Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm

The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in various ways. However there are different interpretations in the literature and there are different implementations of the Ward agglomerative algorithm in commonly used software systems, including differing expressions of the agglomerative criterion. Our survey work and case studies will be useful for all those involved in developing software for data analysis using Ward's hierarchical clustering method.Comment: 20 pages, 21 citations, 4 figure

Patient and health care professional decision-making to commence and withdraw from renal dialysis: A systematic review of qualitative research

Background and objectives. To ensure decisions to start and stop dialysis in end stage kidney disease are shared, the factors that affect patients and healthcare professionals in making such decisions need to be understood. This systematic review aims to explore how and why different factors mediate the choices about dialysis treatment. Design, setting, participants, and measurements. Medline, Embase, CINAHL and PsychINFO were searched for qualitative studies of factors that affect patients’ and/or healthcare professionals’ decisions to commence or withdraw from dialysis. A thematic synthesis was conducted. Results. Of 494 articles screened, 12 studies (conducted: 1985-2014) were included. These involved 206 predominantly haemodialysis patients and 64 healthcare professionals (age range: patients 26-93; professionals 26-61 years). (i) Commencing dialysis: patients based their choice on ‘gut-instinct’ as well as deliberating the impact of treatment on quality-of-life and survival. How individuals coped with decision-making was influential, some tried to take control of the problem of progressive renal failure, whilst others focussed on controlling their emotions. Healthcare professionals weighed-up biomedical factors and were led by an instinct to prolong life. Both patients and healthcare professionals described feeling powerless. (ii) Dialysis withdrawal: Only after prolonged periods of time on dialysis, were the realities of life on dialysis fully appreciated and past choice questioned. By this stage however patients were physically treatment dependent. Similar to commencing dialysis, individuals coped with treatment withdrawal in a problem or emotion-controlling way. Families struggled to differentiate choosing versus allowing death. Healthcare teams avoided and queried discussions regarding dialysis withdrawal. Patients however missed the dialogue they experienced during pre-dialysis education. Conclusions. Decision-making in end stage kidney disease is complex, dynamic, and evolves over time and towards death. The factors at work are multi-faceted and operate differently for patients and health professionals. More training and research on open-communication and shared decision-making is needed

Degenerating families of dendrograms

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist $p$-adic representation of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the $p$-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are $p$-adic parameter spaces of (families of) dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.Comment: 13 pages, 8 figure

Fast, Linear Time Hierarchical Clustering using the Baire Metric

The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. In this work we evaluate empirically this new approach to hierarchical clustering. We compare hierarchical clustering based on the Baire metric with (i) agglomerative hierarchical clustering, in terms of algorithm properties; (ii) generalized ultrametrics, in terms of definition; and (iii) fast clustering through k-means partititioning, in terms of quality of results. For the latter, we carry out an in depth astronomical study. We apply the Baire distance to spectrometric and photometric redshifts from the Sloan Digital Sky Survey using, in this work, about half a million astronomical objects. We want to know how well the (more costly to determine) spectrometric redshifts can predict the (more easily obtained) photometric redshifts, i.e. we seek to regress the spectrometric on the photometric redshifts, and we use clusterwise regression for this.Comment: 27 pages, 6 tables, 10 figure

Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

Decision boundaries using Bayes factors: the case of cloud masks

We assess the use of an approximation to the Bayes factor for objectively assessing spatial segmentation models. The Bayes factor allows us to automatically determine thresholds, in multidimensional feature space, for such objectives as cloud mask definition. We compare our results with a cloud map currently provided as a data product

Network Resources for Astronomers

The amount of data produced by large observational facilities and space missions has led to the archiving and on-line accessibility of much of this data, available to the entire astronomical community. This allows a much wider multi-frequency approach to astronomical research than previously possible. Here we provide an overview of these services, and give a basic description of their contents and possibilities for accessing them. Apart from services providing observational data, many of those providing general information, e.g. on addresses, bibliographies, software etc. are also described. The field is rapidly growing with improved network technology, and our attempt to keep the report as complete and up-to-date as possible will inevitably be outdated shortly. We will endeavor to maintain an updated version of this document on-line.Comment: 53 pages; uuencoded compressed PostScript; includes one table, no figures; Lyon-41 (Aug'94) and ESO-1033 (Sept'94), to appear in PASP, November 1994 issu