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1.
Diseases ; 6(2)2018 Apr 13.
Artigo em Inglês | MEDLINE | ID: mdl-29652794

RESUMO

Increased blood pressure in the pulmonary artery is referred to as pulmonary hypertension and often is linked to loud pulmonic valve closures. For the purpose of this paper, it was hypothesized that pulmonary circulation vibrations will create sounds similar to sounds created by vocal cords during speech and that subjects with pulmonary artery hypertension (PAH) could have unique sound signatures across four auscultatory sites. Using a digital stethoscope, heart sounds were recorded at the cardiac apex, 2nd left intercostal space (2LICS), 2nd right intercostal space (2RICS), and 4th left intercostal space (4LICS) undergoing simultaneous cardiac catheterization. From the collected heart sounds, relative power of the frequency band, energy of the sinusoid formants, and entropy were extracted. PAH subjects were differentiated by applying the linear discriminant analysis with leave-one-out cross-validation. The entropy of the first sinusoid formant decreased significantly in subjects with a mean pulmonary artery pressure (mPAp) ≥ 25 mmHg versus subjects with a mPAp < 25 mmHg with a sensitivity of 84% and specificity of 88.57%, within a 10-s optimized window length for heart sounds recorded at the 2LICS. First sinusoid formant entropy reduction of heart sounds in PAH subjects suggests the existence of a vowel-like pattern. Pattern analysis revealed a unique sound signature, which could be used in non-invasive screening tools.

2.
Sci Rep ; 6: 33182, 2016 09 09.
Artigo em Inglês | MEDLINE | ID: mdl-27609672

RESUMO

We hypothesized that an automated speech- recognition-inspired classification algorithm could differentiate between the heart sounds in subjects with and without pulmonary hypertension (PH) and outperform physicians. Heart sounds, electrocardiograms, and mean pulmonary artery pressures (mPAp) were recorded simultaneously. Heart sound recordings were digitized to train and test speech-recognition-inspired classification algorithms. We used mel-frequency cepstral coefficients to extract features from the heart sounds. Gaussian-mixture models classified the features as PH (mPAp ≥ 25 mmHg) or normal (mPAp < 25 mmHg). Physicians blinded to patient data listened to the same heart sound recordings and attempted a diagnosis. We studied 164 subjects: 86 with mPAp ≥ 25 mmHg (mPAp 41 ± 12 mmHg) and 78 with mPAp < 25 mmHg (mPAp 17 ± 5 mmHg) (p < 0.005). The correct diagnostic rate of the automated speech-recognition-inspired algorithm was 74% compared to 56% by physicians (p = 0.005). The false positive rate for the algorithm was 34% versus 50% (p = 0.04) for clinicians. The false negative rate for the algorithm was 23% and 68% (p = 0.0002) for physicians. We developed an automated speech-recognition-inspired classification algorithm for the acoustic diagnosis of PH that outperforms physicians that could be used to screen for PH and encourage earlier specialist referral.


Assuntos
Diagnóstico por Computador , Hipertensão Pulmonar/diagnóstico , Interface para o Reconhecimento da Fala , Acústica , Adolescente , Adulto , Idoso , Idoso de 80 Anos ou mais , Algoritmos , Criança , Pré-Escolar , Feminino , Ruídos Cardíacos , Humanos , Lactente , Masculino , Pessoa de Meia-Idade , Médicos , Curva ROC , Adulto Jovem
3.
Pulm Circ ; 5(4): 631-9, 2015 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-26697170

RESUMO

We hypothesized that vibrations created by the pulmonary circulation would create sound like the vocal cords during speech and that subjects with pulmonary artery hypertension (PAH) might have a unique sound signature. We recorded heart sounds at the cardiac apex and the second left intercostal space (2LICS), using a digital stethoscope, from 27 subjects (12 males) with a median age of 7 years (range: 3 months-19 years) undergoing simultaneous cardiac catheterization. Thirteen subjects had mean pulmonary artery pressure (mPAp) < 25 mmHg (range: 8-24 mmHg). Fourteen subjects had mPAp ≥ 25 mmHg (range: 25-97 mmHg). We extracted the relative power of the frequency band, the entropy, and the energy of the sinusoid formants from the heart sounds. We applied linear discriminant analysis with leave-one-out cross validation to differentiate children with and without PAH. The significance of the results was determined with a t test and a rank-sum test. The entropy of the first sinusoid formant contained within an optimized window length of 2 seconds of the heart sounds recorded at the 2LICS was significantly lower in subjects with mPAp ≥ 25 mmHg relative to subjects with mPAp < 25 mmHg, with a sensitivity of 93% and specificity of 92%. The reduced entropy of the first sinusoid formant of the heart sounds in children with PAH suggests the existence of an organized pattern. The analysis of this pattern revealed a unique sound signature, which could be applied to a noninvasive method to diagnose PAH.

4.
PLoS One ; 10(12): e0143146, 2015.
Artigo em Inglês | MEDLINE | ID: mdl-26629704

RESUMO

BACKGROUND: Automatic detection of the 1st (S1) and 2nd (S2) heart sounds is difficult, and existing algorithms are imprecise. We sought to develop a wavelet-based algorithm for the detection of S1 and S2 in children with and without pulmonary arterial hypertension (PAH). METHOD: Heart sounds were recorded at the second left intercostal space and the cardiac apex with a digital stethoscope simultaneously with pulmonary arterial pressure (PAP). We developed a Daubechies wavelet algorithm for the automatic detection of S1 and S2 using the wavelet coefficient 'D6' based on power spectral analysis. We compared our algorithm with four other Daubechies wavelet-based algorithms published by Liang, Kumar, Wang, and Zhong. We annotated S1 and S2 from an audiovisual examination of the phonocardiographic tracing by two trained cardiologists and the observation that in all subjects systole was shorter than diastole. RESULTS: We studied 22 subjects (9 males and 13 females, median age 6 years, range 0.25-19). Eleven subjects had a mean PAP < 25 mmHg. Eleven subjects had PAH with a mean PAP ≥ 25 mmHg. All subjects had a pulmonary artery wedge pressure ≤ 15 mmHg. The sensitivity (SE) and positive predictivity (+P) of our algorithm were 70% and 68%, respectively. In comparison, the SE and +P of Liang were 59% and 42%, Kumar 19% and 12%, Wang 50% and 45%, and Zhong 43% and 53%, respectively. Our algorithm demonstrated robustness and outperformed the other methods up to a signal-to-noise ratio (SNR) of 10 dB. For all algorithms, detection errors arose from low-amplitude peaks, fast heart rates, low signal-to-noise ratio, and fixed thresholds. CONCLUSION: Our algorithm for the detection of S1 and S2 improves the performance of existing Daubechies-based algorithms and justifies the use of the wavelet coefficient 'D6' through power spectral analysis. Also, the robustness despite ambient noise may improve real world clinical performance.


Assuntos
Ruídos Cardíacos , Hipertensão Pulmonar/fisiopatologia , Análise de Ondaletas , Adolescente , Algoritmos , Criança , Pré-Escolar , Feminino , Humanos , Hipertensão Pulmonar/diagnóstico , Lactente , Masculino , Processamento de Sinais Assistido por Computador , Razão Sinal-Ruído , Estetoscópios , Adulto Jovem
5.
Int J Environ Res Public Health ; 12(10): 12776-91, 2015 Oct 14.
Artigo em Inglês | MEDLINE | ID: mdl-26473907

RESUMO

Recent clinical studies show that the contour of the photoplethysmogram (PPG) wave contains valuable information for characterizing cardiovascular activity. However, analyzing the PPG wave contour is difficult; therefore, researchers have applied first or higher order derivatives to emphasize and conveniently quantify subtle changes in the filtered PPG contour. Our hypothesis is that analyzing the whole PPG recording rather than each PPG wave contour or on a beat-by-beat basis can detect heat-stressed subjects and that, consequently, we will be able to investigate the impact of global warming on human health. Here, we explore the most suitable derivative order for heat stress assessment based on the energy and entropy of the whole PPG recording. The results of our study indicate that the use Int. J. Environ. Res. Public Health 2015, 7 12777 of the entropy of the seventh derivative of the filtered PPG signal shows promising results in detecting heat stress using 20-second recordings, with an overall accuracy of 71.6%. Moreover, the combination of the entropy of the seventh derivative of the filtered PPG signal with the root mean square of successive differences, or RMSSD (a traditional heart rate variability index of heat stress), improved the detection of heat stress to 88.9% accuracy.


Assuntos
Aquecimento Global , Frequência Cardíaca , Transtornos de Estresse por Calor/diagnóstico , Fotopletismografia , Adulto , Feminino , Voluntários Saudáveis , Humanos , Masculino
6.
Comput Methods Programs Biomed ; 122(3): 503-12, 2015 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-26498064

RESUMO

There are a limited number of studies on heat stress dynamics during exercise using the photoplethysmogram (PPG). We investigate the PPG signal and its derivatives for heat stress assessment using Welch (non-parametric) and autoregressive (parametric) spectral estimation methods. The preliminary results of this study indicate that applying the first and second derivatives to PPG waveforms is useful for determining heat stress level using 20-s recordings. Interestingly, Welch's and Yule-Walker's methods in agreement that the second derivative is an improved detector for heat stress. In fact, both spectral estimation methods showed a clear separation in the frequency domain between measurements before and after simulated heat-stress induction when the second derivative is applied. Moreover, the results demonstrate superior performance of the Welch's method over the Yule-Walker's method in separating before and after the three simulated heat-stress inductions.


Assuntos
Transtornos de Estresse por Calor/prevenção & controle , Fotopletismografia/métodos , Adulto , Feminino , Humanos , Masculino
7.
Sensors (Basel) ; 15(10): 24716-34, 2015 Sep 25.
Artigo em Inglês | MEDLINE | ID: mdl-26404271

RESUMO

There are a limited number of studies on heat stress dynamics during exercise using the photoplethysmogram (PPG) and its second derivative (APG). However, we investigate the most suitable index from short PPG signal recordings for heat stress assessment. The APG waveform consists of a, b, c and d waves in systole and an e wave in diastole. Our preliminary results indicate that the use of the energy of aa area, derived from PPG signals measured from emergency responders in tropical conditions, is promising in determining the heat stress level using 20-s recordings. After examining 14 time domain features using leave-one-out cross-validation, we found that the aa energy extracted from PPG signals is the most informative feature for classifying heat-stressed subjects, with an overall accuracy of 79%. Moreover, the combination of the aa energy with the traditional Sensors 2015, 15 24717 heart rate variability index of heat stress (i.e., the square root of the mean of the squares of the successive aa intervals) improved the heat stress detection to an overall accuracy of 83%.


Assuntos
Exercício Físico/fisiologia , Transtornos de Estresse por Calor/diagnóstico , Monitorização Ambulatorial/instrumentação , Adulto , Feminino , Dedos , Aquecimento Global , Frequência Cardíaca/fisiologia , Temperatura Alta , Humanos , Masculino , Monitorização Ambulatorial/métodos , Fotopletismografia/instrumentação , Fotopletismografia/métodos , Processamento de Sinais Assistido por Computador/instrumentação
8.
Biomed Eng Online ; 13: 139, 2014 Sep 25.
Artigo em Inglês | MEDLINE | ID: mdl-25252971

RESUMO

BACKGROUND: Analyzing acceleration photoplethysmogram (APG) signals measured after exercise is challenging. In this paper, a novel algorithm that can detect a waves and consequently b waves under these conditions is proposed. Accurate a and b wave detection is an important first step for the assessment of arterial stiffness and other cardiovascular parameters. METHODS: Nine algorithms based on fixed thresholding are compared, and a new algorithm is introduced to improve the detection rate using a testing set of heat stressed APG signals containing a total of 1,540 heart beats. RESULTS: The new a detection algorithm demonstrates the highest overall detection accuracy--99.78% sensitivity, 100% positive predictivity--over signals that suffer from 1) non-stationary effects, 2) irregular heartbeats, and 3) low amplitude waves. In addition, the proposed b detection algorithm achieved an overall sensitivity of 99.78% and a positive predictivity of 99.95%. CONCLUSIONS: The proposed algorithm presents an advantage for real-time applications by avoiding human intervention in threshold determination.


Assuntos
Aceleração , Fotopletismografia/métodos , Análise de Onda de Pulso/métodos , Adulto , Algoritmos , Arritmias Cardíacas/diagnóstico , Voluntários Saudáveis , Coração/anatomia & histologia , Frequência Cardíaca , Humanos , Masculino , Processamento de Sinais Assistido por Computador , Adulto Jovem
9.
Int J Cardiol ; 173(1): 92-9, 2014 Apr 15.
Artigo em Inglês | MEDLINE | ID: mdl-24630336

RESUMO

BACKGROUND: Pulmonary artery hypertension (PAH) is difficult to recognize clinically. Digital stethoscopes offer an opportunity to re-evaluate the diagnosis of PAH. We hypothesized that spectral analysis of heart sound frequencies using recordings from a digital stethoscope would differ between children with and without PAH. METHODS: We recorded heart sounds using a digital stethoscope from 27 subjects (12 males) with a median age of 7 years (3 months to 19 years) undergoing simultaneous cardiac catheterization. 13 subjects had a mean pulmonary artery pressure (mPAp)<25 mm Hg (8-24 mm Hg). 14 subjects had a mPAp≥25 mm Hg (25-97 mm Hg). We applied the fast Fourier transform, power spectral analysis, separability testing, and linear discriminant analysis with leave-one-out cross-validation to the heart sounds recorded from the cardiac apex and 2nd left intercostal space (LICS) to examine the frequency domain. The significance of the results was determined using a t-test and rank-sum test. RESULTS: The relative power of the frequencies 21-22 Hz of the heart sounds recorded at the 2nd LICS was decreased significantly in subjects mPAp≥25 mm Hg versus<25 mm Hg. CONCLUSIONS: Heart sound signals of patients with PAH contain significantly less relative power in the band 21-22 Hz compared to subjects with normal PAp. Information contained in the frequency domain may be useful in diagnosing PAH and aid the development of auscultation based techniques for diagnosing PAH. In the future, utilizing the diagnostic information contained in heart sounds recordings may require analysis of both the time and frequency domains.


Assuntos
Ruídos Cardíacos/fisiologia , Hipertensão Pulmonar/diagnóstico , Hipertensão Pulmonar/fisiopatologia , Artéria Pulmonar/fisiologia , Estetoscópios , Adolescente , Cateterismo Cardíaco/métodos , Criança , Pré-Escolar , Feminino , Humanos , Lactente , Masculino , Estetoscópios/estatística & dados numéricos , Adulto Jovem
10.
Pulm Circ ; 4(4): 685-95, 2014 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-25610604

RESUMO

We studied digital stethoscope recordings in children undergoing simultaneous catheterization of the pulmonary artery (PA) to determine whether time-domain analysis of heart sound intensity would aid in the diagnosis of PA hypertension (PAH). Heart sounds were recorded and stored in .wav mono audio format. We performed recordings for 20 seconds with sampling frequencies of 4,000 Hz at the second left intercostal space and the cardiac apex. We used programs written in the MATLAB 2010b environment to analyze signals. We annotated events representing the first (S1) and second (S2) heart sounds and the aortic (A2) and pulmonary (P2) components of S2. We calculated the intensity (I) of the extracted event area (x) as [Formula: see text], where n is the total number of heart sound samples in the extracted event and k is A2, P2, S1, or S2. We defined PAH as mean PA pressure (mPAp) of at least 25 mmHg with PA wedge pressure of less than 15 mmHg. We studied 22 subjects (median age: 6 years [range: 0.25-19 years], 13 female), 11 with PAH (median mPAp: 55 mmHg [range: 25-97 mmHg]) and 11 without PAH (median mPAp: 15 mmHg [range: 8-24 mmHg]). The P2∶A2 (P = .0001) and P2∶S2 (P = .0001) intensity ratios were significantly different between subjects with and those without PAH. There was a linear correlation (r > 0.7) between the P2∶S2 and P2∶A2 intensity ratios and mPAp. We found that the P2∶A2 and P2∶S2 intensity ratios discriminated between children with and those without PAH. These findings may be useful for developing an acoustic device to diagnose PAH.

11.
PLoS One ; 8(10): e76585, 2013.
Artigo em Inglês | MEDLINE | ID: mdl-24167546

RESUMO

Photoplethysmogram (PPG) monitoring is not only essential for critically ill patients in hospitals or at home, but also for those undergoing exercise testing. However, processing PPG signals measured after exercise is challenging, especially if the environment is hot and humid. In this paper, we propose a novel algorithm that can detect systolic peaks under challenging conditions, as in the case of emergency responders in tropical conditions. Accurate systolic-peak detection is an important first step for the analysis of heart rate variability. Algorithms based on local maxima-minima, first-derivative, and slope sum are evaluated, and a new algorithm is introduced to improve the detection rate. With 40 healthy subjects, the new algorithm demonstrates the highest overall detection accuracy (99.84% sensitivity, 99.89% positive predictivity). Existing algorithms, such as Billauer's, Li's and Zong's, have comparable although lower accuracy. However, the proposed algorithm presents an advantage for real-time applications by avoiding human intervention in threshold determination. For best performance, we show that a combination of two event-related moving averages with an offset threshold has an advantage in detecting systolic peaks, even in heat-stressed PPG signals.


Assuntos
Algoritmos , Transtornos de Estresse por Calor/parasitologia , Adulto , Feminino , Humanos , Masculino , Fotopletismografia/métodos , Sístole , Clima Tropical
12.
Pac Symp Biocomput ; : 41-52, 2013.
Artigo em Inglês | MEDLINE | ID: mdl-23424110

RESUMO

Given the difficulty of experimental determination of drug-protein interactions, there is a significant motivation to develop effective in silico prediction methods that can provide both new predictions for experimental verification and supporting evidence for experimental results. Most recently, classification methods such as support vector machines (SVMs) have been applied to drug-target prediction. Unfortunately, these methods generally rely on measures of the maximum "local similarity" between two protein sequences, which could mask important drug-protein interaction information since drugs are much smaller molecules than proteins and drug-target binding regions must comprise only small local regions of the proteins. We therefore develop a novel sparse learning method that considers sets of short peptides. Our method integrates feature selection, multi-instance learning, and Gaussian kernelization into an L(1) norm support vector machine classifier. Experimental results show that it not only outperformed the previous methods but also pointed to an optimal subset of potential binding regions. Supplementary materials are available at "www.cs.ualberta.ca/~ys3/drug_target".


Assuntos
Descoberta de Drogas/métodos , Proteínas/química , Proteínas/efeitos dos fármacos , Máquina de Vetores de Suporte , Sítios de Ligação , Biologia Computacional , Simulação por Computador , Bases de Dados de Produtos Farmacêuticos , Bases de Dados de Proteínas , Descoberta de Drogas/estatística & dados numéricos , Humanos , Ligantes , Ligação Proteica , Conformação Proteica/efeitos dos fármacos , Proteínas/metabolismo
13.
IEEE Trans Image Process ; 20(5): 1401-14, 2011 May.
Artigo em Inglês | MEDLINE | ID: mdl-20959270

RESUMO

The authors examine the problem of segmenting foreground objects in live video when background scene textures change over time. In particular, we formulate background subtraction as minimizing a penalized instantaneous risk functional--yielding a local online discriminative algorithm that can quickly adapt to temporal changes. We analyze the algorithm's convergence, discuss its robustness to nonstationarity, and provide an efficient nonlinear extension via sparse kernels. To accommodate interactions among neighboring pixels, a global algorithm is then derived that explicitly distinguishes objects versus background using maximum a posteriori inference in a Markov random field (implemented via graph-cuts). By exploiting the parallel nature of the proposed algorithms, we develop an implementation that can run efficiently on the highly parallel graphics processing unit (GPU). Empirical studies on a wide variety of datasets demonstrate that the proposed approach achieves quality that is comparable to state-of-the-art offline methods, while still being suitable for real-time video analysis ( ≥ 75 fps on a mid-range GPU).


Assuntos
Aumento da Imagem/métodos , Processamento de Imagem Assistida por Computador/métodos , Algoritmos , Gráficos por Computador , Cadeias de Markov , Reconhecimento Automatizado de Padrão/métodos
14.
IEEE Trans Pattern Anal Mach Intell ; 28(10): 1646-63, 2006 Oct.
Artigo em Inglês | MEDLINE | ID: mdl-16986545

RESUMO

This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes.


Assuntos
Inteligência Artificial , Gráficos por Computador , Aumento da Imagem/métodos , Interpretação de Imagem Assistida por Computador/métodos , Reconhecimento Automatizado de Padrão/métodos , Processamento de Sinais Assistido por Computador , Técnica de Subtração , Algoritmos , Simulação por Computador , Armazenamento e Recuperação da Informação/métodos , Modelos Estatísticos , Análise Numérica Assistida por Computador
15.
Artigo em Inglês | MEDLINE | ID: mdl-17369624

RESUMO

Protein structure prediction is one of the most important and difficult problems in computational molecular biology. Protein threading represents one of the most promising techniques for this problem. One of the critical steps in protein threading, called fold recognition, is to choose the best-fit template for the query protein with the structure to be predicted. The standard method for template selection is to rank candidates according to the z-score of the sequence-template alignment. However, the z-score calculation is time-consuming, which greatly hinders structure prediction at a genome scale. In this paper, we present a machine learning approach that treats the fold recognition problem as a regression task and uses a least-squares boosting algorithm (LS_Boost) to solve it efficiently. We test our method on Lindahl's benchmark and compare it with other methods. According to our experimental results we can draw the conclusions that: (1) Machine learning techniques offer an effective way to solve the fold recognition problem. (2) Formulating protein fold recognition as a regression rather than a classification problem leads to a more effective outcome. (3) Importantly, the LS_Boost algorithm does not require the calculation of the z-score as an input, and therefore can obtain significant computational savings over standard approaches. (4) The LS_Boost algorithm obtains superior accuracy, with less computation for both training and testing, than alternative machine learning approaches such as SVMs and neural networks, which also need not calculate the z-score. Finally, by using the LS_Boost algorithm, one can identify important features in the fold recognition protocol, something that cannot be done using a straightforward SVM approach.


Assuntos
Biologia Computacional/métodos , Dobramento de Proteína , Proteínas/química , Proteômica/métodos , Algoritmos , Inteligência Artificial , Modelos Estatísticos , Modelos Teóricos , Reconhecimento Automatizado de Padrão , Análise de Regressão , Reprodutibilidade dos Testes , Sensibilidade e Especificidade , Software , Fatores de Tempo
16.
IEEE Trans Neural Netw ; 15(4): 903-16, 2004 Jul.
Artigo em Inglês | MEDLINE | ID: mdl-15461082

RESUMO

This paper presents a new approach to estimating mixture models based on a recent inference principle we have proposed: the latent maximum entropy principle (LME). LME is different from Jaynes' maximum entropy principle, standard maximum likelihood, and maximum aposteriori probability estimation. We demonstrate the LME principle by deriving new algorithms for mixture model estimation, and show how robust new variants of the expectation maximization (EM) algorithm can be developed. We show that a regularized version of LME (RLME), is effective at estimating mixture models. It generally yields better results than plain LME, which in turn is often better than maximum likelihood and maximum a posterior estimation, particularly when inferring latent variable models from small amounts of data.


Assuntos
Algoritmos , Inteligência Artificial , Armazenamento e Recuperação da Informação/métodos , Teoria da Informação , Modelos Estatísticos , Redes Neurais de Computação , Reconhecimento Automatizado de Padrão , Simulação por Computador , Técnicas de Apoio para a Decisão , Entropia , Aprendizagem por Probabilidade
17.
Neural Netw ; 16(5-6): 809-16, 2003.
Artigo em Inglês | MEDLINE | ID: mdl-12850038

RESUMO

This paper proposes a generic criterion that defines the optimum number of basis functions for radial basis function (RBF) neural networks. The generalization performance of an RBF network relates to its prediction capability on independent test data. This performance gives a measure of the quality of the chosen model. An RBF network with an overly restricted basis gives poor predictions on new data, since the model has too little flexibility (yielding high bias and low variance). By contrast, an RBF network with too many basis functions also gives poor generalization performance since it is too flexible and fits too much of the noise on the training data (yielding low bias but high variance). Bias and variance are complementary quantities, and it is necessary to assign the number of basis function optimally in order to achieve the best compromise between them. In this paper we use Stein's unbiased risk estimator to derive an analytical criterion for assigning the appropriate number of basis functions. Two cases of known and unknown noise have been considered and the efficacy of this criterion in both situations is illustrated experimentally. The paper also shows an empirical comparison between this method and two well known classical methods, cross validation and the Bayesian information criterion, BIC.


Assuntos
Processamento Eletrônico de Dados/métodos , Redes Neurais de Computação
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