Gunter Ritter

A robust method for cluster analysis

Let there be given a contaminated list of n R d -valued observations coming from g different, normally distributed populations with a common covariance matrix. We compute the ML-estimator with respect to a certain statistical model with n - r outliers for the parameters of the g populations; it detects outliers and simultaneously partitions their complement into g clusters. It turns out that the estimator unites both the minimum-covariance-determinant rejection method and the well-known pooled determinant criterion of cluster analysis. We also propose an efficient algorithm for approximating this estimator and study its breakdown points for mean values and pooled SSP matrix.

Diagnostics and characterisation of preocclusive stenoses and occlusions of the internal carotid artery with B-flow.

The purpose was to evaluate whether B-flow can improve the ultrasonographic diagnosis of preocclusive stenosis and occlusion of the internal carotid artery (ICA) compared with colour-coded Doppler and power Doppler. Ninety patients with occlusions or preocclusive stenoses of the ICA suspected by Doppler sonography were examined with B-flow in comparison with colour-coded Doppler sonography (CCDS), power Doppler (PD) and intra-arterial digital subtraction angiography (DSA). Intrastenotic flow detection and lengths of stenoses were the main criteria. Ulcerated plaques found by surgery in 42/90 patients were compared by ultrasonography (US). Diagnosis of ICA occlusion with CCDS, PD and B-flow was correct in all 42 cases. A preocclusive ICA stenosis in DSA was detected correctly in all 48/48 cases (100%) for B-flow, in 44/48 (92%) for PD and in 39/48 (81%) for CCDS. Surgical findings showed in 17/42 cases ulcerated plaques; 15/17 (89%) of these cases were detected with B-flow, 12/17 (71%) with PD, 10/17 (59%) with CCDS, and 8/17 (47%) with DSA. With B-flow the extent of stenosis was appraised more precisely than with PD and CCDS (P<0.0001). In conclusion, B-flow is a reliable method for preocclusive stenosis of the ICA with less intrastenotic flow artefacts. B-flow facilitates the characterization of plaque morphologies.

Using dominant points and variants for profile extraction from chromosomes

Abstract The most accurate methods for automatic analysis of chromosomes under a light microscope today extract numerical features from band-pattern profiles along their longitudinal axes. The construction of a reliable axis is a crucial step in this process. We propose a new way based on the dominant points of the contour and cubic splines. The dominant points serve as candidates for the tips of the chromosome. Ambiguities are dissolved by the recently developed method of variants for object identification. A Voronoi diagram decomposes the chromosome in slices for profile extraction. The method improves the currently best classification results significantly yielding a test-set error rate of 0.61%.

Trimming algorithms for clustering contaminated grouped data and their robustness

We establish an affine equivariant, constrained heteroscedastic model and criterion with trimming for clustering contaminated, grouped data. We show existence of the maximum likelihood estimator, propose a method for determining an appropriate constraint, and design a strategy for finding reasonable clusterings. We finally compute breakdown points of the estimated parameters thereby showing asymptotic robustness of the method.

Automatic context-sensitive karyotyping of human chromosomes based on elliptically symmetric statistical distributions

We introduce a statistical model of a metaphase cell consisting of independent chromosomes with elliptically symmetric feature vectors. From this model we derive the ML-classifier for classification in the 24 chromosomal classes, taking into account the correct number of chromosomes in each class. Experimental results show that error rates of the best of these classifiers are less than 2% with respect to chromosomes if applied to the large Copenhagen data set Cpr. Simulation studies suggest that there should be even more information contained in the features of this data set.

Profile and feature extraction from chromosomes

The most accurate methods for automatic classification of chromosomes under a light microscope today extract numerical features from band-pattern profiles along their longitudinal axes. The construction of a reliable axis is a crucial step in this process. We propose a new way based on the dominant points of the contour and cubic splines. The dominant points serve as candidates for the tips of the chromosome or its chromatid. Ambiguities are dissolved by the recently proposed method of variants for object identification. A Voronoi diagram decomposes the chromosome in slices for profile extraction. The method improves the currently best classification results significantly yielding a test-set error rate of 0.6% applied to a data set of the band level 200.

Polarity-free automatic classification of chromosomes

Automatic classification of the chromosomes of a metaphase eukaryotic cell under a light microscope into their biological classes is usually done in three steps: First, their centromeres are estimated in order to find their polarities, next a number of features are extracted from profiles of the oriented chromosomes, and finally the feature sets are assigned to classes. The first step is prone to errors since it is often not easy to detect the centromere. If it is determined on the wrong half of the chromosome then polarity is false leading to erroneous features in the second step and often to a misclassification. We reduce the error rate by applying the recently developed Bayesian method of variants to the profiles; applied to polarities, this method uses two feature sets for each chromosome, one for each polarity. We also take another look at feature extraction from profiles further reducing the error rate. Applied to the profiles of the Edinburgh MRC chromosome analysis system the most accurate methods reported here achieve cross-validation error rates below 1%.

Automatic classification of chromosomes by means of quadratically asymmetric statistical distributions

Abstract We use quadratically asymmetric distributions as introduced in Ritter [1, 2] as statistical models of human chromosomes for automatic constrained Bayesian classification into their 24 classes. These distributions are able to reflect asymmetries in the data. Moreover, we design algorithms for constrained classification of cells with missing and extra chromosomes (trisomies). Applied to the Edinburgh features of the large Copenhagen data set Cpr , the best classifier reported here reduces the cross-validation error rate from 2.7% (classical normal model) to 1.2% with respect to chromosomes. On the average, five out of six cells are completely correctly classified.

Using combinatorial optimization in model-based trimmed clustering with cardinality constraints

Statistical clustering criteria with free scale parameters and unknown cluster sizes are inclined to create small, spurious clusters. To mitigate this tendency a statistical model for cardinality-constrained clustering of data with gross outliers is established, its maximum likelihood and maximum a posteriori clustering criteria are derived, and their consistency and robustness are analyzed. The criteria lead to constrained optimization problems that can be solved by using iterative, alternating trimming algorithms of k-means type. Each step in the algorithms requires the solution of a @l-assignment problem known from combinatorial optimization. The method allows one to estimate the numbers of clusters and outliers. It is illustrated with a synthetic data set and a real one.

Automatic segmentation of metaphase cells based on global context and variant analysis

We treat the problem of chromosome segmentation with the aid of shape analysis and classification. Our approach consists of a combination of two phases, a purely rule-based phase and a phase driven by constrained discriminant analysis. In the first phase, obvious prototypical shape elements related to touchings and overlaps are recursively identified, in the second, remaining complex and ambiguous cases are treated. The latter phase exploits global context by using variant analysis, a statistical theory of ambiguity recently established. The method turns out to be quite accurate. The system works on whole clinical cells and to a certain degree when band patterns are not or not well visible.