A tale of two logits, compositional data analysis and zero observations

The application of compositional data analysis through log ratio trans- formations corresponds to a multinomial logit model for the shares themselves. This model is characterized by the property of Independence of Irrelevant Alter- natives (IIA). IIA states that the odds ratio in this case the ratio of shares is invariant to the addition or deletion of outcomes to the problem. It is exactly this invariance of the ratio that underlies the commonly used zero replacement procedure in compositional data analysis. In this paper we investigate using the nested logit model that does not embody IIA and an associated zero replacement procedure and compare its performance with that of the more usual approach of using the multinomial logit model. Our comparisons exploit a data set that com- bines voting data by electoral division with corresponding census data for each division for the 2001 Federal election in Australia

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completely absent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involved parts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method is introduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that the theoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approach has reasonable properties from a compositional point of view. In particular, it is “natural” in the sense that it recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in the same paper a substitution method for missing values on compositional data sets is introduced

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by a simplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able to generate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow defining monitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

The allometry of non-employment. What can compositional data analysis tell us about labour market performance across the UK's regions?

The low levels of unemployment recorded in the UK in recent years are widely cited as evidence of the country’s improved economic performance, and the apparent convergence of unemployment rates across the country’s regions used to suggest that the longstanding divide in living standards between the relatively prosperous ‘south’ and the more depressed ‘north’ has been substantially narrowed. Dissenters from these conclusions have drawn attention to the greatly increased extent of non-employment (around a quarter of the UK’s working age population are not in employment) and the marked regional dimension in its distribution across the country. Amongst these dissenters it is generally agreed that non-employment is concentrated amongst older males previously employed in the now very much smaller ‘heavy’ industries (e.g. coal, steel, shipbuilding). This paper uses the tools of compositiona l data analysis to provide a much richer picture of non-employment and one which challenges the conventional analysis wisdom about UK labour market performance as well as the dissenters view of the nature of the problem. It is shown that, associated with the striking ‘north/south’ divide in nonemployment rates, there is a statistically significant relationship between the size of the non-employment rate and the composition of non-employment. Specifically, it is shown that the share of unemployment in non-employment is negatively correlated with the overall non-employment rate: in regions where the non-employment rate is high the share of unemployment is relatively low. So the unemployment rate is not a very reliable indicator of regional disparities in labour market performance. Even more importantly from a policy viewpoint, a significant positive relationship is found between the size of the non-employment rate and the share of those not employed through reason of sickness or disability and it seems (contrary to the dissenters) that this connection is just as strong for women as it is for men

Compositional ideas in the bayesian analysis of categorical data with application to dose finding clinical trials

Compositional random vectors are fundamental tools in the Bayesian analysis of categorical data. Many of the issues that are discussed with reference to the statistical analysis of compositional data have a natural counterpart in the construction of a Bayesian statistical model for categorical data. This note builds on the idea of cross-fertilization of the two areas recommended by Aitchison (1986) in his seminal book on compositional data. Particular emphasis is put on the problem of what parameterization to use

Alternative ways to estimate change points in multinomial sequences. An application to an authorship attribution problem

The statistical analysis of literary style is the part of stylometry that compares measurable characteristics in a text that are rarely controlled by the author, with those in other texts. When the goal is to settle authorship questions, these characteristics should relate to the author’s style and not to the genre, epoch or editor, and they should be such that their variation between authors is larger than the variation within comparable texts from the same author. For an overview of the literature on stylometry and some of the techniques involved, see for example Mosteller and Wallace (1964, 82), Herdan (1964), Morton (1978), Holmes (1985), Oakes (1998) or Lebart, Salem and Berry (1998). Tirant lo Blanc, a chivalry book, is the main work in catalan literature and it was hailed to be “the best book of its kind in the world” by Cervantes in Don Quixote. Considered by writters like Vargas Llosa or Damaso Alonso to be the first modern novel in Europe, it has been translated several times into Spanish, Italian and French, with modern English translations by Rosenthal (1996) and La Fontaine (1993). The main body of this book was written between 1460 and 1465, but it was not printed until 1490. There is an intense and long lasting debate around its authorship sprouting from its first edition, where its introduction states that the whole book is the work of Martorell (1413?-1468), while at the end it is stated that the last one fourth of the book is by Galba (?-1490), after the death of Martorell. Some of the authors that support the theory of single authorship are Riquer (1990), Chiner (1993) and Badia (1993), while some of those supporting the double authorship are Riquer (1947), Coromines (1956) and Ferrando (1995). For an overview of this debate, see Riquer (1990). Neither of the two candidate authors left any text comparable to the one under study, and therefore discriminant analysis can not be used to help classify chapters by author. By using sample texts encompassing about ten percent of the book, and looking at word length and at the use of 44 conjunctions, prepositions and articles, Ginebra and Cabos (1998) detect heterogeneities that might indicate the existence of two authors. By analyzing the diversity of the vocabulary, Riba and Ginebra (2000) estimates that stylistic boundary to be near chapter 383. Following the lead of the extensive literature, this paper looks into word length, the use of the most frequent words and into the use of vowels in each chapter of the book. Given that the features selected are categorical, that leads to three contingency tables of ordered rows and therefore to three sequences of multinomial observations. Section 2 explores these sequences graphically, observing a clear shift in their distribution. Section 3 describes the problem of the estimation of a suden change-point in those sequences, in the following sections we propose various ways to estimate change-points in multinomial sequences; the method in section 4 involves fitting models for polytomous data, the one in Section 5 fits gamma models onto the sequence of Chi-square distances between each row profiles and the average profile, the one in Section 6 fits models onto the sequence of values taken by the first component of the correspondence analysis as well as onto sequences of other summary measures like the average word length. In Section 7 we fit models onto the marginal binomial sequences to identify the features that distinguish the chapters before and after that boundary. Most methods rely heavily on the use of generalized linear models

Application of compositional data analysis to geochemical data of marine sediments

In an earlier investigation (Burger et al., 2000) five sediment cores near the Rodrigues Triple Junction in the Indian Ocean were studied applying classical statistical methods (fuzzy c-means clustering, linear mixing model, principal component analysis) for the extraction of endmembers and evaluating the spatial and temporal variation of geochemical signals. Three main factors of sedimentation were expected by the marine geologists: a volcano-genetic, a hydro-hydrothermal and an ultra-basic factor. The display of fuzzy membership values and/or factor scores versus depth provided consistent results for two factors only; the ultra-basic component could not be identified. The reason for this may be that only traditional statistical methods were applied, i.e. the untransformed components were used and the cosine-theta coefficient as similarity measure. During the last decade considerable progress in compositional data analysis was made and many case studies were published using new tools for exploratory analysis of these data. Therefore it makes sense to check if the application of suitable data transformations, reduction of the D-part simplex to two or three factors and visual interpretation of the factor scores would lead to a revision of earlier results and to answers to open questions . In this paper we follow the lines of a paper of R. Tolosana- Delgado et al. (2005) starting with a problem-oriented interpretation of the biplot scattergram, extracting compositional factors, ilr-transformation of the components and visualization of the factor scores in a spatial context: The compositional factors will be plotted versus depth (time) of the core samples in order to facilitate the identification of the expected sources of the sedimentary process. Kew words: compositional data analysis, biplot, deep sea sediments

Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developed to explore patterns in high-dimensional multivariate data. The conventional version of the algorithm involves the use of Euclidean metric in the process of adaptation of the model vectors, thus rendering in theory a whole methodology incompatible with non-Euclidean geometries. In this contribution we explore the two main aspects of the problem: 1. Whether the conventional approach using Euclidean metric can shed valid results with compositional data. 2. If a modification of the conventional approach replacing vectorial sum and scalar multiplication by the canonical operators in the simplex (i.e. perturbation and powering) can converge to an adequate solution. Preliminary tests showed that both methodologies can be used on compositional data. However, the modified version of the algorithm performs poorer than the conventional version, in particular, when the data is pathological. Moreover, the conventional ap- proach converges faster to a solution, when data is \well-behaved". Key words: Self Organizing Map; Artificial Neural networks; Compositional data

Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering of compositional data in situations where observations are constituted by trajectories of compositional data, that is, by sequences of composition measurements along a domain. Observed trajectories are known as “functional data” and several methods have been proposed for their analysis. In particular, methods for clustering functional data, known as Functional Cluster Analysis (FCA), have been applied by practitioners and scientists in many fields. To our knowledge, FCA techniques have not been extended to cope with the problem of clustering compositional data trajectories. In order to extend FCA techniques to the analysis of compositional data, FCA clustering techniques have to be adapted by using a suitable compositional algebra. The present work centres on the following question: given a sample of compositional data trajectories, how can we formulate a segmentation procedure giving homogeneous classes? To address this problem we follow the steps described below. First of all we adapt the well-known spline smoothing techniques in order to cope with the smoothing of compositional data trajectories. In fact, an observed curve can be thought of as the sum of a smooth part plus some noise due to measurement errors. Spline smoothing techniques are used to isolate the smooth part of the trajectory: clustering algorithms are then applied to these smooth curves. The second step consists in building suitable metrics for measuring the dissimilarity between trajectories: we propose a metric that accounts for difference in both shape and level, and a metric accounting for differences in shape only. A simulation study is performed in order to evaluate the proposed methodologies, using both hierarchical and partitional clustering algorithm. The quality of the obtained results is assessed by means of several indices

Revisiting the compositional data. Some fundamental questions and new prospects in Archaeometry and Archaeology

In this paper we examine the problem of compositional data from a different starting point. Chemical compositional data, as used in provenance studies on archaeological materials, will be approached from the measurement theory. The results will show, in a very intuitive way that chemical data can only be treated by using the approach developed for compositional data. It will be shown that compositional data analysis is a particular case in projective geometry, when the projective coordinates are in the positive orthant, and they have the properties of logarithmic interval metrics. Moreover, it will be shown that this approach can be extended to a very large number of applications, including shape analysis. This will be exemplified with a case study in architecture of Early Christian churches dated back to the 5th-7th centuries AD

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data

INFO6003 (2013) Data Exfiltration -- Papers

This is a fun paper about data exfiltration. It's suggested reading, I'd like you to try and grasp how difficult the problem is why looking at one 'creative" attack. The second paper is a technical approach, only for the people seriously interested in this topic.

WAIS seminar: Alan Walks Wales: Data and Challenges

Abstract This seminar is a research discussion around a very interesting problem, which may be a good basis for a WAISfest theme. A little over a year ago Professor Alan Dix came to tell us of his plans for a magnificent adventure:to walk all of the way round Wales - 1000 miles 'Alan Walks Wales'. The walk was a personal journey, but also a technological and community one, exploring the needs of the walker and the people along the way. Whilst walking he recorded his thoughts in an audio diary, took lots of photos, wrote a blog and collected data from the tech instruments he was wearing. As a result Alan has extensive quantitative data (bio-sensing and location) and qualitative data (text, images and some audio). There are challenges in analysing individual kinds of data, including merging similar data streams, entity identification, time-series and textual data mining, dealing with provenance, ontologies for paths, and journeys. There are also challenges for author and third-party annotation, linking the data-sets and visualising the merged narrative or facets of it.

Big Data or Right Data?

Abstract Big data nowadays is a fashionable topic, independently of what people mean when they use this term. But being big is just a matter of volume, although there is no clear agreement in the size threshold. On the other hand, it is easy to capture large amounts of data using a brute force approach. So the real goal should not be big data but to ask ourselves, for a given problem, what is the right data and how much of it is needed. For some problems this would imply big data, but for the majority of the problems much less data will and is needed. In this talk we explore the trade-offs involved and the main problems that come with big data using the Web as case study: scalability, redundancy, bias, noise, spam, and privacy. Speaker Biography Ricardo Baeza-Yates Ricardo Baeza-Yates is VP of Research for Yahoo Labs leading teams in United States, Europe and Latin America since 2006 and based in Sunnyvale, California, since August 2014. During this time he has lead the labs in Barcelona and Santiago de Chile. Between 2008 and 2012 he also oversaw the Haifa lab. He is also part time Professor at the Dept. of Information and Communication Technologies of the Universitat Pompeu Fabra, in Barcelona, Spain. During 2005 he was an ICREA research professor at the same university. Until 2004 he was Professor and before founder and Director of the Center for Web Research at the Dept. of Computing Science of the University of Chile (in leave of absence until today). He obtained a Ph.D. in CS from the University of Waterloo, Canada, in 1989. Before he obtained two masters (M.Sc. CS & M.Eng. EE) and the electronics engineer degree from the University of Chile in Santiago. He is co-author of the best-seller Modern Information Retrieval textbook, published in 1999 by Addison-Wesley with a second enlarged edition in 2011, that won the ASIST 2012 Book of the Year award. He is also co-author of the 2nd edition of the Handbook of Algorithms and Data Structures, Addison-Wesley, 1991; and co-editor of Information Retrieval: Algorithms and Data Structures, Prentice-Hall, 1992, among more than 500 other publications. From 2002 to 2004 he was elected to the board of governors of the IEEE Computer Society and in 2012 he was elected for the ACM Council. He has received the Organization of American States award for young researchers in exact sciences (1993), the Graham Medal for innovation in computing given by the University of Waterloo to distinguished ex-alumni (2007), the CLEI Latin American distinction for contributions to CS in the region (2009), and the National Award of the Chilean Association of Engineers (2010), among other distinctions. In 2003 he was the first computer scientist to be elected to the Chilean Academy of Sciences and since 2010 is a founding member of the Chilean Academy of Engineering. In 2009 he was named ACM Fellow and in 2011 IEEE Fellow.

Data-Driven Text Generation using Neural Networks & Provenance is Complicated and Boring — Is there a solution?

Title: Data-Driven Text Generation using Neural Networks Speaker: Pavlos Vougiouklis, University of Southampton Abstract: Recent work on neural networks shows their great potential at tackling a wide variety of Natural Language Processing (NLP) tasks. This talk will focus on the Natural Language Generation (NLG) problem and, more specifically, on the extend to which neural network language models could be employed for context-sensitive and data-driven text generation. In addition, a neural network architecture for response generation in social media along with the training methods that enable it to capture contextual information and effectively participate in public conversations will be discussed. Speaker Bio: Pavlos Vougiouklis obtained his 5-year Diploma in Electrical and Computer Engineering from the Aristotle University of Thessaloniki in 2013. He was awarded an MSc degree in Software Engineering from the University of Southampton in 2014. In 2015, he joined the Web and Internet Science (WAIS) research group of the University of Southampton and he is currently working towards the acquisition of his PhD degree in the field of Neural Network Approaches for Natural Language Processing. Title: Provenance is Complicated and Boring — Is there a solution? Speaker: Darren Richardson, University of Southampton Abstract: Paper trails, auditing, and accountability — arguably not the sexiest terms in computer science. But then you discover that you've possibly been eating horse-meat, and the importance of provenance becomes almost palpable. Having accepted that we should be creating provenance-enabled systems, the challenge of then communicating that provenance to casual users is not trivial: users should not have to have a detailed working knowledge of your system, and they certainly shouldn't be expected to understand the data model. So how, then, do you give users an insight into the provenance, without having to build a bespoke system for each and every different provenance installation? Speaker Bio: Darren is a final year Computer Science PhD student. He completed his undergraduate degree in Electronic Engineering at Southampton in 2012.