EN
Environmental microorganisms (EMs) are single-celled or multi-cellular microscopic organ-isms living in the environments. They are crucial to nutrient recycling in ecosystems as they act as decomposers. Occurrence of certain EMs and their species are very informative indicators to evaluate environmental quality. However, the manual recognition of EMs in microbiological laboratories is very time-consuming and expensive. Therefore, in this article an automatic EM classification system based on content-based image analysis (CBIA) techniques is proposed. Our approach starts with image segmentation that determines the region of interest (EM shape). Then, the EM is described by four different shape descriptors, whereas the Internal Structure Histogram (ISH), a new and original shape feature extraction technique introduced in this paper, has turned out to possess the most discriminative properties in this application domain. Afterwards, for each descriptor a support vector machine (SVM) is constructed to distinguish different classes of EMs. At last, results of SVMs trained for all four feature spaces are fused in order to obtain the final classification result. Experimental results certify the effectiveness and practicability of our automatic EM classification system.
19
PL
Metody automatycznego rozpoznawania wieku i płci pozwalają na rozpoznanie cech osoby mówiącej tylko na podstawie nagrania jej wypowiedzi. Mowa ludzka, poza werbalnym komunikatem, niesie ze sobą informacje dotyczące osoby mówiącej. Nagranie mowy osoby pozwala na wyodrębnienie takich informacji, jak jej płeć, wiek, a także emocje. Zaprezentowano przegląd metod rozpoznawania wieku i płci osób na podstawie ich mowy oraz wykonano implementację i przetestowano połączenie metod wyznaczania parametrów MFCC (współczynniki analizy cepstralnej w skali mel (Mel-frequency Cepstral Coefficients) i wysokości tonu głosu f0 oraz algorytmu SVM (metoda wektorów nośnych - Support Vector Machines) do klasyfikacji próbek głosowych. Testy zaimplementowanego rozwiązania pozwalają stwierdzić, że metoda jest skuteczna w większości przypadków testowych.
EN
Methods for automatic recognition of the age and gender characteristics allow the identification of the person only on the basis of recording of this person speech. Human speech, beyond verbal communication, gives an information about the speaking person. Speech recording allows the identification personal characteristics such as gender, age, and the emotions. The paper presents an overview of methods of age and gender recognition of people based on their speech. A combination of methods for determining the parameters MFCC (Mel-frequency Cepstral Coefficients) and pitch of voice (f0) and SVM (Support Vector Machines) algorithm for the classification of voice samples is implanted and tested. It was demonstrated that the method is effective in the majority of test cases.
PL
W artykule przedstawiono podstawowe zasady budowania i uczenia sieci neuronowych, zwane techniką wektorów podtrzymujących (ang. Support Vector Machine - SVM), wraz z perspektywą aplikacji tego rodzaju sieci. Sieci SVM znajdują zastosowanie głównie w rozwiązywaniu zadań klasyfikacji danych liniowo separowalnych i liniowo nieseparowalnych oraz zadań regresji. W podjętej pracy sieci SVM wykorzystano do klasyfikacji danych separowalnych liniowo, w celu sformułowania modelu przemieszczeń punktów reprezentujących monitorowany obiekt. Zagadnienie uczenia sieci wymaga implementacji programowania kwadratowego w poszukiwaniu punktu optymalnego funkcji Lagrange’a względem optymalizowanych parametrów. Estymowane parametry decydują o położeniu hiperpłaszczyzny maksymalizującej margines separacji obu klas.
EN
The article presents an approach for constructing and teaching networks called the SVM (Support Vector Machine) technique. The SVM network is used for classifying linearly separable and linearly inseparable data, and the problem of regression. In this paper the SVM technique is used for classifying linearly separable data in the form of vertical displacements of points in a measurement-control geodetic network set up on a building situated on expansive soil.
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