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PubMed2005

Effective gaussian mixture learning for video background subtraction.

Adaptive Gaussian mixtures have been used for modeling nonstationary temporal distributions of pixels in video surveillance applications. However, a common problem for this approach is balancing between model convergence speed and stability. This paper proposes an effective scheme to improve the convergence rate without compromising model stability. This is achieved by replacing the global, static retention factor with an adaptive learning rate calculated for each Gaussian at every frame. Significant improvements are shown on both synthetic and real video data. Incorporating this algorithm into a statistical framework for background subtraction leads to an improved segmentation performance compared to a standard method.

Algorithms↗
PubMed2005

Unified segmentation.

A probabilistic framework is presented that enables image registration, tissue classification, and bias correction to be combined within the same generative model. A derivation of a log-likelihood objective function for the unified model is provided. The model is based on a mixture of Gaussians and is extended to incorporate a smooth intensity variation and nonlinear registration with tissue probability maps. A strategy for optimising the model parameters is described, along with the requisite partial derivatives of the objective function.

Algorithms↗
PubMed2006

PACK: Profile Analysis using Clustering and Kurtosis to find molecular classifiers in cancer.

MOTIVATION: Elucidating the molecular taxonomy of cancers and finding biological and clinical markers from microarray experiments is problematic due to the large number of variables being measured. Feature selection methods that can identify relevant classifiers or that can remove likely false positives prior to supervised analysis are therefore desirable. RESULTS: We present a novel feature selection procedure based on a mixture model and a non-gaussianity measure of a gene's expression profile. The method can be used to find genes that define either small outlier subgroups or major subdivisions, depending on the sign of kurtosis. The method can also be used as a filtering step, prior to supervised analysis, in order to reduce the false discovery rate. We validate our methodology using six independent datasets by rediscovering major classifiers in ER negative and ER positive breast cancer and in prostate cancer. Furthermore, our method finds two novel subtypes within the basal subgroup of ER negative breast tumours, associated with apoptotic and immune response functions respectively, and with statistically different clinical outcome. AVAILABILITY: An R-function pack that implements the methods used here has been added to vabayelMix, available from (www.cran.r-project.org). CONTACT: aet21@cam.ac.uk SUPPLEMENTARY INFORMATION: Supplementary information is available at Bioinformatics online.

Algorithms↗
PubMed2006

Unsupervised image-set clustering using an information theoretic framework.

In this paper, we combine discrete and continuous image models with information-theoretic-based criteria for unsupervised hierarchical image-set clustering. The continuous image modeling is based on mixture of Gaussian densities. The unsupervised image-set clustering is based on a generalized version of a recently introduced information-theoretic principle, the information bottleneck principle. Images are clustered such that the mutual information between the clusters and the image content is maximally preserved. Experimental results demonstrate the performance of the proposed framework for image clustering on a large image set. Information theoretic tools are used to evaluate cluster quality. Particular emphasis is placed on the application of the clustering for efficient image search and retrieval.

Algorithms↗
PubMed2006

Enhancing digital cephalic radiography with mixture models and local gamma correction.

We present a new algorithm, called the soft-tissue filter, that can make both soft and bone tissue clearly visible in digital cephalic radiographies under a wide range of exposures. It uses a mixture model made up of two Gaussian distributions and one inverted lognormal distribution to analyze the image histogram. The image is clustered in three parts: background, soft tissue, and bone using this model. Improvement in the visibility of both structures is achieved through a local transformation based on gamma correction, stretching, and saturation, which is applied using different parameters for bone and soft-tissue pixels. A processing time of 1 s for 5 Mpixel images allows the filter to operate in real time. Although the default value of the filter parameters is adequate for most images, real-time operation allows adjustment to recover under- and overexposed images or to obtain the best quality subjectively. The filter was extensively clinically tested: quantitative and qualitative results are reported here.

Algorithms↗
PubMed2006

Context-based segmentation of image sequences.

We describe an algorithm for context-based segmentation of visual data. New frames in an image sequence (video) are segmented based on the prior segmentation of earlier frames in the sequence. The segmentation is performed by adapting a probabilistic model learned on previous frames, according to the content of the new frame. We utilize the maximum a posteriori version of the EM algorithm to segment the new image. The Gaussian mixture distribution that is used to model the current frame is transformed into a conjugate-prior distribution for the parametric model describing the segmentation of the new frame. This semisupervised method improves the segmentation quality and consistency and enables a propagation of segments along the segmented images. The performance of the proposed approach is illustrated on both simulated and real image data.

Algorithms↗
PubMed2001

Two resting potential levels regulated by the inward-rectifier potassium channel in the guinea-pig spiral modiolar artery.

1. Intracellular in vitro recordings were made from 771 cells from the spiral modiolar artery (SMA). The initial resting potentials (RPs) displayed a bimodal distribution that was well modelled as a mixture of two Gaussian distributions. About half of the cells had an average RP of -74 mV, and were termed high-RP cells, whereas the other half had an average RP around -41 mV, and were termed low-RP cells. Preparations that were incubated for longer than 24 h contained significantly more high-RP cells than those incubated for less than 8 h. 2. When labelled with the fluorescent dye propidium iodide, 68 and 36 cells were identified as smooth muscle cells (SMC) and endothelial cells (EC), respectively. The RP and input resistance were not significantly different between these two types of cell. Dye coupling was observed only in ECs. Dual cell recordings with 0.2-1.0 mm separation demonstrated the simultaneous existence of high- and low-RP cells and a heterogeneous low-strength electrical coupling. 3. The high-RP cells were depolarized by ACh and by high extracellular potassium concentration (high K(+)). The low-RP cells were usually hyperpolarized by moderately high K(+) (7.5-20 mM) and by ACh. The high K(+)-induced hyperpolarization was suppressed by barium (Ba(2+), 10-50 microM). The putative gap junction blocker 18 beta-glycyrrhetinic acid suppressed the ACh-induced responses in SMCs, but not in ECs. 4. Low-RP cells could rapidly shift the membrane potential to a permanent high-RP state spontaneously or, more often, after a brief application of hyperpolarizing agents including high K(+), ACh, nitric oxide and pinacidil. Once shifted to a high-RP state, the responses of these cells to high K(+) and ACh became similar to those of the original high-RP cells. 5. High-RP cells occasionally shifted their potentials to a low-RP state either spontaneously or after a brief application of 10-50 microM Ba(2+) or 100 microM ouabain. Once shifted to the low-RP state, the response of these cells to high K(+) and ACh became a hyperpolarization. The shift between high- and low-RP states was largely mimicked by wash-in and wash-out of low concentrations of Ba(2+). The shift often showed a regenerative process as a fast phase in its middle course. 6. It is concluded that the cochlear SMA in vitro is composed of poorly and heterogeneously coupled SMCs and ECs, simultaneously resting in one of two distinct states, one a high-RP state and the other a low-RP state. The two RP states are exchangeable mainly due to all-or-none-like conductance changes of the inward-rectifier K(+) channel.

Acetylcholine↗
PubMed2003

Robust, automatic spike sorting using mixtures of multivariate t-distributions.

A number of recent methods developed for automatic classification of multiunit neural activity rely on a Gaussian model of the variability of individual waveforms and the statistical methods of Gaussian mixture decomposition. Recent evidence has shown that the Gaussian model does not accurately capture the multivariate statistics of the waveform samples' distribution. We present further data demonstrating non-Gaussian statistics, and show that the multivariate t-distribution, a wide-tailed family of distributions, provides a significantly better fit to the true statistics. We introduce an adaptation of a new expectation-maximization based competitive mixture decomposition algorithm and show that it efficiently and reliably performs mixture decomposition of t-distributions. Our algorithm determines the number of units in multiunit neural recordings, even in the presence of significant noise contamination resulting from random threshold crossings and overlapping spikes.

Action Potentials↗
PubMed2006

Spike sorting: Bayesian clustering of non-stationary data.

Spike sorting involves clustering spikes recorded by a micro-electrode according to the source neurons. It is a complicated task, which requires much human labor, in part due to the non-stationary nature of the data. We propose to automate the clustering process in a Bayesian framework, with the source neurons modeled as a non-stationary mixture-of-Gaussians. At a first search stage, the data are divided into short time frames, and candidate descriptions of the data as mixtures-of-Gaussians are computed for each frame separately. At a second stage, transition probabilities between candidate mixtures are computed, and a globally optimal clustering solution is found as the maximum-a-posteriori solution of the resulting probabilistic model. The transition probabilities are computed using local stationarity assumptions, and are based on a Gaussian version of the Jensen-Shannon divergence. We employ synthetically generated spike data to illustrate the method and show that it outperforms other spike sorting methods in a non-stationary scenario. We then use real spike data and find high agreement of the method with expert human sorters in two modes of operation: a fully unsupervised and a semi-supervised mode. Thus, this method differs from other methods in two aspects: its ability to account for non-stationary data, and its close to human performance.

Algorithms↗
PubMed2004

Admixture analysis of age at onset in schizophrenia.

In schizophrenia, clinical, familial and biological characteristics according to age at onset (AAO) suggest that AAO is a valid candidate symptom for genetic studies. However, none of the various thresholds used to define AAO subgroups in schizophrenia has been validated. We aim to define different AAO subtypes by admixture analysis in a sample of prospectively recruited subjects with schizophrenia. Consecutive inpatients and outpatients (N=141) meeting DSM IV criteria for schizophrenia were included. We used admixture analysis to investigate whether the observed AAO distribution consisted of a mixture of gaussian distributions and then compared clinical features and familial risks in the various groups of subjects. The model that best fitted the observed AAO distribution was a mixture of two gaussian distributions (mean+/-S.D.): (19.91+/-3.56 years) and (33.48+/-8.2 years), with a cutoff point at 28 years. The existence of two subgroups according to AAO was further confirmed by the different clinical and familial profiles of these subgroups. The early-onset group consisted predominantly of male patients, with non-paranoid subtypes and with a higher familial risk of schizophrenia spectrum disorders and affective disorders. The late-onset group of patients presented predominantly paranoid subtype, preponderance of females; they were more likely to be married and to have children. We identified two subgroups of schizophrenic subjects with different clinical and familial profiles. This study provides a mathematical validation of the existence of two subgroups defined by an onset of schizophrenia before or after 28 years. These results may have important implications for the search for schizophrenia susceptibility factors. Working with homogeneous subgroups defined on the basis of AAO may facilitate the identification of genetic vulnerability factors in schizophrenia.

Adult↗
PubMed2006

Neuroanatomical phenotypes in the reeler mouse.

The reeler mouse (Reln) has been proposed as a neurodevelopmental model for certain neurological and psychiatric conditions and has been studied by qualitative histochemistry and electron microscopy. Using magnetic resonance microscopy (MRM), we have quantitated for the first time the neuromorphology of Reln mice at a resolution of 21.5 microm. The neuroanatomical phenotypes of heterozygous and homozygous mutant Reln mice were compared to those of wild type (WT) littermates using morphometry and texture analysis. The cortical, hippocampal, and cerebellar phenotypes of the heterozygous and homozygous mutant Reln mice were confirmed, and new features were revealed. The Reln(rl/rl) mice possessed a smaller brain, and both Reln(rl/+) and Reln(rl/rl) mice had increased ventricles compared to WT controls. Shape differences were found between WT and Reln(rl/rl) brains, specifically in cerebellum, olfactory bulbs, dorsomedial frontal and parietal cortex, certain regions of temporal and occipital lobes, as well as in the lateral ventricles and ventral hippocampus. These findings suggest that certain brain regions may be more severely impacted by the Reln mutation than others. Gadolinium-based active staining demonstrated that layers of the hippocampus were disorganized in Reln(rl/rl) mice and differences in thickness of these layers were identified between WT and Reln(rl/rl) mice. The intensity distributions characteristic to the dorsal, middle, and ventral hippocampus were altered in the Reln(rl/rl), especially in the ventral hippocampus. These differences were quantified using skewness and modeling the intensity distributions with a Gaussian mixture. Our results suggest that structural features of Reln(rl/rl) brain most closely phenocopy those of patients with Norman-Roberts lissencephaly.

Animals↗
PubMed1979

Segregation of noisy Mendelian traits and the effect of age-dependence: a prolegomenon.

A discussion of the primordial confusion between the multiplicative Galtonian ("lognormal") trait and the imperfectly segregating Mendelian trait is laid out from a probabilistic standpoint. Several criteria used in comparing them (bimodality; bitangentiality; goodness of fit to the multinomialized form of the distribution; cumulants of the distributions) are reviewed and the inadequacy of their probabilistic properties discussed in some detail. The logical asymmetry of the normalized score ("Roberts" correction") and hence its invalidity as a criterion for distinguishing between the models is pointed out. The form of a mixture of two Gaussian distributions with fixed and equal variances but with differing age-dependent means ("the Platt model") is explored. The epistemological implications are exhibited. As a first step to restoring symmetry, a general model is proposed of which these and other models in wide use emerge as special cases. No attempt is made to deal here with the statistical aspects of the problem.

Age Factors↗
PubMed2002

High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity.

Magnetic resonance (MR) diffusion tensor imaging (DTI) can resolve the white matter fiber orientation within a voxel provided that the fibers are strongly aligned. However, a given voxel may contain a distribution of fiber orientations due to, for example, intravoxel fiber crossing. The present study sought to test whether a geodesic, high b-value diffusion gradient sampling scheme could resolve multiple fiber orientations within a single voxel. In regions of fiber crossing the diffusion signal exhibited multiple local maxima/minima as a function of diffusion gradient orientation, indicating the presence of multiple intravoxel fiber orientations. The multimodality of the observed diffusion signal precluded the standard tensor reconstruction, so instead the diffusion signal was modeled as arising from a discrete mixture of Gaussian diffusion processes in slow exchange, and the underlying mixture of tensors was solved for using a gradient descent scheme. The multitensor reconstruction resolved multiple intravoxel fiber populations corresponding to known fiber anatomy. Ma

Anisotropy↗
PubMed2006

Identification and separation of DNA mixtures using peak area information.

We introduce a new methodology, based upon probabilistic expert systems, for analysing forensic identification problems involving DNA mixture traces using quantitative peak area information. Peak area is modelled with conditional Gaussian distributions. The expert system can be used for ascertaining whether individuals, whose profiles have been measured, have contributed to the mixture. It can also be used to predict DNA profiles of unknown contributors by separating the mixture into its individual components. The potential of our probabilistic methodology is illustrated on case data examples and compared with alternative approaches. The advantages are that identification and separation issues can be handled in a unified way within a single probabilistic model and the uncertainty associated with the analysis is quantified. Further work, required to bring the methodology to a point where it could be applied to the routine analysis of casework, is discussed.

DNA↗
PubMedDate not supplied

Data smoothing regularization, multi-sets-learning, and problem solving strategies.

First, we briefly introduce the basic idea of data smoothing regularization, which was firstly proposed by Xu [Brain-like computing and intelligent information systems (1997) 241] for parameter learning in a way similar to Tikhonov regularization but with an easy solution to the difficulty of determining an appropriate hyper-parameter. Also, the roles of this regularization are demonstrated on Gaussian-mixture via smoothed versions of the EM algorithm, the BYY model selection criterion, adaptive harmony algorithm as well as its related Rival penalized competitive learning. Second, these studies are extended to a mixture of reconstruction errors of Gaussian types, which provides a new probabilistic formulation for the multi-sets learning approach [Proc. IEEE ICNN94 I (1994) 315] that learns multiple objects in typical geometrical structures such as points, lines, hyperplanes, circles, ellipses, and templates of given shapes. Finally, insights are provided on three problem solving strategies, namely the competition-penalty adaptation based learning, the global evidence accumulation based selection, and the guess-test based decision, with a general problem solving paradigm suggested.

Learning↗
PubMed2005

Segmentation of kidney from ultrasound images based on texture and shape priors.

This paper presents a novel texture and shape priors based method for kidney segmentation in ultrasound (US) images. Texture features are extracted by applying a bank of Gabor filters on test images through a two-sided convolution strategy. The texture model is constructed via estimating the parameters of a set of mixtures of half-planed Gaussians using the expectation-maximization method. Through this texture model, the texture similarities of areas around the segmenting curve are measured in the inside and outside regions, respectively. We also present an iterative segmentation framework to combine the texture measures into the parametric shape model proposed by Leventon and Faugeras. Segmentation is implemented by calculating the parameters of the shape model to minimize a novel energy function. The goal of this energy function is to partition the test image into two regions, the inside one with high texture similarity and low texture variance, and the outside one with high texture variance. The effectiveness of this method is demonstrated through experimental results on both natural images and US data compared with other image segmentation methods and manual segmentation.

Algorithms↗
PubMed1999

Mixtures of probabilistic principal component analyzers.

Principal component analysis (PCA) is one of the most popular techniques for processing, compressing, and visualizing data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Therefore, previous attempts to formulate mixture models for PCA have been ad hoc to some extent. In this article, PCA is formulated within a maximum likelihood framework, based on a specific form of gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analyzers, whose parameters can be determined using an expectation-maximization algorithm. We discuss the advantages of this model in the context of clustering, density modeling, and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.

Algorithms↗
PubMed2006

Perception through visuomotor anticipation in a mobile robot.

Several scientists suggested that certain perceptual qualities are based on sensorimotor anticipation: for example, the softness of a sponge is perceived by anticipating the sensations resulting from a grasping movement. For the perception of spatial arrangements, this article demonstrates that this concept can be realized in a mobile robot. The robot first learned to predict how its visual input changes under movement commands. With this ability, two perceptual tasks could be solved: judging the distance to an obstacle in front by 'mentally' simulating a movement toward the obstacle, and recognizing a dead end by simulating either an obstacle-avoidance algorithm or a recursive search for an exit. A simulated movement contained a series of prediction steps. In each step, a multilayer perceptron anticipated the next image, which, however, became increasingly noisy. To denoise an image, it was split into patches, and each patch was projected onto a manifold obtained by modelling the density of the distribution of training patches with a mixture of Gaussian functions.

Algorithms↗