Suren I. Rathnayake

On the number of components in a Gaussian mixture model

Mixture distributions, in particular normal mixtures, are applied to data with two main purposes in mind. One is to provide an appealing semiparametric framework in which to model unknown distributional shapes, as an alternative to, say, the kernel density method. The other is to use the mixture model to provide a probabilistic clustering of the data into g clusters corresponding to the g components in the mixture model. In both situations, there is the question of how many components to include in the normal mixture model. We review various methods that have been proposed to answer this question. WIREs Data Mining Knowl Discov 2014, 4:341–355. doi: 10.1002/widm.1135

Nonlinear Features for Single-Channel Diagnosis of Sleep-Disordered Breathing Diseases

Studies have shown that algorithms based on single-channel airflow records are effective in screening for sleep-disordered breathing diseases (SDB). In this study, we investigate the diagnostic effectiveness of a classifier trained on a set of features derived from single-channel airflow measurements. The features considered are based on recurrence quantification analysis (RQA) of the measurement time series and are optionally augmented with single measurements of neck circumference and body mass index. The airflow measurement utilized is the nasal pressure (NP). The study used an overnight recording from each of 77 patients undergoing PSG testing. Mixture discriminant analysis was used to obtain a classifier, which predicts whether or not a measurement segment contains an SDB event. Patients were diagnosed as having SDB disease if the recording contained measurement segments predicted to include an SDB event at a rate exceeding a threshold value. A patient can be diagnosed as having SDB disease if the rate of SDB events per hour of sleep, the respiratory disturbance index (RDI), is ≥15 or sometimes ≥5. Here we trained and evaluated the classifier under each assumption, obtaining areas under receiver operating curves using fivefold cross-validation of 0.96 and 0.93, respectively. We used a two-layer structure to select the optimal operating point and assess the resulting classifier to avoid unbiased estimates. The resulting estimates for diagnostic sensitivity/specificity were 71.5%/89.5% for disease classification when RDI ≥ 15 and 63.3%/100% for RDI ≥ 5. These results were found assuming that the costs of misclassifying healthy and diseased subjects are equal, but we provide a framework to vary these costs. The results suggest that a classifier based on RQA features derived from NP measurements could be used in an automated SDB screening device.

On the classification of microarray gene-expression data

We consider the classification of microarray gene-expression data. First, attention is given to the supervised case, where the tissue samples are classified with respect to a number of predefined classes and the intent is to assign a new unclassified tissue to one of these classes. The problems of forming a classifier and estimating its error rate are addressed in the context of there being a relatively small number of observations (tissue samples) compared to the number of variables (that is, the genes, which can number in the tens of thousands). We then proceed to the unsupervised case and consider the clustering of the tissue samples and also the clustering of the gene profiles. Both problems can be viewed as being non-standard ones in statistics and we address some of the key issues involved. The focus is on the use of mixture models to effect the clustering for both problems.

Sleep-Stage and Event Dependency of Brain Asynchrony as manifested through surface EEG

Electroencephalography (EEG) is a core measurement in overnight sleep studies. In this paper we study functional asymmetries of the brain as manifested through spectral correlation coefficient. Our target group is patients symptomatic of sleep apnea and referred for routine Polysomnography (PSG) testing at the hospital. We measured EEG data (using electrodes C4/A1 and C3/A2 of the International 10/20 System) as a part of the routine PSG test. Spectral correlation coefficients were computed between EEG data from the two hemispheres, for each frequency band of interest: delta, thetas, alpha , and beta. Our results indicated that hemispheric correlation distinctly changes with the gross sleep type (REM/NREM) as well as with different sleep stages (stages 1-4) within NREM. It also varies in the presence of arousal events and apnea. These results may provide a basis for novel insights into the functional asymmetries of brain in sleep and sleep associated events such as arousals and apnea.

Dynamic Data Analysis in Obstructive Sleep Apnea

Obstructive Sleep Apnea (OSA) is a serious disease caused by the collapse of upper airways during sleep. The present method of measuring the severity of OSA is the Apnea Hypopnea Index (AHI). The AHI is defined as the average number of Obstructive events (Apnea and Hypopnea, OAH-events) during the total sleep period. The number of occurrence of OAH events during each hour of sleep is a random variable with an unknown probability density function. Thus the measure AHI alone is insufficient to describe its true nature. We propose a new measure Dynamic Apnea Hypopnea Index Time Series (DAHI), which captures the temporal density of Apnea event over shorter time intervals, and use its higher moments to obtain a dynamic characterization of OSA

Modelling of polysomnographic respiratory measurements for artefact detection and signal restoration.

Polysomnography (PSG), which incorporates measures of sleep with measures of EEG arousal, air flow, respiratory movement and oxygenation, is universally regarded as the reference standard in diagnosing sleep-related respiratory diseases such as obstructive sleep apnoea syndrome. Over 15 channels of physiological signals are measured from a subject undergoing a typical overnight PSG session. The signals often suffer from data losses, interferences and artefacts. In a typical sleep scoring session, artefact-corrupted signal segments are visually detected and removed from further consideration. This is a highly time-consuming process, and subjective judgement is required for the job. During typical sleep scoring sessions, the target is the detection of segments of diagnostic interest, and signal restoration is not utilized for distorted segments. In this paper, we propose a novel framework for artefact detection and signal restoration based on the redundancy among respiratory flow signals. We focus on the air flow (thermistor sensors) and nasal pressure signals which are clinically significant in detecting respiratory disturbances. The method treats the respiratory system and other organs that provide respiratory-related inputs/outputs to it (e.g., cardiovascular, brain) as a possibly nonlinear coupled-dynamical system, and uses the celebrated Takens embedding theorem as the theoretical basis for signal prediction. Nonlinear prediction across time (self-prediction) and signals (cross-prediction) provides us with a mechanism to detect artefacts as unexplained deviations. In addition to detection, the proposed method carries the potential to correct certain classes of artefacts and restore the signal. In this study, we categorize commonly occurring artefacts and distortions in air flow and nasal pressure measurements into several groups and explore the efficacy of the proposed technique in detecting/recovering them. The results we obtained from a database of clinical PSG signals indicated that the proposed technique can detect artefacts/distortions with a sensitivity>88.3% and specificity>92.4%. This work has the potential to simplify the work done by sleep scoring technicians, and also to improve automated sleep scoring methods.

A theory for ecological survey methods to map individual distributions

Spatially explicit approaches are widely recommended for ecosystem management. The quality of the data, such as presence/absence or habitat maps, affects the management actions recommended and is, therefore, key to management success. However, available data are often biased and incomplete. Previous studies have advanced ways to resolve data bias and missing data, but questions remain about how we design ecological surveys to develop a dataset through field surveys. Ecological surveys may have multiple spatial scales, including the spatial extent of the target ecosystem (observation window), the resolution for mapping individual distributions (mapping unit), and the survey area within each mapping unit (sampling unit). We developed an ecological survey method for mapping individual distributions by applying spatially explicit stochastic models. We used spatial point processes to describe individual spatial placements using either random or clustering processes. We then designed ecological surveys with different spatial scales and individual detectability. We found that the choice of mapping unit affected the presence mapped fraction, and the fraction of the total individuals covered by the presence mapped patches. Tradeoffs were found between these quantities and the map resolution, associated with equivalent asymptotic behaviors for both metrics at sufficiently small and large mapping unit scales. Our approach enabled consideration of the effect of multiple spatial scales in surveys, and estimation of the survey outcomes such as the presence mapped fraction and the number of individuals situated in the presence detected units. The developed theory may facilitate management decision-making and inform the design of monitoring and data gathering.

Spatially Explicit Approach To Population Abundance Estimation In Field Surveys

The abundance of species is a fundamental consideration in ecology and conservation biology. Although broad models have been proposed to estimate the population abundance using existing data, available data is often limited. With no information available, a population estimation will rely on time consuming field surveys. Typically, time is a critical constraint in conservation and often management decisions must be made quickly under the data limited situation. Depending on time and budgetary constraints, the required accuracy of field survey changes significantly. Hence, it is desirable to set up an effective survey design to minimize time and effort of sampling given required accuracy. We examine a spatially-explicit approach to population estimation using spatial point processes, enabling us to explicitly and consistently discuss various sampling designs. We find that the accuracy of abundance estimation varies with both ecological factors and survey design. Although the spatial scale of sampling does not affect estimation accuracy when the underlying individual distribution is random, it decreases with the sampled unit size if individuals tend to form clusters. These results are derived analytically and checked numerically. Obtained insights provide a benchmark to predict the quality of population estimation, and improve survey designs for ecological studies and conservation.

Testing for Group Structure in High-Dimensional Data

With the use of finite mixture models for the clustering of a data set, the crucial question of how many clusters there are in the data can be addressed by testing for the smallest number of components in the mixture model compatible with the data. We investigate the performance of a resampling approach to this latter problem in the context of high-dimensional data, where the number of variables p is extremely large relative to the number of observations n. In order to be able to fit normal mixture models to such data, some form of dimension reduction has to be performed. This raises the question of whether a practically significant bias results if the bootstrapping is undertaken solely on the basis of the reduced dimensional form of the data, rather than using the full data from which to draw the bootstrap sample replications.

Correction to: A theory for ecological survey methods to map individual distributions

The original version of this article unfortunately contained a mistake. The x-axis in Figs. 4-6 in the original version of this article should be replaced with the x-axis shown in the improved figures below. This does not change the calculations and conclusions.