Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

GLUT4 protein expression in obese and lean 12-month-old rats: insights from different types of data analysis

GLUT4 protein expression in white adipose tissue (WAT) and skeletal muscle (SM) was investigated in 2-month-old, 12-month-old spontaneously obese or 12-month-old calorie-restricted lean Wistar rats, by considering different parameters of analysis, such as tissue and body weight, and total protein yield of the tissue. In WAT, a ~70% decrease was observed in plasma membrane and microsomal GLUT4 protein, expressed as µg protein or g tissue, in both 12-month-old obese and 12-month-old lean rats compared to 2-month-old rats. However, when plasma membrane and microsomal GLUT4 tissue contents were expressed as g body weight, they were the same. In SM, GLUT4 protein content, expressed as µg protein, was similar in 2-month-old and 12-month-old obese rats, whereas it was reduced in 12-month-old obese rats, when expressed as g tissue or g body weight, which may play an important role in insulin resistance. Weight loss did not change the SM GLUT4 content. These results show that altered insulin sensitivity is accompanied by modulation of GLUT4 protein expression. However, the true role of WAT and SM GLUT4 contents in whole-body or tissue insulin sensitivity should be determined considering not only GLUT4 protein expression, but also the strong morphostructural changes in these tissues, which require different types of data analysis.

Sensory evaluation of "dulce de leche" with coffee and whey using different affective data analysis methods

This study sought to evaluate the acceptance of "dulce de leche" with coffee and whey. The results were analyzed through response surface, ANOVA, test of averages, histograms, and preference map correlating the global impression data with results of physical, physiochemical and sensory analysis. The response surface methodology, by itself, was not enough to find the best formulation. For ANOVA, test of averages, and preference map it was observed that the consumers' favorite "dulce de leche" were those of formulation 1 (10% whey and 1% coffee) and 2 (30% whey and 1% coffee), followed by formulation 9 (20% whey and 1.25% coffee). The acceptance of samples 1 and 2 was influenced by the higher acceptability in relation to the flavor and for presenting higher pH, L*, and b* values. It was observed that samples 1 and 2 presented higher purchase approval score and higher percentages of responses for the 'ideal' category in terms of sweetness and coffee flavor. It was found that consumers preferred the samples with low concentrations of coffee independent of the concentration of whey thus enabling the use of whey and coffee in the manufacture of dulce de leche, obtaining a new product.

Automated sugar analysis

Abstract Sugarcane monosaccharides are reducing sugars, and classical analytical methodologies (Lane-Eynon, Benedict, complexometric-EDTA, Luff-Schoorl, Musson-Walker, Somogyi-Nelson) are based on reducing copper ions in alkaline solutions. In Brazil, certain factories use Lane-Eynon, others use the equipment referred to as “REDUTEC”, and additional factories analyze reducing sugars based on a mathematic model. The objective of this paper is to understand the relationship between variations in millivolts, mass and tenors of reducing sugars during the analysis process. Another objective is to generate an automatic model for this process. The work herein uses the equipment referred to as “REDUTEC”, a digital balance, a peristaltic pump, a digital camcorder, math programs and graphics programs. We conclude that the millivolts, mass and tenors of reducing sugars exhibit a good mathematical correlation, and the mathematical model generated was benchmarked to low-concentration reducing sugars (<0.3%). Using the model created herein, reducing sugars analyses can be automated using the new equipment.

Spurring innovation through idea contests : data analysis and process improvements

This research concerns the Urban Living Idea Contest conducted by Creator Space™ of BASF SE during its 150th anniversary in 2015. The main objectives of the thesis are to provide a comprehensive analysis of the Urban Living Idea Contest (ULIC) and propose a number of improvement suggestions for future years. More than 4,000 data points were collected and analyzed to investigate the functionality of different elements of the contest. Furthermore, a set of improvement suggestions were proposed to BASF SE. Novelty of this thesis lies in the data collection and the original analysis of the contest, which identified its critical elements, as well as the areas that could be improved. The author of this research was a member of the organizing team and involved in the decision making process from the beginning until the end of the ULIC.

Development of a Fully Automated Image Analysis Method for High Density cDNA and array CGH Microarray Based Genomic Studies

In this thesis, different techniques for image analysis of high density microarrays have been investigated. Most of the existing image analysis techniques require prior knowledge of image specific parameters and direct user intervention for microarray image quantification. The objective of this research work was to develop of a fully automated image analysis method capable of accurately quantifying the intensity information from high density microarrays images. The method should be robust against noise and contaminations that commonly occur in different stages of microarray development.

Conceptual knowledge discovery and data analysis

In this paper, we discuss Conceptual Knowledge Discovery in Databases (CKDD) in its connection with Data Analysis. Our approach is based on Formal Concept Analysis, a mathematical theory which has been developed and proven useful during the last 20 years. Formal Concept Analysis has led to a theory of conceptual information systems which has been applied by using the management system TOSCANA in a wide range of domains. In this paper, we use such an application in database marketing to demonstrate how methods and procedures of CKDD can be applied in Data Analysis. In particular, we show the interplay and integration of data mining and data analysis techniques based on Formal Concept Analysis. The main concern of this paper is to explain how the transition from data to knowledge can be supported by a TOSCANA system. To clarify the transition steps we discuss their correspondence to the five levels of knowledge representation established by R. Brachman and to the steps of empirically grounded theory building proposed by A. Strauss and J. Corbin.

Lecture Notes on Compositional Data Analysis

These notes have been prepared as support to a short course on compositional data analysis. Their aim is to transmit the basic concepts and skills for simple applications, thus setting the premises for more advanced projects

Compositional data analysis: where we are and where should we be heading?

We take stock of the present position of compositional data analysis, of what has been achieved in the last 20 years, and then make suggestions as to what may be sensible avenues of future research. We take an uncompromisingly applied mathematical view, that the challenge of solving practical problems should motivate our theoretical research; and that any new theory should be thoroughly investigated to see if it may provide answers to previously abandoned practical considerations. Indeed a main theme of this lecture will be to demonstrate this applied mathematical approach by a number of challenging examples

Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By an essential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur in many compositional situations, such as household budget patterns, time budgets, palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful in such situations. From consideration of such examples it seems sensible to build up a model in two stages, the first determining where the zeros will occur and the second how the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data

Some last thoughts on compositional data analysis

One of the disadvantages of old age is that there is more past than future: this, however, may be turned into an advantage if the wealth of experience and, hopefully, wisdom gained in the past can be reflected upon and throw some light on possible future trends. To an extent, then, this talk is necessarily personal, certainly nostalgic, but also self critical and inquisitive about our understanding of the discipline of statistics. A number of almost philosophical themes will run through the talk: search for appropriate modelling in relation to the real problem envisaged, emphasis on sensible balances between simplicity and complexity, the relative roles of theory and practice, the nature of communication of inferential ideas to the statistical layman, the inter-related roles of teaching, consultation and research. A list of keywords might be: identification of sample space and its mathematical structure, choices between transform and stay, the role of parametric modelling, the role of a sample space metric, the underused hypothesis lattice, the nature of compositional change, particularly in relation to the modelling of processes. While the main theme will be relevance to compositional data analysis we shall point to substantial implications for general multivariate analysis arising from experience of the development of compositional data analysis…

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

Compositional data analysis with R

Examples of compositional data. The simplex, a suitable sample space for compositional data and Aitchison's geometry. R, a free language and environment for statistical computing and graphics

CoDaPack. An Excel and Visual Basic based software of compositional data analysis. Current version and discussion form upcoming versions

In the eighties, John Aitchison (1986) developed a new methodological approach for the statistical analysis of compositional data. This new methodology was implemented in Basic routines grouped under the name CODA and later NEWCODA inMatlab (Aitchison, 1997). After that, several other authors have published extensions to this methodology: Marín-Fernández and others (2000), Barceló-Vidal and others (2001), Pawlowsky-Glahn and Egozcue (2001, 2002) and Egozcue and others (2003). (...)

An R Library for Compositional Data Analysis in Archaeometry

Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and cluster analysis, to methods based upon the use of log-ratios. The general aim is to identify groups of chemically similar artefacts that could potentially be used to answer questions of provenance. This paper will demonstrate work in progress on the development of a documented library of methods, implemented using the statistical package R, for the analysis of compositional data. R is an open source package that makes available very powerful statistical facilities at no cost. We aim to show how, with the aid of statistical software such as R, traditional exploratory multivariate analysis can easily be used alongside, or in combination with, specialist techniques of compositional data analysis. The library has been developed from a core of basic R functionality, together with purpose-written routines arising from our own research (for example that reported at CoDaWork'03). In addition, we have included other appropriate publicly available techniques and libraries that have been implemented in R by other authors. Available functions range from standard multivariate techniques through to various approaches to log-ratio analysis and zero replacement. We also discuss and demonstrate a small selection of relatively new techniques that have hitherto been little-used in archaeometric applications involving compositional data. The application of the library to the analysis of data arising in archaeometry will be demonstrated; results from different analyses will be compared; and the utility of the various methods discussed