Agustín Mayo-Iscar

A general trimming approach to robust cluster Analysis

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is de- signed by allowing to handle a proportionof contaminating data to guarantee the robustness of the method. As a characteristic fea- ture, restrictions on the ratio between the maximum and the mini- mum eigenvalues of the groups scatter matrices are introduced. This makes the problem to be well defined and guarantees the consistency of the sample solutions to the population ones. The method covers a wide range of clustering approaches depend- ing on the strength of the chosen restrictions. Our proposal includes an algorithm for approximately solving the sample problem.

A review of robust clustering methods

Deviations from theoretical assumptions together with the presence of certain amount of outlying observations are common in many practical statistical applications. This is also the case when applying Cluster Analysis methods, where those troubles could lead to unsatisfactory clustering results. Robust Clustering methods are aimed at avoiding these unsatisfactory results. Moreover, there exist certain connections between robust procedures and Cluster Analysis that make Robust Clustering an appealing unifying framework. A review of different robust clustering approaches in the literature is presented. Special attention is paid to methods based on trimming which try to discard most outlying data when carrying out the clustering process.

Exploring the number of groups in robust model-based clustering

Two key questions in Clustering problems are how to determine the number of groups properly and measure the strength of group-assignments. These questions are specially involved when the presence of certain fraction of outlying data is also expected.Any answer to these two key questions should depend on the assumed probabilistic-model, the allowed group scatters and what we understand by noise. With this in mind, some exploratory “trimming-based” tools are presented in this work together with their justifications. The monitoring of optimal values reached when solving a robust clustering criteria and the use of some “discriminant” factors are the basis for these exploratory tools.

Interaction between surgical procedure for repairing retinal detachment and clinical risk factors for proliferative vitreoretinopathy.

Purpose: To asses risk factors of proliferative vitreoretinopathy (PVR) and a model for predicting it. Methods: Observational, case-control. 335 patients with non-complicated retinal detachment (RD) were included: 134 developed PVR (Cases); 201 patients did not (Controls). Risk factors for PVR were identified by multivariate analysis. Influence of variables was assayed according to the surgical approach. By logistic regression analysis a model to predict the risk of developing PVR and odds ratio (OR) values for each clinical factor were estimated. Results: Risk was higher in patients > 70 years and with intraocular pressure lower than 14 (OR: 3.84; CI 95%: 2.04–7.30) and in retinal breaks larger than “1 clock hour” (OR: 2.54; CI: 1.28–5.05), extended retinal detachments (OR: 4.01; CI: 1.98–8.10) and reinterventions (OR: 1.55; CI: 1.14–9.22). Scleral surgery also was a risk factor (OR: 3.89; CI: 2.12–7.14) and aphakia/pseudophakia when scleral surgery is performed (OR: 3.33; CI: 1.54–7.22). A model to predict PVR was proposed with these results. Conclusions: Surgical approach modifies risk factors of PVR, and should be taken into account to improve the models for predicting it.

A constrained robust proposal for mixture modeling avoiding spurious solutions

The high prevalence of spurious solutions and the disturbing effect of outlying observations in mixture modeling are well known problems that pose serious difficulties for non-expert practitioners of this kind of models in different applied areas. An approach which combines the use of Trimmed Maximum Likelihood ideas and the imposition of restrictions on the maximization problem will be presented and studied in this paper. The proposed methodology is shown to have nice mathematical properties as well as good performance in avoiding the appearance of spurious solutions in a quite automatic manner.

Design and Evaluation of a Customized Reading Rehabilitation Program for Patients with Age-related Macular Degeneration

PURPOSE To evaluate the efficacy of a reading rehabilitation program (RRP) specifically designed for patients with impaired central vision from age-related macular degeneration (AMD) and the impact of the program on the quality of life (QoL) and to determine any predictable reading performance improvements between visits. DESIGN Prospective case series. PARTICIPANTS Forty-one patients with AMD who attended to the Institute of Applied Ophthalmobiology Eye Institute. METHODS An ad hoc-created RRP comprising 4 customized in-office training and in-home training visits over 6 weeks was undertaken by AMD patients. The RRP was based on the principle of stepwise progressive goal achievement: the difficulty of training tasks increased depending on the success obtained when performing previous easier ones. Reading performance was evaluated during each in-office training visit, and the individuals perception of his or her QoL was assessed before and after the RRP. Reading performance parameters were assessed to evaluate RRP effectiveness. MAIN OUTCOME MEASURES Best-corrected visual acuity (BCVA), reading speed, reading duration, near visual acuity (VA), font size, and the World Health Organization Quality of Life (WHOQOL-BREF) questionnaire scores. The effect sizes (mean differences and standard deviations) also were calculated. RESULTS The mean distance BCVA was 0.81±0.29 logarithm of the minimum angle of resolution units. The mean near VA with the appropriate low-vision aid was 0.91±0.18 (M notation) at baseline. The mean near magnification was 4.32±1.15 at the last in-office visit. The mean reading speed, reading duration, and font size improvement after the reading rehabilitation program were 48.31±22.06 words per minute (P<0.001), 35.46±15.68 minutes (P<0.001), and -4.08±2.19 font points (P<0.001), respectively. The effect sizes of reading speed, reading duration, and font size after the last visit were 2.19, 2.26, and -1.86, respectively. The final score of each WHOQOL-BREF domain improved significantly (P≤0.004) after the RRP. The increased ability to read a smaller font size was correlated with improvement in the physical health domain score of the WHOQOL-BREF (r=0.35; P=0.04). CONCLUSIONS This customized RRP significantly enhanced reading performance and perceived QoL in patients with AMD. The improvement between visits seemed to be consistent. FINANCIAL DISCLOSURE(S) The author(s) have no proprietary or commercial interest in any materials discussed in this article.

Proliferative vitreoretinopathy: cytologic findings in vitreous samples.

Purpose: To compare the cellularity of vitreous samples obtained from patients with rhegmatogenous retinal detachment complicated by proliferative vitreoretinopathy (PVR) and from patients with uncomplicated rhegmatogenous retinal detachment (RD) to detect possible variations in cellularity over time. Methods: One hundred and twenty-five vitreous specimens collected from patients with RD (n = 41) and PVR (n = 84) were processed through direct paraffin embedding and cytospin. Different cell types were identified by light-microscopy (hematoxylin-eosin and Papanicolaou stain) according to their morphologic features, and a scale of cellular density was established for each cell type. Student’s t test was used to analyze differences in the cellularity of RD versus PVR. A quadratic model was used to identify variations in the density of each cellular type in the PVR group, based on its evolution time. Results: During the first months after surgery, more macrophages and fibroblast-like cells were observed in the PVR group, but at other times no differences were found. Conclusions: There are some differences in vitreous cellularity in PVR specimens when compared with RD. Especially relevant could be the large number of macrophages in earlier stages and their constant presence over time in PVR samples. The cytology of vitreous samples may shed light on the chronology of PVR cell pathobiology.

Trimming and likelihood: Robust location and dispersion estimation in the elliptical model

Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here we analyze some one (or k)-step Maximum Likelihood Estimators computed on a subsample obtained with such a procedure. We introduce different models which arise naturally from the ways in which the discarded data can be treated, leading to truncated or censored likelihoods, as well as to a likelihood based on an only outliers gross errors model. Results on existence, uniqueness, robustness and asymptotic properties of the proposed estimators are included. A remarkable fact is that the proposed estimators generally keep the breakdown point of the initial (robust) estimators, but they could improve the rate of convergence of the initial estimator because our estimators always converge at rate n 1/2 , independently of the rate of convergence of the initial estimator.

Avoiding spurious local maximizers in mixture modeling

The maximum likelihood estimation in the finite mixture of distributions setting is an ill-posed problem that is treatable, in practice, through the EM algorithm. However, the existence of spurious solutions (singularities and non-interesting local maximizers) makes difficult to find sensible mixture fits for non-expert practitioners. In this work, a constrained mixture fitting approach is presented with the aim of overcoming the troubles introduced by spurious solutions. Sound mathematical support is provided and, which is more relevant in practice, a feasible algorithm is also given. This algorithm allows for monitoring solutions in terms of the constant involved in the restrictions, which yields a natural way to discard spurious solutions and a valuable tool for data analysts.

The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers

Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering-at the same time-dimension reduction and model-based clustering. The high prevalence of spurious solutions and the disturbing effects of outlying observations in maximum likelihood estimation may cause biased or misleading inferences. Restrictions for the component covariances are considered in order to avoid spurious solutions, and trimming is also adopted, to provide robustness against violations of normality assumptions of the underlying latent factors. A detailed AECM algorithm for this new approach is presented. Simulation results and an application to the AIS dataset show the aim and effectiveness of the proposed methodology.