[pt] A álgebra de Clifford é uma álgebra associativa que pode ser realizada matricialmente. O grupo Spin é uma superfície contida na álgebra de Clifford e fechada por multiplicação. Estudamos os geradores de tal grupo, assim como do grupo finito gerado pelos elementos agúdos e o grupo Quat, ambos grupos de matrizes e subconjuntos do grupo Spin. Uma permutação no grupo de permutações, pode ser expressa como uma palavra reduzida, por meio de geradores de Coxeter. Os mapas acute e grave nos fornecem elementos no grupo finito, já mencionado, gerado pelos elementos agúdos, a partir das palavras reduzidas de uma permutação. Um elemento da álgebra de Clifford pode ser escrito como uma combinação linear de elementos do grupo Quat, onde o coeficiente independente é conhecido como parte real. Estudamos resultados que relacionam as características de uma permutação no grupo de permutações, com o elemento a ela relacionado na álgebra de Clifford. / [en] The Clifford algebra is an associative algebra that can be constructed as an algebra of matrices. The group Spin is a surface contained in the Clifford algebra and closed by multiplication. We studied the generators of such group, as well as of the finite group contained in Spin and generated by the acute elements and the group Quat, both matrix groups and subsets of Spin. A permutation in the permutation group, can be expressed as a reduced word, using transpositions to define the family of Coxeter generators. The acute and grave maps provide us with elements in the finite group, already mentioned, generated by the acute elements, based on the reduced words of a permutation. An element of Clifford algebra can be written as a linear combination of elements in Quat, where the independent coefficient is known as the real part. We studied results that relate the characteristics of a permutation in the permutation group, with the element related to it in the Clifford algebra.

State and Federal agencies have created sanctuaries and speed zones to help reduce manatee mortality while incorporating the recreational and commercial resource needs of these same habitats for humans. Specific habitat resources are considered necessary to increase manatee survivorship. We have only recently begun to address how manatees use some of these resources based on physiological or reproductive strategies. In this study, I quantified patterns of habitat use during seasonal and diel periods for different sex and reproductive manatee classes using data from a radio-telemetry study conducted by the Florida Fish and Wildlife Conservation Commission during 1991-1996. I used five environmental geographic data layers: bathymetry, distance to seagrass, distance to shoreline, distance to warm water refuge sites, and distance to fresh water sources, to discriminate seasonal and diel habitat use patterns for different manatee classes: males (M), females with calves (FWC), and females without calves (FNC). Mean occupancy values were calculated for environmental variable locations and seasonal, diel, and manatee class differences were tested using a Multi-Response Permutation Procedure (MRPP). Nonmetric Multidimensional Scaling (NMS) was used to visualize the ordination patterns of the manatee classes and to assess importance of correlated environmental variables. Significant differences in habitat use were noted between summer and winter based on distances to warm water, seagrass, and fresh water sources but similar habitat use patterns were exhibited within summer diel periods among manatee classes. All manatee classes appeared to have used a higher proportion of locations closer in proximity to seagrass at night than day in winter indicating a disproportionate difference in feeding bouts between diel periods. These differences may be attributed to adjusting feeding strategies to reduce thermoregulatory costs or to decrease human interactions. Differences in patterns were exhibited for the winter diel periods specifically for the FWC manatee classes during winter days. FWC had a higher proportion of locations within the warm water refuges during the day indicating a possible trade off situation between food consumption and thermal exposure. This study demonstrates coarse and fine scale patterns of variation in habitat use for manatees both seasonally and daily within winter. It also suggests that during winter months, manatees were not just utilizing their habitat but they appeared to have preferences and selection for certain habitat types. Recovery of a species is greatly enhanced when patterns of habitat use within the species' environment has been clearly defined. Understanding more specifically what types of habitats manatees choose might allow management to adjust strategies for protection of key habitats while encouraging further recovery of this species.

Completely locked-in state (CLIS) patients are unable to speak and have lost all muscle movement. From the external view, the internal brain activity of such patients cannot be easily perceived, but CLIS patients are considered to still be conscious and cognitively active. Detecting the current state of consciousness of CLIS patients is non-trivial, and it is difficult to ascertain whether CLIS patients are conscious or not. Thus, it is important to find alternative ways to re-establish communication with these patients during periods of awareness, and one such alternative is through a brain–computer interface (BCI). In this study, multiscale-based methods (multiscale sample entropy, multiscale permutation entropy and multiscale Poincaré plots) were applied to analyze electrocorticogram signals from a CLIS patient to detect the underlying consciousness level. Results from these different methods converge to a specific period of awareness of the CLIS patient in question, coinciding with the period during which the CLIS patient is recorded to have communicated with an experimenter. The aim of the investigation is to propose a methodology that could be used to create reliable communication with CLIS patients.

With advanced technology and information explosion, the data of interest often have complex structures, with the large size and dimensions in the form of continuous or discrete features. There is an emerging need for data reduction, efficient modeling, and model inference. For example, data can contain millions of observations with thousands of features. Traditional methods, such as linear regression or LASSO regression, cannot effectively deal with such a large dataset directly. This dissertation aims to develop several techniques to effectively analyze large datasets with complex structures in the observational, experimental and time series data. In Chapter 2, I focus on the data reduction for model estimation of sparse regression. The commonly-used subdata selection method often considers sampling or feature screening. Un- der the case of data with both large number of observation and predictors, we proposed a filtering approach for model estimation (FAME) to reduce both the size of data points and features. The proposed algorithm can be easily extended for data with discrete response or discrete predictors. Through simulations and case studies, the proposed method provides a good performance for parameter estimation with efficient computation. In Chapter 3, I focus on modeling the experimental data with quantitative-sequence (QS) factor. Here the QS factor concerns both quantities and sequence orders of several compo- nents in the experiment. Existing methods usually can only focus on the sequence orders or quantities of the multiple components. To fill this gap, we propose a QS transformation to transform the QS factor to a generalized permutation matrix, and consequently develop a simple Gaussian process approach to model the experimental data with QS factors. In Chapter 4, I focus on forecasting multivariate time series data by leveraging the au- toregression and clustering. Existing time series forecasting method treat each series data independently and ignore their inherent correlation. To fill this gap, I proposed a clustering based on autoregression and control the sparsity of the transition matrix estimation by adap- tive lasso and clustering coefficient. The clustering-based cross prediction can outperforms the conventional time series forecasting methods. Moreover, the the clustering result can also enhance the forecasting accuracy of other forecasting methods. The proposed method can be applied on practical data, such as stock forecasting, topic trend detection. / Doctor of Philosophy / This dissertation focuses on three projects that are related to data reduction and statistical modeling of data with complex structures. In chapter 2, we propose a filtering approach of data for parameter estimation of sparse regression. Given data with thousands of ob- servations and predictors or even more, large storage and computation spaces is need to handle these data. It is challenging to computational power and takes long time in terms of computational cost. So we come up with an algorithm (FAME) that can reduce both the number of observations and predictors. After data reduction, this subdata selected by FAME keeps most information of the original dataset in terms of parameter estimation. Compare with existing methods, the dimension of the subdata generated by the proposed algorithm is smaller while the computational time does not increase. In chapter 3, we use quantitative-sequence (QS) factor to describe experimental data. One simple example of experimental data is milk tea. Adding 1 cup of milk first or adding 2 cup of tea first will influence the flavor. And this case can be extended to cases when there are thousands of ingredients need to be input into the experiment. Then the order and amount of ingredients will generate different experimental results. We use QS factor to describe this kind of order and amount. Then by transforming the QS factor to a matrix containing continuous value and set this matrix as input, we model the experimental results with a simple Gaussian process. In chapter 4, we propose an autoregression-based clustering and forecasting method of multi- variate time series data. Existing research works often treat each time series independently. Our approach incorporates the inherent correlation of data and cluster related series into one group. The forecasting is built based on each cluster and data within one cluster can cross predict each other. One application of this method is on topic trending detection. With thousands of topics, it is unfeasible to apply one model for forecasting all time series. Considering the similarity of trends among related topics, the proposed method can cluster topics based on their similarity, and then perform forecasting in autoregression model based on historical data within each cluster.

Semiparametric modeling is a hybrid of the parametric and nonparametric modelings where some function forms are known and others are unknown. In this dissertation, we have made several contributions to semiparametric modeling based on the single index model related to the following three topics: the first is to propose a model for detecting change points simultaneously with estimating the unknown function; the second is to develop two models for spatially correlated data; and the third is to further develop two models for spatially-temporally correlated data. To address the first topic, we propose a unified approach in its ability to simultaneously estimate the nonlinear relationship and change points. We propose a single index change point model as our unified approach by adjusting for several other covariates. We nonparametrically estimate the unknown function using kernel smoothing and also provide a permutation based testing procedure to detect multiple change points. We show the asymptotic properties of the permutation testing based procedure. The advantage of our approach is demonstrated using the mortality data of Seoul, Korea from January, 2000 to December, 2007. On the second topic, we propose two semiparametric single index models for spatially correlated data. One additively separates the nonparametric function and spatially correlated random effects, while the other does not separate the nonparametric function and spatially correlated random effects. We estimate these two models using two algorithms based on Markov Chain Expectation Maximization algorithm. Our approaches are compared using simulations, suggesting that the semiparametric single index nonadditive model provides more accurate estimates of spatial correlation. The advantage of our approach is demonstrated using the mortality data of six cities, Korea from January, 2000 to December, 2007. The third topic involves proposing two semiparametric single index models for spatially and temporally correlated data. Our first model has the nonparametric function which can separate from spatially and temporally correlated random effects. We refer it to "semiparametric spatio-temporal separable single index model (SSTS-SIM)", while the second model does not separate the nonparametric function from spatially correlated random effects but separates the time random effects. We refer our second model to "semiparametric nonseparable single index model (SSTN-SIM)". Two algorithms based on Markov Chain Expectation Maximization algorithm are introduced to simultaneously estimate parameters, spatial effects, and times effects. The proposed models are then applied to the mortality data of six major cities in Korea. Our results suggest that SSTN-SIM is more flexible than SSTS-SIM because it can estimate various nonparametric functions while SSTS-SIM enforces the similar nonparametric curves. SSTN-SIM also provides better estimation and prediction. / Ph. D.

Nitrogen-fixing bacteria in soybean nodules convert atmospheric nitrogen to plant-available forms in exchange for carbon from the plant, but other non-nitrogen-fixing bacteria also reside in nodules, and their role in the nodule is not well understood. This study was conducted to determine the effect of three non-nitrogen-fixing Pseudomonas spp. strains isolated from nodules on soybean, and we hypothesized these strains benefit soybean. A greenhouse study in which two cultivars of soybean (Asgrow AG46X6 and Pioneer P48A60X) were treated with three fluorescent Pseudomonas spp. strains (referred to in this study as Bullseye, Pancake, and Starfish) and an uninoculated control. Soybeans were harvested at two time points: the R2/R3 growth stage and the R6 growth stage. Following each harvest, measures of growth, yield, and nitrogen fixation were taken, and data were analyzed using two non-parametric, multivariate analyses: multiple response permutation procedure (MRPP) and permutational multivariate analysis of variance (PERMANOVA). Both analyses showed soybeans of both cultivars treated with Pancake differed from controls following the first harvest but not the second. When analyzed individually, most metrics for growth, yield, and nitrogen fixation following the first harvest were not significantly different between Pancake and control treatments, but Pancake treatment means were still generally higher than controls. If metrics are considered collectively in conjunction with the results of the multivariate analyses, the results show Pancake generally increased soybean growth and nitrogen fixation. These findings support the hypothesis that non-nitrogen-fixing bacteria from nodules benefit plants, and such bacteria have the potential to serve as biofertilizers. / Master of Science in Life Sciences / Soybeans are one of the most commonly grown crops in the world, and nitrogen-fixing bacteria colonize the roots of soybeans and initiate the formation of spherical nodules attached to the roots. Inside the nodules, these bacteria convert atmospheric nitrogen to plant-available forms in exchange for sugar from the plant, and such bacteria reduce the need to add nitrogen fertilizer to agricultural fields. Other non-nitrogen-fixing bacteria also reside in nodules, but their role in the nodule is not well understood. If these bacteria benefit soybeans, they have the potential to serve as biofertilizers (microbial inoculants that promote plant growth). This study was conducted to determine whether non-nitrogen-fixing bacteria isolated from nodules benefit soybean. A greenhouse study in which two cultivars of soybean (Asgrow AG46X6 and Pioneer P48A60X) were grown in soil and were either left uninoculated or were inoculated with one of three strains of bacteria from the genus, Pseudomonas (referred to in this study as Bullseye, Pancake, and Starfish). Following harvest, measures of growth, yield, and nitrogen fixation were taken, and data showed the bacteria generally benefited the soybean plants. Although, these results showed the bacteria benefitted the plants, field trials and further testing in the greenhouse should be conducted before using these bacteria as commercial biofertilizers. Additionally, the effects of other non-nitrogen-fixing nodule bacteria on soybeans should also be tested to identify other beneficial strains, and the cost of production should be compared to the potential gains of using such bacteria before they are developed into biofertilizers.

Cette thèse est rédigée par articles. Les articles sont rédigés en anglais et le reste de la thèse est rédigée en français. / Le travail établit une équivalence en termes de puissance entre les tests basés sur la alpha-distance de covariance et sur le critère d'indépendance de Hilbert-Schmidt (HSIC) avec fonction caractéristique de distribution de probabilité stable d'indice alpha avec paramètre d'échelle suffisamment petit. Des simulations en grandes dimensions montrent la supériorité des tests de distance de covariance et des tests HSIC par rapport à certains tests utilisant les copules. Des simulations montrent également que la distribution de Pearson de type III, très utile et moins connue, approche la distribution exacte de permutation des tests et donne des erreurs de type I précises. Une nouvelle méthode de sélection adaptative des paramètres d'échelle pour les tests HSIC est proposée. Trois simulations, dont deux sont empruntées de l'apprentissage automatique, montrent que la nouvelle méthode de sélection améliore la puissance des tests HSIC. Le problème de tests d'indépendance entre deux vecteurs est généralisé au problème de tests d'indépendance mutuelle entre plusieurs vecteurs. Le travail traite aussi d'un problème très proche à savoir, le test d'indépendance sérielle d'une suite multidimensionnelle stationnaire. La décomposition de Möbius des fonctions caractéristiques est utilisée pour caractériser l'indépendance. Des tests généralisés basés sur le critère d'indépendance de Hilbert-Schmidt et sur la distance de covariance en sont obtenus. Une équivalence est également établie entre le test basé sur la distance de covariance et le test HSIC de noyau caractéristique d'une distribution stable avec des paramètres d'échelle suffisamment petits. La convergence faible du test HSIC est obtenue. Un calcul rapide et précis des valeurs-p des tests développés utilise une distribution de Pearson de type III comme approximation de la distribution exacte des tests. Un résultat fascinant est l'obtention des trois premiers moments exacts de la distribution de permutation des statistiques de dépendance. Une méthodologie similaire a été développée pour le test d'indépendance sérielle d'une suite. Des applications à des données réelles environnementales et financières sont effectuées. / The main result establishes the equivalence in terms of power between the alpha-distance covariance test and the Hilbert-Schmidt independence criterion (HSIC) test with the characteristic kernel of a stable probability distribution of index alpha with sufficiently small scale parameters. Large-scale simulations reveal the superiority of these two tests over other tests based on the empirical independence copula process. They also establish the usefulness of the lesser known Pearson type III approximation to the exact permutation distribution. This approximation yields tests with more accurate type I error rates than the gamma approximation usually used for HSIC, especially when dimensions of the two vectors are large. A new method for scale parameter selection in HSIC tests is proposed which improves power performance in three simulations, two of which are from machine learning. The problem of testing mutual independence between many random vectors is addressed. The closely related problem of testing serial independence of a multivariate stationary sequence is also considered. The Möbius transformation of characteristic functions is used to characterize independence. A generalization to p vectors of the alpha -distance covariance test and the Hilbert-Schmidt independence criterion (HSIC) test with the characteristic kernel of a stable probability distributionof index alpha is obtained. It is shown that an HSIC test with sufficiently small scale parameters is equivalent to an alpha -distance covariance test. Weak convergence of the HSIC test is established. A very fast and accurate computation of p-values uses the Pearson type III approximation which successfully approaches the exact permutation distribution of the tests. This approximation relies on the exact first three moments of the permutation distribution of any test which can be expressed as the sum of all elements of a componentwise product of p doubly-centered matrices. The alpha -distance covariance test and the HSIC test are both of this form. A new selection method is proposed for the scale parameter of the characteristic kernel of the HSIC test. It is shown in a simulation that this adaptive HSIC test has higher power than the alpha-distance covariance test when data are generated from a Student copula. Applications are given to environmental and financial data.

This thesis is divided into three main parts. In the first, we discuss that, although permutation tests can provide exact control of false positives under the reasonable assumption of exchangeability, there are common examples in which global exchangeability does not hold, such as in experiments with repeated measurements or tests in which subjects are related to each other. To allow permutation inference in such cases, we propose an extension of the well known concept of exchangeability blocks, allowing these to be nested in a hierarchical, multi-level definition. This definition allows permutations that retain the original joint distribution unaltered, thus preserving exchangeability. The null hypothesis is tested using only a subset of all otherwise possible permutations. We do not need to explicitly model the degree of dependence between observations; rather the use of such permutation scheme leaves any dependence intact. The strategy is compatible with heteroscedasticity and can be used with permutations, sign flippings, or both combined. In the second part, we exploit properties of test statistics to obtain accelerations irrespective of generic software or hardware improvements. We compare six different approaches using synthetic and real data, assessing the methods in terms of their error rates, power, agreement with a reference result, and the risk of taking a different decision regarding the rejection of the null hypotheses (known as the resampling risk). In the third part, we investigate and compare the different methods for assessment of cortical volume and area from magnetic resonance images using surface-based methods. Using data from young adults born with very low birth weight and coetaneous controls, we show that instead of volume, the permutation-based non-parametric combination (NPC) of thickness and area is a more sensitive option for studying joint effects on these two quantities, giving equal weight to variation in both, and allowing a better characterisation of biological processes that can affect brain morphology.

Si la traduction est simplement définie comme un processus de communication bilingue dont le but général est de reproduire en langue cible un texte qui soit fonctionnellement équivalent au texte de départ (Reiss 2004 : 168-169), l’approche empruntée dans la présente thèse est celle d’une opération interculturelle et systématique qui vise à capturer le message issu d’une langue étrangère, à le décrypter en tenant en compte des nuances culturelles ou inhérentes à la discipline, et à le rendre le plus clairement possible en se servant d'éléments linguistiques et extralinguistiques compréhensibles dans la langue du locuteur cible. L'objectif est de déterminer la contribution de la traduction à l’expansion lexicale du sesotho, domaine qui demeure peu exploré par les spécialistes de cette langue. La problématique de ce travail repose sur la constatation que les néologismes en sesotho ne sont pas documentés de manière satisfaisante, si bien qu’il est difficile d'évaluer la contribution de la traduction à l’expansion lexicale. Les études antérieures sur la morphologie, la dérivation, la composition, l’emprunt et la dénomination s’appuient sur la mesure de la productivité, soulevant la question de savoir si la traduction en soi contribue à l’enrichissement terminologique du sesotho. Le point de départ de la thèse est l'hypothèse selon laquelle l’interaction avec le monde européen a nécessité de traduire de nombreux concepts qui n’existaient pas dans les systèmes traditionnels du Lesotho, ce qui a entraîné un nouveau dynamisme qui a permis de combler des lacunes terminologiques évidentes et de s’ouvrir et de s’adapter aux nouvelles réalités. Pour mettre cette hypothèse à l’épreuve et arriver à des conclusions éclairées et fiables, je cherche à répondre à trois questions : 1) Quelle est la structure des mots sesothos par rapport à celle de l’anglais en tant que langue source de traduction en sesotho, et du français en tant que langue de rédaction de la thèse ? 2) Etant donné que le sesotho est utilisé concomitamment avec l’anglais sans pour autant être la langue d'une culture inventrice en matière technologique, quel est le rôle que joue l’emprunt dans son expansion lexicale ? 3) D’un point de vue lexicologique, comment le sesotho répond-il aux besoins terminologiques dans les domaines de spécialité techno-scientifiques ? Pour y répondre, je m'appuie sur Doke (1954) et Matšela et al. (1981) pour situer le sesotho parmi les langues bantoues, préciser les fonctions du préfixe classificateur et établir la différence entre les composés sesothos d'une part et les composés anglais et français d'autre part. J’utilise ensuite la théorie avancée par Lederer (1990) pour démontrer l’influence syntaxique, sémantique et morphologique que l’anglais a sur le sesotho et pour présenter les différents procédés d’emprunt du sesotho. Diki-Kidiri (2008), Dispaldro et al. (2010) et Baboya (2008) démontrent la nécessité de faire appel aux informateurs-spécialistes pour confirmer l’hypothèse de départ. Les résultats obtenus mettent en évidence qu’en effet, la traduction a contribué à l’expansion du sesotho moderne, bien que cela n’ait pas été documenté, d’où la recommandation d'un travail collaboratif entre lexicologues au Lesotho, au Botswana, en Namibie et en Afrique du Sud, pour ouvrir de nouvelles perspectives d’études linguistiques sur le sesotho et pouvoir suivre et mesurer l’évolution de la langue. / Whilst translation is simply defined as a communication process whose main objective is to reproduce in the target language a text that is functionally equivalent to the source text (Reiss 2004: 168-169), the approach taken in this study views translation as an intercultural and systematic operation whose objective is to capture the message from the foreign language, to decrypt it taking into account cultural nuances or those inherent in the field at hand and to render it in the clearest possible manner using linguistic and extra linguistic elements which are comprehensible to the speaker of the target language. This study is aimed at determining the contribution of translation to the lexical expansion of Sesotho, an area which has been little explored by specialists of the language. The core issue is centred on the observation that Sesotho neologisms are not well documented, so that it is hard to measure the contribution of translation towards the lexical expansion of Sesotho. Analyses of morphology, derivation, compounding, borrowing and denomination are mainly focused on productivity in order to determine whether translation as a discipline contributes towards the creation of new words in the language.The study begins by positing the hypothesis that the interaction with the Western world necessitated the translation of numerous concepts which were absent from the then existing Sesotho systems. This process of interaction contributed a new dynamism that helped the language to bridge the terminological gap, to open up and adapt to new realities. In order to put this hypothesis to the test and arrive at well-researched and reliable conclusions, I attempt to probe three issues of concern: firstly, what is the structure of the Sesotho language compared to that of the English language as the source language of most translations into Sesotho and compared to that of the French language as the language in which this study is presented? Secondly, considering that Sesotho is used simultaneously with English even though it is not a techno-scientifically inventing language, what is the role played by the processes of borrowing in the lexical expansion of Sesotho? Thirdly, from the word-formation point of view, how does Sesotho respond to the terminological deficiencies in various fields of specialisation?To address these issues, Doke (1954) and Matšela et al. (1981) serve as references to situate Sesotho among the Bantu languages, to highlight the functions of the class prefix and to establish the difference between Sesotho and English and French compounding. Secondly, the theory advanced by Lederer (1990) serves as a springboard to analyse the syntactic, semantic and morphological influences that English has on Sesotho and to present the different borrowing processes. The third issue is addressed based on the theories presented by Diki-Kidiri (2008) while the theories proposed by Dispaldro et al. (2010) and Baboya (2008) led to the decision to call upon specialist informants to confirm the original hypothesis. The results obtained provide evidence that translation has, in fact, contributed to the lexical expansion of modern Sesotho, even though this has not been well documented. The study recommends collaborative work between Lesotho, Botswana, Namibian and South African linguists in order to open new avenues of linguistic studies on Sesotho with the aim to measure and monitor the evolution of the language.

L'IRMd est un moyen non invasif permettant d'étudier in vivo la structure des fibres nerveuses du cerveau. Dans cette thèse, nous modélisons des données IRMd à l'aide de tenseurs d'ordre 4 (T4). Les problèmes de comparaison de groupes ou d'individu avec un groupe normal sont abordés, et résolus à l'aide d'analyses statistiques sur les T4s. Les approches utilisent des réductions non linéaires de dimension, et bénéficient des métriques non euclidiennes pour les T4s. Les statistiques sont calculées dans l'espace réduit, et permettent de quantifier la dissimilarité entre le groupe (ou l'individu) d'intérêt et le groupe de référence. Les approches proposées sont appliquées à la neuromyélite optique et aux patients atteints de locked in syndrome. Les conclusions tirées sont cohérentes avec les connaissances médicales actuelles. / DW-MRI is a non-invasive way to study in vivo the structure of nerve fibers in the brain. In this thesis, fourth order tensors (T4) were used to model DW-MRI data. In addition, the problems of group comparison or individual against a normal group were discussed and solved using statistical analysis on T4s. The approaches use nonlinear dimensional reductions, assisted by non-Euclidean metrics for T4s. The statistics are calculated in the reduced space and allow us to quantify the dissimilarity between the group (or the individual) of interest and the reference group. The proposed approaches are applied to neuromyelitis optica and patients with locked in syndrome. The derived conclusions are consistent with the current medical knowledge.