In this survey article, we review glyph-based visualization techniques, which have been exploited when visualizing spatial multivariate medical data. To classify these techniques, we derive a taxonomy of glyph properties, which is based on classification concepts established in information visualization. By considering both the glyph visualization as well as the interaction techniques that are employed to generate or explore the glyph visualization, we are able to classify glyph techniques into two main groups: those supporting pre-attentive and those supporting attentive processing. With respect to this classification, we review glyph-based techniques described in the medical visualization literature. Based on the outcome of the literature review, we propose design guidelines for glyph visualizations in the medical domain.

No description available.

The original SMVCIR algorithm was developed by Simon J. Sheather, Joseph W. McKean, and Kimberly Crimin. The dissertation first presents a new version of this algorithm that uses the scaling standardization rather than the Mahalanobis standardization. This algorithm takes grouped multivariate data as input and then outputs a new coordinate space that contrasts the groups in location, scale, and covariance. The central goal of research is to develop a method to determine the dimension of this space with statistical confidence. A dimensionality test is developed that can be used to make this determination. The new SMVCIR algorithm is compared with two other inverse regression algorithms, SAVE and SIR in the process of developing the dimensionality test and testing it. The dimensionality test is based on the singular values of the kernel of the spanning set of the vector space. The asymptotic distribution of the spanning set is found by using the central limit theorem, delta method, and finally Slutsky's Theorem with a permutation matrix. This yields a mean adjusted asymptotic distribution of the spanning set. Theory by Eaton, Tyler, and others is then used to show an equivalence between the singular values of the mean adjusted spanning set statistic and the singular values of the spanning set statistic. The test statistic is a sample size scaled sum of squared singular values of the spanning set. This statistic is asymptotically equivalent in distribution to that of a linear combination of independent 21 random variables. Simulations are performed to corroborate these theoretic findings. Additionally, based on work by Bentler and Xie, an approximation to the test statistic reference distribution is proposed and tested. This is also corroborated with simulations. Examples are performed that demonstrate how SMVCIR is used and how the developed tests for dimensionality are performed. Finally, further directions of research are hinted at for SMVCIR and the dimensionality test. One of the more interesting directions is explored by briefly examining how SMVCIR can be used to identify potentially complex functions that link predictors and a continuous response variable.

<p>Lung cancer is the cancer form that has the highest mortality worldwide and inaddition the survival of lung cancer is very low. Only 15% of the patients are alivefive years from set diagnosis. More research is needed to understand the biologyof lung cancer and thus make it possible to discover the disease at an early stage.Early diagnosis leads to an increased chance of survival. In this thesis 179 lungcancer- and 116 control samples of blood serum were analyzed for identificationof metabolomic biomarkers. The control samples were derived from patients withbenign lung diseases.Data was gained from GC/TOF-MS analysis and analyzed with the help ofthe multivariate analysis methods PCA and OPLS/OPLS-DA. In this thesis it isinvestigated how to pre-treat and analyze the data in the best way in order todiscover biomarkers. One part of the aim was to give directions for how to selectsamples from a biobank for further biological validation of suspected biomarkers.Models for different stages of lung cancer versus control samples were computedand validated. The most influencing metabolites in the models were selected andconfoundings with other clinical characteristics like gender and hemoglobin levelswere studied. 13 lung cancer biomakers were identified and validated by raw dataand new OPLS models based solely upon the biomarkers.In summary the identified biomarkers are able to separate fairly good betweencontrol samples and late lung cancer, but are poor for separation of early lungcancer from control samples. The recommendation is to select controls and latelung cancer samples from the biobank for further confirmation of the biomarkers.NyckelordLung cancer is the cancer form that has the highest mortality worldwide and inaddition the survival of lung cancer is very low. Only 15% of the patients are alivefive years from set diagnosis. More research is needed to understand the biologyof lung cancer and thus make it possible to discover the disease at an early stage.Early diagnosis leads to an increased chance of survival. In this thesis 179 lungcancer- and 116 control samples of blood serum were analyzed for identificationof metabolomic biomarkers. The control samples were derived from patients withbenign lung diseases.Data was gained from GC/TOF-MS analysis and analyzed with the help ofthe multivariate analysis methods PCA and OPLS/OPLS-DA. In this thesis it isinvestigated how to pre-treat and analyze the data in the best way in order todiscover biomarkers. One part of the aim was to give directions for how to selectsamples from a biobank for further biological validation of suspected biomarkers.Models for different stages of lung cancer versus control samples were computedand validated. The most influencing metabolites in the models were selected andconfoundings with other clinical characteristics like gender and hemoglobin levelswere studied. 13 lung cancer biomakers were identified and validated by raw dataand new OPLS models based solely upon the biomarkers.In summary the identified biomarkers are able to separate fairly good betweencontrol samples and late lung cancer, but are poor for separation of early lungcancer from control samples. The recommendation is to select controls and latelung cancer samples from the biobank for further confirmation of the biomarkers.Nyckelord</p>

Lung cancer is the cancer form that has the highest mortality worldwide and inaddition the survival of lung cancer is very low. Only 15% of the patients are alivefive years from set diagnosis. More research is needed to understand the biologyof lung cancer and thus make it possible to discover the disease at an early stage.Early diagnosis leads to an increased chance of survival. In this thesis 179 lungcancer- and 116 control samples of blood serum were analyzed for identificationof metabolomic biomarkers. The control samples were derived from patients withbenign lung diseases.Data was gained from GC/TOF-MS analysis and analyzed with the help ofthe multivariate analysis methods PCA and OPLS/OPLS-DA. In this thesis it isinvestigated how to pre-treat and analyze the data in the best way in order todiscover biomarkers. One part of the aim was to give directions for how to selectsamples from a biobank for further biological validation of suspected biomarkers.Models for different stages of lung cancer versus control samples were computedand validated. The most influencing metabolites in the models were selected andconfoundings with other clinical characteristics like gender and hemoglobin levelswere studied. 13 lung cancer biomakers were identified and validated by raw dataand new OPLS models based solely upon the biomarkers.In summary the identified biomarkers are able to separate fairly good betweencontrol samples and late lung cancer, but are poor for separation of early lungcancer from control samples. The recommendation is to select controls and latelung cancer samples from the biobank for further confirmation of the biomarkers.NyckelordLung cancer is the cancer form that has the highest mortality worldwide and inaddition the survival of lung cancer is very low. Only 15% of the patients are alivefive years from set diagnosis. More research is needed to understand the biologyof lung cancer and thus make it possible to discover the disease at an early stage.Early diagnosis leads to an increased chance of survival. In this thesis 179 lungcancer- and 116 control samples of blood serum were analyzed for identificationof metabolomic biomarkers. The control samples were derived from patients withbenign lung diseases.Data was gained from GC/TOF-MS analysis and analyzed with the help ofthe multivariate analysis methods PCA and OPLS/OPLS-DA. In this thesis it isinvestigated how to pre-treat and analyze the data in the best way in order todiscover biomarkers. One part of the aim was to give directions for how to selectsamples from a biobank for further biological validation of suspected biomarkers.Models for different stages of lung cancer versus control samples were computedand validated. The most influencing metabolites in the models were selected andconfoundings with other clinical characteristics like gender and hemoglobin levelswere studied. 13 lung cancer biomakers were identified and validated by raw dataand new OPLS models based solely upon the biomarkers.In summary the identified biomarkers are able to separate fairly good betweencontrol samples and late lung cancer, but are poor for separation of early lungcancer from control samples. The recommendation is to select controls and latelung cancer samples from the biobank for further confirmation of the biomarkers.Nyckelord

No description available.

In this thesis we introduce the spherical, central, angular, halfspace and regression symmetry of random vectors and their measures. Firstly we deal with their mutual relations and equivalent expressions. We also study the uniqueness of the center of individual symmetries and other interesting properties. Then we define the halfspace, projection, spatial and regression multidimensional median and show their properties. Finally we look at the relationships between these medians and symmetric distributions. 1

<p> Application of four statistical techniques of discrimination is made to a set of multivariate data. The techniques, proposed by R.A . Fisher [6], C.R. Rao Q4] , D.F. Andrews [l] and H. Chernoff [4], are reviewed, applied and criticized in an intercomparison of the four methods. Graphic illustrations are also utilized to aid in the classification of sampling units. </p> / Thesis / Master of Science (MSc)

<p>Evolution of enzymes with novel functional properties has gained much attention in recent years. Naturally evolved enzymes are adapted to work in living cells under physiological conditions, circumstances that are not always available for industrial processes calling for novel and better catalysts. Furthermore, altering enzyme function also affords insight into how enzymes work and how natural evolution operates. </p><p>Previous investigations have explored catalytic properties in the directed evolution of mutant libraries with high sequence variation. Before this study was initiated, functional analysis of mutant libraries was, to a large extent, restricted to uni- or bivariate methods. Consequently, there was a need to apply multivariate data analysis (MVA) techniques in this context. Directed evolution was approached by DNA shuffling of glutathione transferases (GSTs) in this thesis. GSTs are multifarious enzymes that have detoxication of both exo- and endogenous compounds as their primary function. They catalyze the nucleophilic attack by the tripeptide glutathione on many different electrophilic substrates. </p><p>Several multivariate analysis tools, <i>e.g.</i> principal component (PC), hierarchical cluster, and K-means cluster analyses, were applied to large mutant libraries assayed with a battery of GST substrates. By this approach, evolvable units (quasi-species) fit for further evolution were identified. It was clear that different substrates undergoing different kinds of chemical transformation can group together in a multi-dimensional substrate-activity space, thus being responsible for a certain quasi-species cluster. Furthermore, the importance of the chemical environment, or substrate matrix, in enzyme evolution was recognized. Diverging substrate selectivity profiles among homologous enzymes acting on substrates performing the same kind of chemistry were identified by MVA. Important structure-function activity relationships with the prodrug azathioprine were elucidated by segment analysis of a shuffled GST mutant library. Together, these results illustrate important methods applied to molecular enzyme evolution.</p>

Tester l’indépendance entre plusieurs vecteurs aléatoires est une question importante en statistique. Puisqu’il y a une infinité de manières par lesquelles une quantité aléatoire X peut dépendre d’une autre quantité aléatoire Y , ce n’est pas une question triviale, et plusieurs tests “classiques” comme Spearman [33], Wilks [40], Kendall [18] ou Puri and Sen [24] sont inefficaces pour détecter plusieurs formes de dépendance. De significatifs progrès dans ce domaine ont été réalisés récemment, par exemple dans Székely et al. [34], Gretton et al. [14] ou Heller et al. [15]. Cela dit, la majorité des tests disponibles détectent l’indépendance entre deux quantités aléatoires uniquement. L’indépendance par paires ne garantissant pas l’indépendance mutuelle, il est pertinent de développer des méthodes testant l’hypothèse d’indépendance mutuelle entre n’importe quel nombre de variables. Dans cette recherche nous proposons un test non-paramétrique et toujours convergent, applicable à un nombre quelconque de vecteurs aléatoires. Précisément, nous étendons la méthode décrite dans Heller et al. [15] de deux manières. Premièrement, nous proposons d’appliquer leur test aux rangs des observations, plutôt qu’aux observations elles-mêmes. Ensuite, nous étendons leur méthode pour qu’elle puisse tester l’indépendance entre un nombre quelconque de vecteurs. La distribution de notre statistique de test étant inconnue, nous utilisons une méthode de permutations pour calculer sa valeur-p. Des simulations sont menées pour obtenir la puissance du test, que nous comparons à celles d’autres test décrits dans Genest and Rémillard [10], Gretton et al. [14], Székely et al. [34], Beran et al. [3] et Heller et al. [15]. Nous investiguons divers exemples et dans plusieurs de ceux-ci la puissance de notre test est meilleure que celle des autres tests. En particulier, lorsque les variables aléatoires sont Cauchy notre test performe bien mieux que les autres. Pour le cas de vecteurs aléatoires strictement discrets, nous présentons une preuve que notre test est toujours convergent. / Testing for independence between random vectors is an important question in statistics. Because there is an infinite number of ways by which a random quantity X can be dependent of another random quantity Y , it is not a trivial question. It has been found that classical tests such has Spearman [33],Wilks [40], Kendall [18] or Puri and Sen [24] are ineffective to detect many forms of dependence. Recent, significant results on the topic include Székely et al. [35], Gretton et al. [14] or Heller et al. [15]. However, most of the available tests can only detect dependence between two random quantities. Because pairwise independence does not guarantee mutual independence, techniques testing the hypothesis of mutual independence between any number of random quantities are required. In this research we propose a non-parametric and universally consistent test of independence, applicable to any number of random vectors of any size. Precisely, we extend the procedure described in Heller et al. [15] in two ways. Firstly, we propose to use the ranks of the observations instead of the observations themselves. Secondly, we extend their method to test for independence between any number of random vectors. As the distribution of our test statistic is not known, a permutation method is used to compute p−values. Then, simulations are performed to obtain the power of the test. We compare the power of our new test to that of other tests, namely those in Genest and Rémillard [10], Gretton et al. [14], Székely et al. [34], Beran et al. [3] and Heller et al. [15]. Examples featuring random variables and random vectors are considered. For many examples investigated we find that our new test has similar or better power than that of the other tests. In particular, when the random variables are Cauchy, our new test outperforms the others. In the case of strictly discrete random vectors, we present a proof that our test is universally consistent.