Jiucang Hao

Bayesian Machine Learning Classifiers for Combining Structural and Functional Measurements to Classify Healthy and Glaucomatous Eyes

PURPOSE To determine whether combining structural (optical coherence tomography, OCT) and functional (standard automated perimetry, SAP) measurements as input for machine learning classifiers (MLCs; relevance vector machine, RVM; and subspace mixture of Gaussians, SSMoG) improves diagnostic accuracy for detecting glaucomatous eyes compared with using each measurement method alone. METHODS Sixty-nine eyes of 69 healthy control subjects (average age, 62.0, SD 9.7 years; visual field mean deviation [MD], -0.70, SD 1.41 dB) and 156 eyes of 156 patients with glaucoma (average age, 66.4, SD 10.2 years; visual field MD, -3.12, SD 3.43 dB) were imaged with OCT (Stratus OCT, Carl Zeiss Meditec, Inc., Dublin, CA) and tested with SAP (Humphrey Field Analyzer II with Swedish Interactive Thresholding Algorithm, SITA; Carl Zeiss Meditec, Inc.) within 3 months of each other. RVM and SSMoG MLCs were trained and tested on OCT-determined RNFL thickness measurements from 32 sectors ( approximately 11.25 degrees each) obtained in the circumpapillary area under the instrument-defined measurement ellipse and SAP pattern deviation values from 52 points from the 24-2 grid, independently and in combination. Tenfold cross-validation was used to train and test classifiers on unique subsets of the full 225-eye data set, and areas under the receiver operating characteristic curve (AUROC) for the classification of eyes in the test set were generated. AUROC results from classifiers trained on OCT and SAP alone and those trained on OCT and SAP in combination were compared. In addition, these results were compared to currently available OCT measurements (mean retinal nerve fiber layer [RNFL] thickness, inferior RNFL thickness, and superior RNFL thickness) and SAP indices (MD and pattern standard deviation [PSD]). RESULTS The AUROCs for RVM trained on OCT parameters alone, SAP parameters alone and OCT and SAP parameters combined were 0.809, 0.815, and 0.845, respectively. The AUROCs for SSMoG trained on OCT parameters alone, SAP parameters alone, and OCT and SAP parameters combined were 0.817, 0.841, and 0.869, respectively. Combining techniques using both RVM and SSMoG significantly improved on MLC analysis of OCT, but not SAP, measurements alone. Classification performance using RVM and SSMoG was statistically similar. CONCLUSIONS RVM and SSMoG Bayesian MLCs trained on OCT and SAP data can successfully discriminate between healthy and early glaucomatous eyes. Combining OCT and SAP measurements using RVM and SSMoG increased diagnostic performance marginally compared with MLC analysis of data obtained using each technology alone.

Speech Enhancement, Gain, and Noise Spectrum Adaptation Using Approximate Bayesian Estimation

This paper presents a new approximate Bayesian estimator for enhancing a noisy speech signal. The speech model is assumed to be a Gaussian mixture model (GMM) in the log-spectral domain. This is in contrast to most current models in frequency domain. Exact signal estimation is a computationally intractable problem. We derive three approximations to enhance the efficiency of signal estimation. The Gaussian approximation transforms the log-spectral domain GMM into the frequency domain using minimal Kullback-Leiber (KL)-divergency criterion. The frequency domain Laplace method computes the maximum a posteriori (MAP) estimator for the spectral amplitude. Correspondingly, the log-spectral domain Laplace method computes the MAP estimator for the log-spectral amplitude. Further, the gain and noise spectrum adaptation are implemented using the expectation-maximization (EM) algorithm within the GMM under Gaussian approximation. The proposed algorithms are evaluated by applying them to enhance the speeches corrupted by the speech-shaped noise (SSN). The experimental results demonstrate that the proposed algorithms offer improved signal-to-noise ratio, lower word recognition error rate, and less spectral distortion.

Independent vector analysis for source separation using a mixture of gaussians prior

Convolutive mixtures of signals, which are common in acoustic environments, can be difficult to separate into their component sources. Here we present a uniform probabilistic framework to separate convolutive mixtures of acoustic signals using independent vector analysis (IVA), which is based on a joint distribution for the frequency components originating from the same source and is capable of preventing permutation disorder. Different gaussian mixture models (GMM) served as source priors, in contrast to the original IVA model, where all sources were modeled by identical multivariate Laplacian distributions. This flexible source prior enabled the IVA model to separate different type of signals. Three classes of models were derived and tested: noiseless IVA, online IVA, and noisy IVA. In the IVA model without sensor noise, the unmixing matrices were efficiently estimated by the expectation maximization (EM) algorithm. An online EM algorithm was derived for the online IVA algorithm to track the movement of the sources and separate them under nonstationary conditions. The noisy IVA model included the sensor noise and combined denoising with separation. An EM algorithm was developed that found the model parameters and separated the sources simultaneously. These algorithms were applied to separate mixtures of speech and music. Performance as measured by the signal-to-interference ratio (SIR) was substantial for all three models.

Combining Functional and Structural Tests Improves the Diagnostic Accuracy of Relevance Vector Machine Classifiers

PurposeTo investigate whether combining optic disc topography and short-wavelength automated perimetry (SWAP) data improves the diagnostic accuracy of relevance vector machine (RVM) classifiers for detecting glaucomatous eyes compared with using each test alone. MethodsOne eye of 144 glaucoma patients and 68 healthy controls from the Diagnostic Innovations in Glaucoma Study were included. RVM were trained and tested with cross-validation on optimized (backward elimination) SWAP features (thresholds plus age; pattern deviation; and total deviation) and on Heidelberg retina tomograph II (HRT) optic disc topography features, independently and in combination. RVM performance was also compared with 2 HRT linear discriminant functions and to SWAP mean deviation and pattern standard deviation. Classifier performance was measured by the area under the receiver operating characteristic curves (AUROCs) generated for each feature set and by the sensitivities at set specificities of 75%, 90%, and 96%. ResultsRVM trained on combined HRT and SWAP thresholds plus age had significantly higher AUROC (0.93) than RVM trained on HRT (0.88) and SWAP (0.76) alone. AUROCs for the SWAP global indices (mean deviation: 0.68; pattern standard deviation: 0.72) offered no advantage over SWAP thresholds plus age, whereas the linear discriminant functions AUROCs were significantly lower than RVM trained on the combined SWAP and HRT feature set and on HRT alone feature set. ConclusionsTraining RVM on combined optimized HRT and SWAP data improved diagnostic accuracy compared with training on SWAP and HRT parameters alone. Future research may identify other combinations of tests and classifiers that can also improve diagnostic accuracy.

Speech Enhancement Using Gaussian Scale Mixture Models

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress.

Adaptive independent vector analysis for the separation of convoluted mixtures using EM algorithm

This paper presents a novel adaptive approach to the separation of convolutedly mixed acoustic signals based on independent vector analysis (IVA). IVA, as an extension of independent component analysis (ICA) from univariate components to multivariate components, provides an efficient framework for avoiding the well-known permutation problem in frequency-domain blind source separation (BSS). However, since IVA has been mostly employing pre-specified and simple source priors which are good fits to speech signals, the performance degrades when the mixture includes unknown sources other than speech. Also, sensor noise has not been considered. To tackle these limitations, we employ multivariate Gaussian mixture model (GMM) as the source priors and add sensor noise into the model. We derive an expectation maximization (EM) algorithm that estimates the separating matrices and the parameters of the unknown source prior together. The performance is demonstrated by experimental results that include the comparison with the IVA results using fixed source priors.