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.

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.

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.

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.

We propose a new blind source separation approach that models the inherent signal dependencies such as those observed in speech signals in order to solve the problem of separating convolved sources. The frequency domain methods for the convolved mixture problem require a solution to the well-known permutation problem. Our approach is based on assuming a vector representation of the source signal where its multidimensional joint densities are non-spherical. Spherical distributions may be adequate for signals that exhibit uniform dependencies across frequencies but in case of speech signals we can observe stronger dependencies for neighboring frequency bins and almost no dependency for frequency bins that are far apart. The non-spherical joint density model takes into account this phenomenon. For the separation of convolved sources, the proposed method demonstrates consistent performance over previous methods and improved performance over the spherical joint density representations.

A new consistent objective function for nonparametric complex independent component analysis (ICA) is proposed where the complex variables are restricted to be circular, or radially symmetric. This objective function is derived using an order statistics based density estimator which orders the complex data by their absolute values. The objective function is unconditional to the source distribution other than the circularity and it measures the statistical independence directly from the data. Using this objective function, a nonparametric complex independent component analysis algorithm can be derived. Also, the generalization of this objective function allows it to be combined with other algorithms to increase their separation performances. Experiments demonstrate the usefulness of the new objective function.

We present a probabilistic graphical model that learns the joint statistical structures of text, audio, and video for the purpose of classification and retrieval of multimedia documents. The proposed model, which we call multi-modal LDA (MM-LDA), builds on the basic latent Dirichlet allocation (LDA) model by postulating common hidden factors, termed topics, that are shared among the 3 data modalities. These hidden topics correspond to patterns of word co-occurrences in multimedia documents and describe how text words co-occur with certain visual and acoustic features. We demonstrate the power of MM-LDA in representing TV clips containing closed-captions, video, and audio, and show promising results in 3 challenging applications: TV clip classification, retrieval, and auto-annotation.

A new independent component analysis (ICA) formulation called independent vector analysis (IVA) was proposed in order to solve the permutation problem in frequency-domain blind source separation. Instead of running ICA in each frequency bin and matching the permutation afterwards, IVA exploits the dependency among the frequency components of a source and deal with them altogether as a multivariate data by capturing the dependency with a multivariate joint probability density function (PDF). For modelling the frequency components of speech, sparse and spherically symmetric PDFs have been chosen. In this paper, we compare the separation performance of IVA with a group of PDFs where the density is uniformly distributed for the data points of the same lp-norm value by changing both the value of p and the sparseness. Also we derive an IVA algorithm from a nonparametric perspective with the constraint of spherical symmetry and high dimension. Simulation results show that sparseness and spherical symmetry together is a good assumption for the speech model in the frequency domain.

Blind source separation (BSS) is a challenging problem in real-world environments where sources are time delayed and convolved. The problem becomes more difficult in very reverberant conditions, with an increasing number of sources, and geometric configurations of the sources such that finding directionality is not sufficient for source separation. In this paper, we propose a new algorithm that exploits higher order frequency dependencies of source signals in order to separate them when they are mixed. In the frequency domain, this formulation assumes that dependencies exist between frequency bins instead of defining independence for each frequency bin. In this manner, we can avoid the well-known frequency permutation problem. To derive the learning algorithm, we define a cost function, which is an extension of mutual information between multivariate random variables. By introducing a source prior that models the inherent frequency dependencies, we obtain a simple form of a multivariate score function. In experiments, we generate simulated data with various kinds of sources in various environments. We evaluate the performances and compare it with other well-known algorithms. The results show the proposed algorithm outperforms the others in most cases. The algorithm is also able to accurately recover six sources with six microphones. In this case, we can obtain about 16-dB signal-to-interference ratio (SIR) improvement. Similar performance is observed in real conference room recordings with three human speakers reading sentences and one loudspeaker playing music

A new independent component analysis (ICA) formulation called independent vector analysis (IVA) was proposed in order to solve the permutation problem in convolutive blind source separation (BSS). Instead of running ICA in each frequency bin separately and correcting the disorder with an additional algorithmic scheme afterwards, IVA exploited the dependency among the frequency components of a source and dealt with them as a multivariate source by modeling it with sparse and spherically, or radially, symmetric joint probability density functions (pdfs). In this paper, we compare the speech separation performances of IVA by using a group of lp-norm-invariant sparse pdfs where the value of and the sparseness can be controlled. Also, we derive an IVA algorithm from a nonparametric perspective with the constraint of spherical symmetry and high dimensionality. Simulation results confirm the efficiency of assuming sparseness and spherical symmetry for the speech model in the frequency domain.

This work investigates the use of nonlinear dependencies in natural image sequence statistics to learn higher-order structures in natural videos. We propose a two-layer model that learns variance correlation between linear ICA coefficients and present a novel nonlinear representation of natural videos. The first layer performs a linear mapping from pixel values to ICA coefficients. In doing so, the spatiotemporal dynamics in natural videos are decomposed into a set of bases each encoding "independent motion." By assuming that the nonlinear dependency of ICA coefficients takes the form of variance correlation, the second layer learns the joint distribution of ICA sources that captures how these independent bases co-activate. Experimental results show that the abstract representation correspond to various activation patterns of bases with similar motion, hence the term "motion patterns." Our model offers a novel description of higher-order structures in natural videos. We illustrate the usefulness of the proposed representation in video segmentation and denoising tasks.

We propose a novel approach to the blind source separation (BSS) that exploits frequency dependencies within a source. In contrast to conventional algorithms that separate the sources independently in each frequency bin, we assume that dependencies exist between frequency bins in a source signal. In this manner, we can reduce or eliminate the well-known frequency permutation problem. We derive the learning algorithm by defining a cost function as an extension of mutual information between multivariate random variables and by introducing a source prior that models the inherent frequency dependencies. This results in a simple form of a multivariate score function. In simulations and real recording experiments, we evaluate the performance of the proposed method and compare it against other well-known algorithms under various conditions. Our results indicate that modeling dependencies yields improved performance and robust scaling to higher number of sources and mixtures.

In this letter, we discuss the multivariate Laplace probability model in the context of a normal variance mixture model. We briefly review the derivation of the probability density function (pdf) and discuss a few important properties. We then present two methods for estimating its parameters from data and include an example of usage, where we apply the model to represent the statistics of the discrete Fourier transform coefficients of a speech signal. Since the pdf is given in closed form, and the model parameters can be easily obtained, this distribution may be useful for representing multivariate, sparsely distributed data, with mutually dependent components.

The paper presents a fast new algorithm for estimating the relative time delay between a microphone pair in noisy reverberant conditions. The algorithm is derived from a novel approach to this problem, which we formulate in the framework of probabilistic graphical models. We construct a probabilistic model of the microphone signals, using models of speech and noise as building blocks. The reverberation filter coefficients and the relative time delay appear as model parameters, and are estimated by our algorithm from data. The resulting delay estimate is Bayes optimal and takes into account noise and reverberation in a principled manner. We demonstrate very good performance on data from real and simulated room environments.

We report work on speech enhancement that combines sequential noise estimation and perceptual filtering. The sequential estimation employs an extension of the sequential EM-type algorithm. In the algorithm, statistics of clean speech are modeled by hidden Markov models (HMM) and noise is assumed to be Gaussian distributed with a time-varying mean vector (the noise parameter) to be estimated. The estimation process uses a non-linear function that relates speech statistics, noise, and noisy observation. With the estimated noise parameter, the subtraction-type algorithm for speech enhancement may be extended to non-stationary environments. In particular, a perceptual filter with frequency masking is constructed with a tradeoff between noise reduction and speech distortion considering the sensitivity of speech recognition systems to speech distortion. Our experiments in speech enhancement and speech recognition in non-stationary noise confirmed that this approach seems promising in improving performances compared to alternative speech enhancement algorithms.

A speech enhancement scheme including blind source separation and background denoising based on minimum statistics is studied in mobile environments. To accommodate the dependence of the separated output signals on the spatial properties of the recorded source signals, these blind signal processing steps are complemented by an adaptive separated output channel selection stage using prior knowledge about the desired speaker speech content. The resulting scheme performance is illustrated by speech recognition experiments on real recordings corrupted by various noise sources and shown to outperform conventional beamforming and single channel denoising techniques as well as an equivalent scheme with fixed output channel selection.

This paper focuses on detection of a single emotion and verification of a specific emotion type in a test utterance. To utilize a probabilistic output of a classifier as well as to exploit various long term acoustic features, we built a probabilistic output SVM and applied several approximated log likelihood ratio tests for emotion verification. Experimental results on SUSAS and AIBO emotion database show that anger and sadness are easier emotions to be detected than boredom and happiness. Results also verify the efficacy of applying log likelihood ratio with respect to neutral emotion as a measure for emotion verification.

A number of real-life speech applications using BSS have been reported for two channel applications but only a few have been reported for multi-channel (more than 2 channels) applications. Moreover these mostly involve simulation studies or real-life separations in controlled settings. In this paper some practical problems of multichannel applications will be analyzed. A methodology is proposed to bypass the full fledged higher dimensional BSS problem by exploiting the relative spatial arrangement of microphones to achieve improved speech enhancement by selective 2-channel BSS. The concept is illustrated on a 3 source × 3 microphone setup in speech recognition experiments involving an acoustic scene with a human speaker and interferring noise sources.

Capturing dependencies in images in an unsupervised manner is important for many image processing applications. We propose a new method for capturing nonlinear dependencies in images of natural scenes. This method is an extension of the linear Independent Component Analysis (ICA) method by building a hierarchical model based on ICA and mixture of Laplacian distribution. The model parameters are learned via an EM algorithm and it can accurately capture variance correlation and other high order structures in a simple manner. We visualize the learned variance structure and demonstrate applications to image segmentation and denoising.

In this paper, we introduce and investigate a new adaptive equalization method based on minimizing approximate negentropy of the estimation error for a finite-length equalizer. We consider an approximate negentropy using nonpolynomial expansions of the estimation error as a new performance criterion to improve performance of a linear equalizer based on minimizing minimum mean squared error (MMSE). Negentropy includes higher order statistical information and its minimization provides improved converge, performance and accuracy compared to traditional methods such as MMSE in terms of bit error rate (BER). The proposed negentropy minimization (NEGMIN) equalizer has two kinds of solutions, the MMSE solution and the other one, depending on the ratio of the normalization parameters. The NEGMIN equalizer has best BER performance when the ratio of the normalization parameters is properly adjusted to maximize the output power(variance) of the NEGMIN equalizer. Simulation experiments show that BER performance of the NEGMIN equalizer with the other solution than the MMSE one has similar characteristics to the adaptive minimum bit error rate (AMBER) equalizer. The main advantage of the proposed equalizer is that it needs significantly fewer training symbols than the AMBER equalizer. Furthermore, the proposed equalizer is more robust to nonlinear distortions than the MMSE equalizer.

In this paper, we introduce an information theoretic learning method as a new approach to multiuser detection. We propose a new adaptive linear multiuser detector based on approximate negentropy minimization of the output error and investigate its characteristics and performance. Negentropy includes higher order statistical information and its minimization provides improved converge and performance compared to traditional methods such as minimum mean squared error. The proposed algorithm is derived under the assumption that a Gaussian variable has the largest entropy among all random variables of unit variance and hence a normalization process is required. Simulation experiments show that our multiuser detector has similar bit error rate (BER) characteristics to the least BER multiuser detector. Furthermore, the proposed detector has faster convergence speed than the LBER detector.

Our goal is to extract multiple source signals when only a single observation channel is available. We propose a new signal separation algorithm based on a subspace decomposition. The observation is transformed into subspaces of interest with different sets of basis functions. A flexible model for density estimation allows an accurate modeling of the distributions of the source signals in the subspaces, and we develop a filtering technique using a maximum likelihood (ML) approach to match the observed single channel data with the decomposition. Our experimental results show good separation performance on simulated mixtures of two music signals as well as two voice signals.

We propose a new method to design speech/non-speech classifiers for voice activity detection and robust endpoint detection using the adaptive boosting (AdaBoost) algorithm. The method uses a combination of simple base classifiers through the AdaBoost algorithm and a set of optimized speech features combined with spectral subtraction. The key benefits of this method are the simple implementation and low computational complexity. The AdaBoost classifier combined with spectral subtraction significantly improved the receiver operating characteristic curves of the G.729 voice activity detector. For speech recognition purpose, the method reduced 20-50% of miss errors for the same false alarm rate by using additional band pass energy and spectral distortion based on mel frequency cepstral coefficients.

A speech enhancement scheme is presented integrating spatial and temporal signal processing methods for blind denoising in non stationary noise environments. In a first stage, spatially localized point sources are separated from noisy speech signals recorded by two microphones using a Blind Source Separation (BSS) algorithm assuming no a priori knowledge about the sources involved. Spatially distributed background noise is removed in a second processing step. Here, the BSS output channel containing the desired speaker is filtered with a time-varying Wiener filter. Noise power estimates for the filter coefficients are computed from desired speaker absent time-intervals identified by comparing only signal energy of separated source signals from the BSS stage. The scheme's performance is illustrated by speech recognition experiments on real recordings corrupted by babble noise and compared to conventional beamforming and single channel denoising techniques.

For emotion recognition, we selected pitch, log energy, formant, mel-band energies, and mel frequency cepstral co-efficients (MFCCs) as the base features, and added veloc-ity/acceleration of pitch and MFCCs to form feature streams. We extracted statistics used for discriminative classifiers, as-suming that each stream is a one-dimensional signal. Extracted features were analyzed by using quadratic discriminant analy-sis (QDA) and support vector machine (SVM). Experimental results showed that pitch and energy were the most important factors. Using two different kinds of databases, we compared emotion recognition performance of various classifiers: SVM, linear discriminant analysis (LDA), QDA and hidden Markov model (HMM). With the text-independent SUSAS database, we achieved the best accuracy of 96.3 % for stressed/neutral style classification and 70.1 % for 4-class speaking style clas-sification using Gaussian SVM, which is superior to the previ-ous results. With the speaker-independent AIBO database, we achieved 42.3 % accuracy for 5-class emotion recognition. 1.

We present a generative factor analyzed hidden Markov model (GFA-HMM) for automatic speech recognition. In a traditional HMM, the observation vectors are represented by mixture of Gaussians (MoG) that are dependent on discrete-valued hidden state sequence. The GFA-HMM introduces a hierarchy of continuous-valued latent representation of observation vectors, where latent vectors in one level are acoustic-unit dependent and the latent vectors in a higher level are acoustic-unit independent. An expectation maximization (EM) algorithm is derived for maximum likelihood parameter estimation of the model. The GFA-HMM can achieve a much more compact representation of the intra-frame statistics of observation vectors than traditional HMM. We conducted an experiment to show that the GFA-HMM can achieve better performances over traditional HMM with the same amount of training data but much smaller number of model parameters.

A new front-end processing scheme for robust speech recognition is proposed and evaluated on the multi-lingual Aurora 3 database. The front-end processing scheme consists of Mel-scaled spectral subtraction, speech segmentation, cepstral coefficient extraction, utterance-level frame dropping and eigenspace feature normalization. We also investigated performance on all language databases by post-processing features extracted by the ETSI advanced front-end with an additional eigenspace normalization module. This step consists in linear PCA matrix feature transformation followed by mean and variance normalization of the transformed cepstral coefficients. In speech recognition experiments, our proposed front-end yielded better than 16 percent relative error rate reduction over the ETSI front-end on the Finnish language database. Also, more than 6% in average relative error reduction was observed over all languages with the ETSI front-end augmented by eigenspace normalization.

Missing data are common in real-world data sets and are a problem for many estimation techniques. We have developed a variational Bayesian method to perform independent component analysis (ICA) on high-dimensional data containing missing entries. Missing data are handled naturally in the Bayesian framework by integrating the generative density model. Modeling the distributions of the independent sources with mixture of gaussians allows sources to be estimated with different kurtosis and skewness. Unlike the maximum likelihood approach, the variational Bayesian method automatically determines the dimensionality of the data and yields an accurate density model for the observed data without overfitting problems. The technique is also extended to the clusters of ICA and supervised classification framework.

Neurons in the early stages of processing in the primate visual system efficiently encode natural scenes. In previous studies of the chromatic properties of natural images, the inputs were sampled on a regular array, with complete color information at every location. However, in the retina cone photoreceptors with different spectral sensitivities are arranged in a mosaic. We used an unsupervised neural network model to analyze the statistical structure of retinal cone mosaic responses to calibrated color natural images. The second-order statistical dependencies derived from the covariance matrix of the sensory signals were removed in the first stage of processing. These decorrelating filters were similar to type I receptive fields in parvo- or konio-cellular LGN in both spatial and chromatic characteristics. In the subsequent stage, the decorrelated signals were linearly transformed to make the output as statistically independent as possible, using independent component analysis. The independent component filters showed luminance selectivity with simple-cell-like receptive fields, or had strong color selectivity with large, often double-opponent, receptive fields, both of which were found in the primary visual cortex (V1). These results show that the "form" and "color" channels of the early visual system can be derived from the statistics of sensory signals.

Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave/Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial "25 words or less"), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations. Experiments were performed using synthetic data and natural images. For complete dictionaries, we demonstrate that our algorithms have improved performance over other independent component analysis (ICA) methods, measured in terms of signal-to-noise ratios of separated sources. In the overcomplete case, we show that the true underlying dictionary and sparse sources can be accurately recovered. In tests with natural images, learned overcomplete dictionaries are shown to have higher coding efficiency than complete dictionaries; that is, images encoded with an overcomplete dictionary have both higher compression (fewer bits per pixel) and higher accuracy (lower mean square error).

We present a new technique for achieving blind source separation when given only a single-channel recording. The main idea is based on exploiting the inherent time structure of sound sources by learning a priori sets of time-domain basis functions that encode the sources in a statistically efficient manner. We derive a learning algorithm using a maximum likelihood approach given the observed single-channel data and sets of basis functions. For each time point, we infer the source parameters and their contribution factors using a flexible but simple density model. We show the separation results of two music signals as well as the separation of two voice signals.

In most hidden Markov model-based automatic speech recognition systems, one of the fundamental questions is to determine the intrinsic speech feature dimensionality and the number of clusters used on the Gaussian mixture model. We analyzed mel-frequency band energies using a variational Bayesian principal component analysis method to estimate the feature dimensionality as well as the number of Gaussian mixtures by learning a maximum lower bound of the evidence instead of maximizing the likelihood function as used in conventional speech recognition systems. In analyzing the Texas Instruments/Massachusetts Institute of Technology (TIMIT) speech database, our method revealed the intrinsic structures of vowels and consonants. The usefulness of this method is demonstrated in the superior classification performance for the most difficult phonemes /b/, /d/, and /g/.

In a standard mel-frequency cepstral coefficient-based speech recognizer, it is common to use the same feature dimension and the number of Gaussian mixtures for all subunits. We proposed to use different transformations and different number of mixtures for each subunit. We obtained the transformations from mel-frequency band energies by using the variational Bayesian principal component analysis (PCA) method. In the method, hyperparameters of the Gaussian mixtures and the number of mixtures are automatically learned through maximization of a lower bound of the evidence instead of the likelihood in the conventional maximum likelihood paradigm. Analyzing the TIMIT speech data, we revealed intrinsic structures of vowels and consonants. We demonstrated the userfulness of the method for speech recognition by performing phoneme classification of /b/, /d/ and /g/ phonemes.

Missing data is common in real-world datasets and is a problem for many estimation techniques. We have developed a variational Bayesian method to perform Independent Component Analysis (ICA) on high-dimensional data containing missing entries. Missing data are handled naturally in the Bayesian framework by integrating the generative density model. Mod- eling the distributions of the independent sources with mixture of Gaus- sians allows sources to be estimated with different kurtosis and skewness. The variational Bayesian method automatically determines the dimen- sionality of the data and yields an accurate density model for the ob- served data without overfitting problems. This allows direct probability estimation of missing values in the high dimensional space and avoids dimension reduction preprocessing which is not feasible with missing data.

We present a new technique for achieving source separation when given only a single channel recording. The main idea is based on exploiting the inherent time structure of sound sources by learning a priori sets of basis filters in time domain that encode the sources in a statistically efficient manner. We derive a learning algorithm using a maximum likelihood approach given the observed single channel data and sets of basis filters. For each time point we infer the source signals and their contribution factors. This inference is possible due to the prior knowledge of the basis filters and the associated coefficient densities. A flexible model for density estimation allows accurate modeling of the observation and our experimental results exhibit a high level of separation performance for mixtures of two music signals as well as the separation of two voice signals.

An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent, non-Gaussian densities. The algorithm estimates the data density in each class by using parametric nonlinear functions that fit to the non-Gaussian structure of the data. This improves classification accuracy compared with standard Gaussian mixture models. When applied to images, the algorithm can learn efficient codes (basis functions) for images that capture the statistically significant structure intrinsic in the images. We apply this technique to the problem of unsupervised classification, segmentation, and denoising of images. We demonstrate that this method was effective in classifying complex image textures such as natural scenes and text. It was also useful for denoising and filling in missing pixels in images with complex structures. The advantage of this model is that image codes can be learned with increasing numbers of classes thus providing greater flexibility in modeling structure and in finding more image features than in either Gaussian mixture models or standard independent component analysis (ICA) algorithms.

We apply independent component analysis for extracting an optimal basis to the problem of finding efficient features for a speaker. The basis functions learned by the algorithm are oriented and localized in both space and frequency, bearing a resemblance to Gabor functions. The speech segments are assumed to be generated by a linear combination of the basis functions, thus the distribution of speech segments of a speaker is modeled by a basis, which is calculated so that each component should be independent upon others on the given training data. The speaker distribution is modeled by the basis functions. To assess the efficiency of the basis functions, we performed speaker classification experiments and compared our results with the conventional Fourier-basis. Our results show that the proposed method is more efficient than the conventional Fourier-based features, in that they can obtain a higher classification rate.

The goal of this paper is to learn or adapt statistical features of gender specific speech signals. The adaptation is performed by finding basis functions that encode the speech signal such that the resulting coefficients are statistically independent and the information redundancy is minimized. We use a flexible independent component analysis (ICA) algorithm to adapt the basis functions as well as the source coefficients for male and female speakers respectively. The learned features show significant differences in frequency and time span. Our results suggest that the male speech features can be described by Gabor-like wavelet filters whereas the female speech signal has a much longer time span. We present a detailed time-frequency analysis strongly suggesting that those features can be used to qualify and quantify gender-specific speech signal differences.

The analysis of electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings is important both for basic brain research and for medical diagnosis and treatment. Independent component analysis (ICA) is an effective method for removing artifacts and separating sources of the brain signals from these recordings. A similar approach is proving useful for analyzing functional magnetic resonance brain imaging (fMRI) data. In this paper, we outline the assumptions underlying ICA and demonstrate its application to a variety of electrical and hemodynamic recordings from the human brain.

In this paper, we proposed new speech features using independent component analysis to human speeches. When independent component analysis is applied to speech signals for efficient encoding the adapted basis functions resemble Gabor-like features. Trained basis functions have some redundancies, so we select some of the basis functions by the reordering method. The basis functions are almost ordered from the low frequency basis vector to the high frequency basis vector. And this is compatible with the fact that human speech signals have much more information in the low frequency range. Those features can be used in automatic speech recognition systems and the proposed method gives much better recognition rates than conventional mel-frequency cepstral features.

The human visual system encodes the chromatic signals conveyed by the three types of retinal cone photoreceptors in an opponent fashion. This color opponency has been shown to constitute an efficient encoding by spectral decorrelation of the receptor signals. We analyze the spatial and chromatic structure of natural scenes by decomposing the spectral images into a set of linear basis functions such that they constitute a representation with minimal redun(cid:173) dancy. Independent component analysis finds the basis functions that transforms the spatiochromatic data such that the outputs (activations) are statistically as independent as possible, i.e. least redundant. The resulting basis functions show strong opponency along an achromatic direction (luminance edges), along a blue(cid:173) yellow direction, and along a red-blue direction. Furthermore, the resulting activations have very sparse distributions, suggesting that the use of color opponency in the human visual system achieves a highly efficient representation of colors. Our findings suggest that color opponency is a result of the properties of natural spectra and not solely a consequence of the overlapping cone spectral sensitiv(cid:173) ities. 1 Statistical structure of natural scenes Efficient encoding of visual sensory information is an important task for informa(cid:173) tion processing systems and its study may provide insights into coding principles of biological visual systems. An important goal of sensory information processing Electronic version available at www. cnl. salk . edu/ ""tewon. is to transform the input signals such that the redundancy between the inputs is reduced. In natural scenes, the image intensity is highly predictable from neighbor(cid:173) ing measurements and an efficient representation preserves the information while the neuronal output is minimized. Recently, several methods have been proposed for finding efficient codes for achromatic images of natural scenes [1, 2, 3, 4]. While luminance dominates the structure of the visual world, color vision provides impor(cid:173) tant additional information about our environment. Therefore, we are interested in efficient, i.e. redundancy reducing representations for the chromatic structure of natural scenes. 2 Learning efficient representation for chromatic image Our goal was to find efficient representations of the chromatic sensory information such that its spatial and chromatic redundancy is reduced significantly. The method we used for finding statistically efficient representations is independent component analysis (ICA). ICA is a way of finding a linear non-orthogonal co-ordinate system in multivariate data that minimizes mutual information among the axial projections of the data. The directions of the axes of this co-ordinate system (basis functions) are determined by both second and higher-order statistics of the original data, com(cid:173) pared to Principal Component Analysis (PCA) which is used solely in second order statistics and has orthogonal basis functions. The goal of ICA is to perform a linear transform which makes the resulting source outputs as statistically indepen(cid:173) dent from each other as possible [5]. ICA assumes an unknown source vector s with mutually independent components Si. A small patch of the observed image is stretched into a vector x that can be represented as a linear combination of sources components Si such that

An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent, non-Gaussian densities. The algorithm estimates the density of each class and is able to model class distributions with non-Gaussian structure. The new algorithm can improve classification accuracy compared with standard Gaussian mixture models. When applied to blind source separation in nonstationary environments, the method can switch automatically between classes, which correspond to contexts with different mixing properties. The algorithm can learn efficient codes for images containing both natural scenes and text. This method shows promise for modeling non-Gaussian structure in high-dimensional data and has many potential applications.

An extension of the infomax algorithm of Bell and Sejnowski (1995) is presented that is able blindly to separate mixed signals with sub- and supergaussian source distributions. This was achieved by using a simple type of learning rule first derived by Girolami (1997) by choosing negentropy as a projection pursuit index. Parameterized probability distributions that have sub- and supergaussian regimes were used to derive a general learning rule that preserves the simple architecture proposed by Bell and Sejnowski (1995), is optimized using the natural gradient by Amari (1998), and uses the stability analysis of Cardoso and Laheld (1996) to switch between sub- and supergaussian regimes. We demonstrate that the extended infomax algorithm is able to separate 20 sources with a variety of source distributions easily. Applied to high-dimensional data from electroencephalographic recordings, it is effective at separating artifacts such as eye blinks and line noise from weaker electrical signals that arise from sources in the brain.

Empirical results were obtained for the blind source separation of more sources than mixtures using a previously proposed framework for learning overcomplete representations. This technique assumes a linear mixing model with additive noise and involves two steps: (1) learning an overcomplete representation for the observed data and (2) inferring sources given a sparse prior on the coefficients. We demonstrate that three speech signals can be separated with good fidelity given only two mixtures of the three signals. Similar results were obtained with mixtures of two speech signals and one music signal.

We present methods to separate blindly mixed signals recorded in a room. The learning algorithm is based on the information maximization in a single layer neural network. We focus on the implementation of the learning algorithm and on issues that arise when separating speakers in room recordings. We used an infomax approach in a feedforward neural network implemented in the frequency domain using the polynomial filter matrix algebra technique. A fast convergence speed was achieved by using a time-delayed decorrelation method as a preprocessing step. Under minimum-phase mixing conditions this preprocessing step was sufficient for the separation of signals. These methods successfully separated a recorded voice with music in the background (cocktail party problem). Finally, we discuss problems that arise in real world recordings and their potential solutions.

We present a new method to tackle the problem of separating mixtures of real sources which have been convolved and time-delayed under real world conditions. To this end, we learn two sets of parameters to unmix the mixtures and to estimate the true density function. The solutions are discussed for feedback and feedforward architectures. Since the quality of separation depends on the modeling of the underlying density we propose different methods to closer approximate the density function using some contest. The proposed density estimation achieves separation of a wider class of sources. Furthermore, we employ the FIR polynomial matrix techniques in the frequency domain to invert a true-phase mixing system. The significance of the new method is demonstrated with the successful separation of two speakers and separation of music and speech recorded with two microphones in a reverberating room.