Area Biplots

Classical multivariate analysis techniques such as principal components analysis and correspondence analysis use inner products to estimate data values. The results of these techniques may be visualized by representing the row and column points jointly in a biplot where the projection of a row point onto a column point vector followed by a multiplication by the length of the column point vector gives the inner-product that estimates the corresponding data element. In this paper, we propose a newvisualization: after a 90 degrees rotation of the row points, the areas spanned by a triangle of a row point, a column point and the origin estimate the data values. In contrast to the projection biplot, the areas spanned by different row and column points can be compared directly. Areas can only be produced for two dimensions at a time, but higher dimensional solutions can be represented by summing areas over subsequent pairs of dimensions. Here, the area biplot is developed for principal components analysis, correspondence analysis, and for interaction biplots but has general applicability.interaction;correspondence analysis;visualization;principal component analysis;biplot

Area Biplots

Classical multivariate analysis techniques such as principal components analysis and correspondence analysis use inner products to estimate data values. The results of these techniques may be visualized by representing the row and column points jointly in a biplot where the projection of a row point onto a column point vector followed by a multiplication by the length of the column point vector gives the inner-product that estimates the corresponding data element. In this paper, we propose a new visualization: after a 90 degrees rotation of the row points, the areas spanned by a triangle of a row point, a column point and the origin estimate the data values. In contrast to the projection biplot, the areas spanned by different row and column points can be compared directly. Areas can only be produced for two dimensions at a time, but higher dimensional solutions can be represented by summing areas over subsequent pairs of dimensions. Here, the area biplot is developed for principal components analysis, correspondence analysis, and for interaction biplots but has general applicability

A kernel extension to handle missing data

An extension for univariate kernels that deals with missing values is proposed. These extended kernels are shown to be valid Mercer kernels and can adapt to many types of variables, such as categorical or continuous. The proposed kernels are tested against standard RBF kernels in a variety of benchmark problems showing different amounts of missing values and variable types. Our experimental results are very satisfactory, because they usually yield slight to much better improvements over those achieved with standard methods.Postprint (author’s final draft

A Methodology and Tool for Rapid Prototyping of Data Warehouses using Data Mining: Application to Birds Biodiversity

International audienceData Warehouses (DWs) are large repositories of data aimed at supporting the decision-making process by enabling flexible and interactive analyses via OLAP systems. Rapid prototyping of DWs is necessary when OLAP applications are complex. Some work about the integration of Data Mining and OLAP systems has been done to enhance OLAP operators with mined indicators, and/or to define the DW schema. However, to best of our knowledge, prototyping methods for DWs do not support this kind of integration. Then, in this paper we present a new prototyping methodology for DWs, extending [3], where DM methods are used to define the DW schema. We validate our approach on a real data set concerning bird biodiversity

Definitions and standardization of a new grading scheme for eyelid contour abnormalities after trichiasis surgery

Background: Clear definitions of outcomes following trichiasis surgery are critical for planning program evaluations and for identifying ways to improve trichiasis surgery. Eyelid contour abnormality is an important adverse outcome of surgery; however, no standard method has been described to categorize eyelid contour abnormalities. Methodology/Principal Findings: A classification system for eyelid contour abnormalities following surgery for trachomatous trichiasis was developed. To determine whether the grading was reproducible using the classification system, six-week postoperative photographs were reviewed by two senior graders to characterize severity of contour abnormalities. Sample photographs defining each contour abnormality category were compiled and used to train four new graders. All six graders independently graded a Standardization Set of 75 eyelids, which included a roughly equal distribution across the severity scale, and weighted kappa scores were calculated. Two hundred forty six-week postoperative photographs from an ongoing clinical trial were randomly selected for evaluating agreement across graders. Two months after initial grading, one grader regraded a subset of the 240 photographs to measure longer-term intra-observer agreement. The weighted kappa for agreement between the two senior graders was 0.80 (95% CI: 0.71-0.89). Among the Standardization Set, agreement between the senior graders and the 4 new graders showed weighted kappa scores ranging from 0.60-0.80. Among 240 eyes comprising the clinical trial dataset, agreement ranged from weighted kappa 0.70-0.71. Longer-term intra-observer agreement was weighted kappa 0.86 (95% CI: 0.80-0.92). Conclusions/Significance: The standard eyelid contour grading system we developed reproducibly delineates differing levels of contour abnormality. This grading system could be useful both for helping to evaluate trichiasis surgery outcomes in clinical trials and for evaluating trichiasis surgery programs

Relationship between immediate post-operative appearance and 6-week operative outcome in trichiasis surgery

Background: Surgical technique, including suture placement and tension, is believed to contribute to the outcome of bilamellar tarsal rotation surgery for trachomatous trichiasis. However, the immediate post-operative appearance that minimizes the chance of recurrence and other adverse outcomes has not been investigated. Methodology/Principal Findings: To explore whether the degree of correction immediately after surgery is predictive of surgical outcome at the 6-week post-operative visit, photographs taken immediately after surgery were used to predict surgical outcomes, including the severity of eyelid contour abnormality and trichiasis recurrence. Both eyelid contour abnormalities and recurrence were accurately predicted from the immediate post-operative photographs by an experienced oculoplastic surgeon 85% and 70% of the time, respectively. Participants with a "slight over-correction" that resulted in no eyelid contour abnormality and no recurrence were used to identify immediate post-operative contours that lead to a successful surgical outcome. Conclusions/Significance: The immediate post-operative eyelid contour is an important indicator of post-operative success of BLTR surgery. Based upon our findings, we developed a Surgery Photocard. This card illustrates some examples of immediate post-surgical appearances, which led to a successful outcome, as well as sub-optimal appearances, which led to poor surgical outcomes. The card also provides suggestions for improving the appearance by adjusting the suture placement or tension based upon standard oculoplastic principles

The taxonomy and anatomy of rauisuchian archosaurs from the Late Triassic of Germany and Poland

The German Late Triassic archosaur Teratosaurus suevicus is a historically important taxon, being the first described rauisuchian. Unfortunately the holotype is a single element, a maxilla, which is poorly preserved and incomplete. We redescribe this maxilla and identify a single potential autapomorphy. The fragmentary type specimen complicates attempts to refer additional material to this taxon, and other unassociated archosaur and rauisuchian specimens from the Mittlerer Stubensandstein of Germany cannot be referred to T. suevicus with any degree of confidence. The stratigraphically older T. silesiacus, from the upper Carnian of Poland, is represented by a much more complete and better preserved specimen. Comparison of the maxillae of T. suevicus and T. silesiacus reveals that the two are distinct taxa, contra recent suggestions, but also that they do not share any synapomorphies or a unique combination of characters relative to Postosuchus kirkpatricki and other rauisuchians. Thus, the Polish material must be transferred to a new genus, Polonosuchus gen. nov. Both Polonosuchus and Teratosaurus are very similar to Postosuchus kirkpatricki, and the three taxa are likely closely related